%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO397^1 : TPTP v9.2.1. 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 : n016.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 09:12:34 AM UTC 2026 % Result : Theorem 0.36s 0.60s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO397^1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n016.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Wed Jun 3 00:07:09 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.51 %----Proving TH0 % 0.36/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.60 % SZS status Theorem % 0.36/0.60 % SZS output start Proof % 0.36/0.60 ( % 0.36/0.60 (declare-sort $$unsorted 0) % 0.36/0.60 (declare-sort tptp.mu 0) % 0.36/0.60 (declare-const tptp.rel_k (-> $$unsorted $$unsorted Bool)) % 0.36/0.60 (declare-const tptp.q (-> $$unsorted Bool)) % 0.36/0.60 (declare-const tptp.p (-> $$unsorted Bool)) % 0.36/0.60 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.36/0.60 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.36/0.60 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.36/0.60 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.36/0.60 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.36/0.60 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.36/0.60 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.36/0.60 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.36/0.60 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.36/0.60 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.36/0.60 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.36/0.60 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.36/0.60 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.36/0.60 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.36/0.60 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.36/0.60 (define tptp.mbox () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.36/0.60 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.36/0.60 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.36/0.60 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.60 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.61 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "T" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.36/0.61 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.36/0.61 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.36/0.61 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.36/0.61 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.36/0.61 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.36/0.61 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "T" $$unsorted))) (let ((_let_5 (@var "S" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.36/0.61 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.36/0.61 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.36/0.61 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.36/0.61 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.36/0.61 (define tptp.mbox_k () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_k _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.36/0.61 (define tptp.mdia_k () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_k (_ tptp.mnot _let_2))) _let_1))))) % 0.36/0.61 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mbox_k tptp.p)) (_ tptp.mbox_k (_ (_ tptp.mimplies tptp.q) tptp.p)))))) % 0.36/0.61 (define @t2 () (@var "Y" tptp.mu)) % 0.36/0.61 (define @t3 () (@var "X" tptp.mu)) % 0.36/0.61 (define @t4 () (@var "W" $$unsorted)) % 0.36/0.61 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.36/0.61 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.36/0.61 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.36/0.61 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.36/0.61 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.36/0.61 (define @t10 () (_ @t9 @t4)) % 0.36/0.61 (define @t11 () (not @t10)) % 0.36/0.61 (define @t12 () (@list @t9 @t4)) % 0.36/0.61 (define @t13 () (lambda @t12 @t11)) % 0.36/0.61 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.36/0.61 (define @t15 () (_ @t14 @t4)) % 0.36/0.61 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.36/0.61 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.36/0.61 (define @t18 () (_ tptp.mnot @t14)) % 0.36/0.61 (define @t19 () (_ tptp.mnot @t9)) % 0.36/0.61 (define @t20 () (_ tptp.mor @t19)) % 0.36/0.61 (define @t21 () (@list @t9 @t14 @t17)) % 0.36/0.61 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.36/0.61 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.36/0.61 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.36/0.61 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.36/0.61 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.36/0.61 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.36/0.61 (define @t28 () (_ @t27 @t3)) % 0.36/0.61 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.36/0.61 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.36/0.61 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.36/0.61 (define @t32 () (_ @t31 @t30)) % 0.36/0.61 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.36/0.61 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.36/0.61 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.36/0.61 (define @t36 () (@list @t4)) % 0.36/0.61 (define @t37 () (lambda @t36 true)) % 0.36/0.61 (define @t38 () (@var "V" $$unsorted)) % 0.36/0.61 (define @t39 () (_ @t9 @t38)) % 0.36/0.61 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.36/0.61 (define @t41 () (@list @t38)) % 0.36/0.61 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.36/0.61 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.36/0.61 (define @t44 () (@var "S" $$unsorted)) % 0.36/0.61 (define @t45 () (_ @t40 @t44)) % 0.36/0.61 (define @t46 () (@list @t44)) % 0.36/0.61 (define @t47 () (@list @t40)) % 0.36/0.61 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.36/0.61 (define @t49 () (@var "T" $$unsorted)) % 0.36/0.61 (define @t50 () (_ @t40 @t49)) % 0.36/0.61 (define @t51 () (_ @t45 @t49)) % 0.36/0.61 (define @t52 () (lambda @t47 (forall (@list @t44 @t49) (=> @t51 (_ @t50 @t44))))) % 0.36/0.61 (define @t53 () (@list @t49)) % 0.36/0.61 (define @t54 () (lambda @t47 (forall @t46 (exists @t53 @t51)))) % 0.36/0.61 (define @t55 () (@var "U" $$unsorted)) % 0.36/0.61 (define @t56 () (_ @t45 @t55)) % 0.36/0.61 (define @t57 () (_ @t50 @t55)) % 0.36/0.61 (define @t58 () (@list @t44 @t49 @t55)) % 0.36/0.61 (define @t59 () (lambda @t47 (forall @t58 (=> (and @t51 @t57) @t56)))) % 0.36/0.61 (define @t60 () (and @t51 @t56)) % 0.36/0.61 (define @t61 () (lambda @t47 (forall @t58 (=> @t60 @t57)))) % 0.36/0.61 (define @t62 () (= @t49 @t55)) % 0.36/0.61 (define @t63 () (lambda @t47 (forall @t58 (=> @t60 @t62)))) % 0.36/0.61 (define @t64 () (@list @t55)) % 0.36/0.61 (define @t65 () (lambda @t47 (forall @t46 (exists @t53 (and @t51 (forall @t64 (=> @t56 @t62))))))) % 0.36/0.61 (define @t66 () (_ @t40 @t55)) % 0.36/0.61 (define @t67 () (_ @t66 @t49)) % 0.36/0.61 (define @t68 () (lambda @t47 (forall @t58 (=> @t51 (exists @t64 (and @t56 @t67)))))) % 0.36/0.61 (define @t69 () (lambda @t47 (forall @t58 (=> @t60 (or @t57 @t62 @t67))))) % 0.36/0.61 (define @t70 () (lambda @t47 (forall @t58 (=> @t60 (exists @t41 (and (_ @t50 @t38) (_ @t66 @t38))))))) % 0.36/0.61 (define @t71 () (forall @t36 @t10)) % 0.36/0.61 (define @t72 () (@list @t9)) % 0.36/0.61 (define @t73 () (lambda @t72 @t71)) % 0.36/0.61 (define @t74 () (lambda @t72 (forall @t36 @t11))) % 0.36/0.61 (define @t75 () (lambda @t72 (exists @t36 @t10))) % 0.36/0.61 (define @t76 () (lambda @t72 (exists @t36 @t11))) % 0.36/0.61 (define @t77 () (_ (_ tptp.rel_k @t4) @t38)) % 0.36/0.61 (define @t78 () (not @t77)) % 0.36/0.61 (define @t79 () (or @t78 @t39)) % 0.36/0.61 (define @t80 () (forall @t41 @t79)) % 0.36/0.61 (define @t81 () (lambda @t12 @t80)) % 0.36/0.61 (define @t82 () (lambda (@list @t9 @t17) (_ (_ tptp.mnot (_ tptp.mbox_k @t19)) @t17))) % 0.36/0.61 (define @t83 () (@var "BOUND_VARIABLE_8455" $$unsorted)) % 0.36/0.61 (define @t84 () (tptp.p @t83)) % 0.36/0.61 (define @t85 () (not (tptp.q @t83))) % 0.36/0.61 (define @t86 () (not (tptp.rel_k @t4 @t83))) % 0.36/0.61 (define @t87 () (tptp.p @t38)) % 0.36/0.61 (define @t88 () (tptp.rel_k @t4 @t38)) % 0.36/0.61 (define @t89 () (not @t88)) % 0.36/0.61 (define @t90 () (forall @t41 (or @t89 @t87))) % 0.36/0.61 (define @t91 () (not @t90)) % 0.36/0.61 (define @t92 () (or @t91 @t86 @t85 @t84)) % 0.36/0.61 (define @t93 () (or @t86 @t85 @t84)) % 0.36/0.61 (define @t94 () (or @t91 @t93)) % 0.36/0.61 (define @t95 () (@list @t4 @t83)) % 0.36/0.61 (define @t96 () (forall @t95 @t94)) % 0.36/0.61 (define @t97 () (@list @t83)) % 0.36/0.61 (define @t98 () (forall @t97 @t94)) % 0.36/0.61 (define @t99 () (forall @t97 @t93)) % 0.36/0.61 (define @t100 () (or @t91 @t99)) % 0.36/0.61 (define @t101 () (tptp.q @t38)) % 0.36/0.61 (define @t102 () (not @t101)) % 0.36/0.61 (define @t103 () (forall @t41 (or @t89 @t102 @t87))) % 0.36/0.61 (define @t104 () (or @t91 @t103)) % 0.36/0.61 (define @t105 () (not (tptp.rel_k @t17 @t38))) % 0.36/0.61 (define @t106 () (forall @t41 (or @t105 @t102 @t87))) % 0.36/0.61 (define @t107 () (forall @t41 (or @t105 @t87))) % 0.36/0.61 (define @t108 () (not @t107)) % 0.36/0.61 (define @t109 () (@list @t17)) % 0.36/0.61 (define @t110 () (lambda @t109 (or @t108 @t106))) % 0.36/0.61 (define @t111 () (_ @t110 @t4)) % 0.36/0.61 (define @t112 () (forall @t36 @t111)) % 0.36/0.61 (define @t113 () (_ @t9 @t4)) % 0.36/0.61 (define @t114 () (lambda @t72 (forall @t36 @t113))) % 0.36/0.61 (define @t115 () (lambda @t36 @t103)) % 0.36/0.61 (define @t116 () (_ @t115 @t17)) % 0.36/0.61 (define @t117 () (or @t108 @t116)) % 0.36/0.61 (define @t118 () (lambda @t109 @t117)) % 0.36/0.61 (define @t119 () (_ @t14 @t17)) % 0.36/0.61 (define @t120 () (@list @t14 @t17)) % 0.36/0.61 (define @t121 () (_ tptp.p @t38)) % 0.36/0.61 (define @t122 () (_ tptp.q @t38)) % 0.36/0.61 (define @t123 () (not @t122)) % 0.36/0.61 (define @t124 () (or @t89 @t123 @t121)) % 0.36/0.61 (define @t125 () (or @t123 @t121)) % 0.36/0.61 (define @t126 () (not (_ tptp.q @t17))) % 0.36/0.61 (define @t127 () (lambda @t109 (or @t126 (_ tptp.p @t17)))) % 0.36/0.61 (define @t128 () (_ @t127 @t38)) % 0.36/0.61 (define @t129 () (or @t89 @t128)) % 0.36/0.61 (define @t130 () (forall @t41 @t129)) % 0.36/0.61 (define @t131 () (lambda @t36 @t130)) % 0.36/0.61 (define @t132 () (_ @t9 @t38)) % 0.36/0.61 (define @t133 () (lambda @t12 (forall @t41 (or @t89 @t132)))) % 0.36/0.61 (define @t134 () (lambda @t120 (or @t126 @t119))) % 0.36/0.61 (define @t135 () (or (not (_ @t9 @t17)) @t119)) % 0.36/0.61 (define @t136 () (lambda @t21 @t135)) % 0.36/0.61 (define @t137 () (_ @t136 tptp.q)) % 0.36/0.61 (define @t138 () (lambda @t36 @t90)) % 0.36/0.61 (define @t139 () (_ @t138 @t17)) % 0.36/0.61 (define @t140 () (not @t139)) % 0.36/0.61 (define @t141 () (or @t140 @t119)) % 0.36/0.61 (define @t142 () (lambda @t120 @t141)) % 0.36/0.61 (define @t143 () (_ @t133 tptp.p)) % 0.36/0.61 (define @t144 () (or @t11 @t15)) % 0.36/0.61 (define @t145 () (lambda @t36 @t144)) % 0.36/0.61 (define @t146 () (@list @t14 @t4)) % 0.36/0.61 (define @t147 () (lambda @t36 @t11)) % 0.36/0.61 (define @t148 () (_ @t147 @t4)) % 0.36/0.61 (define @t149 () (or @t148 @t15)) % 0.36/0.61 (define @t150 () (lambda @t146 @t149)) % 0.36/0.61 (define @t151 () (forall @t95 @t92)) % 0.36/0.61 (define @t152 () (@quantifiers_skolemize @t151 0)) % 0.36/0.61 (define @t153 () (forall @t41 (or (not (tptp.rel_k @t152 @t38)) @t87))) % 0.36/0.61 (define @t154 () (@quantifiers_skolemize @t151 1)) % 0.36/0.61 (define @t155 () (tptp.p @t154)) % 0.36/0.61 (define @t156 () (tptp.rel_k @t152 @t154)) % 0.36/0.61 (define @t157 () (not @t156)) % 0.36/0.61 (define @t158 () (not @t153)) % 0.36/0.61 (define @t159 () (or @t158 @t157 (not (tptp.q @t154)) @t155)) % 0.36/0.61 (define @t160 () (@list true)) % 0.36/0.61 (define @t161 () (@list @t159)) % 0.36/0.61 (define @t162 () (or @t157 @t155)) % 0.36/0.61 (define @t163 () (not @t162)) % 0.36/0.61 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.36/0.61 (assume @p2 @t1) % 0.36/0.61 (assume @p3 true) % 0.36/0.61 (step @p4 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.36/0.61 (step @p5 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.36/0.61 (step @p6 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.36/0.61 (step @p7 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.36/0.61 (step @p8 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.36/0.61 (step @p9 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.36/0.61 (step @p10 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.36/0.61 (step @p11 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.36/0.61 (step @p12 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.36/0.61 (step @p13 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.36/0.61 (step @p14 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.36/0.61 (step @p15 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.36/0.61 (step @p16 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.36/0.61 (step @p17 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.36/0.61 (step @p18 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.36/0.61 (step @p19 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.36/0.61 (step @p20 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.36/0.61 (step @p21 (= tptp.msymmetric @t52) :rule refl :args (@t52)) % 0.36/0.61 (step @p22 (= tptp.mserial @t54) :rule refl :args (@t54)) % 0.36/0.61 (step @p23 (= tptp.mtransitive @t59) :rule refl :args (@t59)) % 0.36/0.61 (step @p24 (= tptp.meuclidean @t61) :rule refl :args (@t61)) % 0.36/0.61 (step @p25 (= tptp.mpartially_functional @t63) :rule refl :args (@t63)) % 0.36/0.61 (step @p26 (= tptp.mfunctional @t65) :rule refl :args (@t65)) % 0.36/0.61 (step @p27 (= tptp.mweakly_dense @t68) :rule refl :args (@t68)) % 0.36/0.61 (step @p28 (= tptp.mweakly_connected @t69) :rule refl :args (@t69)) % 0.36/0.61 (step @p29 (= tptp.mweakly_directed @t70) :rule refl :args (@t70)) % 0.36/0.61 (step @p30 (= tptp.mvalid @t73) :rule refl :args (@t73)) % 0.36/0.61 (step @p31 (= tptp.minvalid @t74) :rule refl :args (@t74)) % 0.36/0.61 (step @p32 (= tptp.msatisfiable @t75) :rule refl :args (@t75)) % 0.36/0.61 (step @p33 (= tptp.mcountersatisfiable @t76) :rule refl :args (@t76)) % 0.36/0.61 (step @p34 (= tptp.mbox_k @t81) :rule refl :args (@t81)) % 0.36/0.61 (step @p35 (= tptp.mdia_k @t82) :rule refl :args (@t82)) % 0.36/0.61 (step @p36 :rule aci_norm :args ((= @t94 @t92))) % 0.36/0.61 (step @p37 :rule cong :premises (@p36) :args (@t96)) % 0.36/0.61 (step @p38 :rule quant-merge-prenex :args ((= (forall @t36 @t98) @t96))) % 0.36/0.61 (step @p39 :rule alpha_equiv :args (@t99 (@list @t83) (@list @t38))) % 0.36/0.61 (step @p40 :rule refl :args (@t91)) % 0.36/0.61 (step @p41 :rule nary_cong :premises (@p40 @p39) :args (@t100)) % 0.36/0.61 (step @p42 :rule quant-miniscope-or :args ((= @t98 @t100))) % 0.36/0.61 (step @p43 :rule trans :premises (@p42 @p41)) % 0.36/0.61 (step @p44 :rule symm :premises (@p43)) % 0.36/0.61 (step @p45 :rule cong :premises (@p44) :args ((forall @t36 @t104))) % 0.36/0.61 (step @p46 :rule trans :premises (@p45 @p38)) % 0.36/0.61 (step @p47 :rule trans :premises (@p46 @p37)) % 0.36/0.61 (step @p48 :rule beta-reduce :args ((= @t111 @t104))) % 0.36/0.61 (step @p49 :rule cong :premises (@p48) :args (@t112)) % 0.36/0.61 (step @p50 :rule trans :premises (@p49 @p47)) % 0.36/0.61 (step @p51 :rule beta-reduce :args ((= (_ @t114 @t110) @t112))) % 0.36/0.61 (step @p52 :rule trans :premises (@p51 @p50)) % 0.36/0.61 (step @p53 :rule beta-reduce :args ((= @t116 @t106))) % 0.36/0.61 (step @p54 :rule refl :args (@t108)) % 0.36/0.61 (step @p55 :rule nary_cong :premises (@p54 @p53) :args (@t117)) % 0.36/0.61 (step @p56 :rule cong :premises (@p55) :args (@t118)) % 0.36/0.61 (step @p57 :rule beta-reduce :args ((= (_ (lambda @t120 (or @t108 @t119)) @t115) @t118))) % 0.36/0.61 (step @p58 :rule trans :premises (@p57 @p56)) % 0.36/0.61 (step @p59 :rule refl :args (@t87)) % 0.36/0.61 (step @p60 :rule refl :args (@t121)) % 0.36/0.61 (step @p61 :rule cong :premises (@p60 @p59) :args ((= @t121 @t87))) % 0.36/0.61 (step @p62 :rule symm :premises (@p61)) % 0.36/0.61 (step @p63 :rule eq_resolve :premises (@p60 @p62)) % 0.36/0.61 (step @p64 :rule refl :args (@t101)) % 0.36/0.61 (step @p65 :rule refl :args (@t122)) % 0.36/0.61 (step @p66 :rule cong :premises (@p65 @p64) :args ((= @t122 @t101))) % 0.36/0.61 (step @p67 :rule symm :premises (@p66)) % 0.36/0.61 (step @p68 :rule eq_resolve :premises (@p65 @p67)) % 0.36/0.61 (step @p69 :rule cong :premises (@p68) :args (@t123)) % 0.36/0.61 (step @p70 :rule refl :args (@t89)) % 0.36/0.61 (step @p71 :rule nary_cong :premises (@p70 @p69 @p63) :args (@t124)) % 0.36/0.61 (step @p72 :rule cong :premises (@p71) :args ((forall @t41 @t124))) % 0.36/0.61 (step @p73 :rule aci_norm :args ((= (or @t89 @t125) @t124))) % 0.36/0.61 (step @p74 :rule beta-reduce :args ((= @t128 @t125))) % 0.36/0.61 (step @p75 :rule refl :args (@t89)) % 0.36/0.61 (step @p76 :rule nary_cong :premises (@p75 @p74) :args (@t129)) % 0.36/0.61 (step @p77 :rule trans :premises (@p76 @p73)) % 0.36/0.61 (step @p78 :rule cong :premises (@p77) :args (@t130)) % 0.36/0.61 (step @p79 :rule trans :premises (@p78 @p72)) % 0.36/0.61 (step @p80 :rule cong :premises (@p79) :args (@t131)) % 0.36/0.61 (step @p81 :rule beta-reduce :args ((= (_ @t133 @t127) @t131))) % 0.36/0.61 (step @p82 :rule trans :premises (@p81 @p80)) % 0.36/0.61 (step @p83 :rule beta-reduce :args ((= (_ @t134 tptp.p) @t127))) % 0.36/0.61 (step @p84 :rule refl :args (tptp.p)) % 0.36/0.61 (step @p85 :rule beta-reduce :args ((= @t137 @t134))) % 0.36/0.61 (step @p86 :rule ho_cong :premises (@p85 @p84)) % 0.36/0.61 (step @p87 :rule trans :premises (@p86 @p83)) % 0.36/0.61 (step @p88 :rule refl :args (@t133)) % 0.36/0.61 (step @p89 :rule ho_cong :premises (@p88 @p87)) % 0.36/0.61 (step @p90 :rule trans :premises (@p89 @p82)) % 0.36/0.61 (step @p91 :rule refl :args (@t119)) % 0.36/0.61 (step @p92 :rule beta-reduce :args ((= @t139 @t107))) % 0.36/0.61 (step @p93 :rule cong :premises (@p92) :args (@t140)) % 0.36/0.61 (step @p94 :rule nary_cong :premises (@p93 @p91) :args (@t141)) % 0.36/0.61 (step @p95 :rule cong :premises (@p94) :args (@t142)) % 0.36/0.61 (step @p96 :rule beta-reduce :args ((= (_ @t136 @t138) @t142))) % 0.36/0.61 (step @p97 :rule trans :premises (@p96 @p95)) % 0.36/0.61 (step @p98 :rule beta-reduce :args ((= @t143 @t138))) % 0.36/0.61 (step @p99 :rule refl :args (@t136)) % 0.36/0.61 (step @p100 :rule ho_cong :premises (@p99 @p98)) % 0.36/0.61 (step @p101 :rule trans :premises (@p100 @p97)) % 0.36/0.61 (step @p102 :rule ho_cong :premises (@p101 @p90)) % 0.36/0.61 (step @p103 :rule trans :premises (@p102 @p58)) % 0.36/0.61 (step @p104 :rule refl :args (@t114)) % 0.36/0.61 (step @p105 :rule ho_cong :premises (@p104 @p103)) % 0.36/0.61 (step @p106 :rule trans :premises (@p105 @p52)) % 0.36/0.61 (step @p107 :rule cong :premises (@p106) :args ((not (_ @t114 (_ (_ @t136 @t143) (_ @t133 (_ @t137 tptp.p))))))) % 0.36/0.61 (step @p108 :rule refl :args (tptp.q)) % 0.36/0.61 (step @p109 :rule beta-reduce :args ((= (_ @t145 @t17) @t135))) % 0.36/0.61 (step @p110 :rule refl :args (@t17)) % 0.36/0.61 (step @p111 :rule beta-reduce :args ((= (_ (lambda @t146 @t144) @t14) @t145))) % 0.36/0.61 (step @p112 :rule refl :args (@t14)) % 0.36/0.61 (step @p113 :rule refl :args (@t15)) % 0.36/0.61 (step @p114 :rule beta-reduce :args ((= @t148 @t11))) % 0.36/0.61 (step @p115 :rule nary_cong :premises (@p114 @p113) :args (@t149)) % 0.36/0.61 (step @p116 :rule cong :premises (@p115) :args (@t150)) % 0.36/0.61 (step @p117 :rule beta-reduce :args ((= (_ @t16 @t147) @t150))) % 0.36/0.61 (step @p118 :rule trans :premises (@p117 @p116)) % 0.36/0.61 (step @p119 :rule beta-reduce :args ((= (_ @t13 @t9) @t147))) % 0.36/0.61 (step @p120 :rule refl :args (@t16)) % 0.36/0.61 (step @p121 :rule ho_cong :premises (@p120 @p119)) % 0.36/0.61 (step @p122 :rule trans :premises (@p121 @p118)) % 0.36/0.61 (step @p123 :rule ho_cong :premises (@p122 @p112)) % 0.36/0.61 (step @p124 :rule trans :premises (@p123 @p111)) % 0.36/0.61 (step @p125 :rule ho_cong :premises (@p124 @p110)) % 0.36/0.61 (step @p126 :rule trans :premises (@p125 @p109)) % 0.36/0.61 (step @p127 :rule refl :args (@t9)) % 0.36/0.61 (step @p128 :rule ho_cong :premises (@p6 @p127)) % 0.36/0.61 (step @p129 :rule ho_cong :premises (@p7 @p128)) % 0.36/0.61 (step @p130 :rule ho_cong :premises (@p129 @p112)) % 0.36/0.61 (step @p131 :rule ho_cong :premises (@p130 @p110)) % 0.36/0.61 (step @p132 :rule trans :premises (@p131 @p126)) % 0.36/0.61 (step @p133 :rule cong :premises (@p132) :args (@t23)) % 0.36/0.61 (step @p134 :rule trans :premises (@p9 @p133)) % 0.36/0.61 (step @p135 :rule ho_cong :premises (@p134 @p108)) % 0.36/0.61 (step @p136 :rule ho_cong :premises (@p135 @p84)) % 0.36/0.61 (step @p137 :rule refl :args (@t132)) % 0.36/0.61 (step @p138 :rule refl :args (@t39)) % 0.36/0.61 (step @p139 :rule cong :premises (@p138 @p137) :args ((= @t39 @t132))) % 0.36/0.61 (step @p140 :rule symm :premises (@p139)) % 0.36/0.61 (step @p141 :rule eq_resolve :premises (@p138 @p140)) % 0.36/0.61 (step @p142 :rule refl :args (@t88)) % 0.36/0.61 (step @p143 :rule refl :args (@t77)) % 0.36/0.61 (step @p144 :rule cong :premises (@p143 @p142) :args ((= @t77 @t88))) % 0.36/0.61 (step @p145 :rule symm :premises (@p144)) % 0.36/0.61 (step @p146 :rule eq_resolve :premises (@p143 @p145)) % 0.36/0.61 (step @p147 :rule cong :premises (@p146) :args (@t78)) % 0.36/0.61 (step @p148 :rule nary_cong :premises (@p147 @p141) :args (@t79)) % 0.36/0.61 (step @p149 :rule cong :premises (@p148) :args (@t80)) % 0.36/0.61 (step @p150 :rule cong :premises (@p149) :args (@t81)) % 0.36/0.61 (step @p151 :rule trans :premises (@p34 @p150)) % 0.36/0.61 (step @p152 :rule ho_cong :premises (@p151 @p136)) % 0.36/0.61 (step @p153 :rule ho_cong :premises (@p151 @p84)) % 0.36/0.61 (step @p154 :rule ho_cong :premises (@p134 @p153)) % 0.36/0.61 (step @p155 :rule ho_cong :premises (@p154 @p152)) % 0.36/0.61 (step @p156 :rule refl :args (@t113)) % 0.36/0.61 (step @p157 :rule refl :args (@t10)) % 0.36/0.61 (step @p158 :rule cong :premises (@p157 @p156) :args ((= @t10 @t113))) % 0.36/0.61 (step @p159 :rule symm :premises (@p158)) % 0.36/0.61 (step @p160 :rule eq_resolve :premises (@p157 @p159)) % 0.36/0.61 (step @p161 :rule cong :premises (@p160) :args (@t71)) % 0.36/0.61 (step @p162 :rule cong :premises (@p161) :args (@t73)) % 0.36/0.61 (step @p163 :rule trans :premises (@p30 @p162)) % 0.36/0.61 (step @p164 :rule ho_cong :premises (@p163 @p155)) % 0.36/0.61 (step @p165 :rule cong :premises (@p164) :args (@t1)) % 0.36/0.61 (step @p166 :rule trans :premises (@p165 @p107)) % 0.36/0.61 (step @p167 :rule eq_resolve :premises (@p2 @p166)) % 0.36/0.61 (step @p168 :rule skolemize :premises (@p167)) % 0.36/0.61 (step @p169 :rule bool-double-not-elim :args (@t153)) % 0.36/0.61 (step @p170 :rule refl :args (@t159)) % 0.36/0.61 (step @p171 :rule nary_cong :premises (@p170 @p169) :args ((or @t159 (not @t158)))) % 0.36/0.61 (step @p172 :rule cnf_or_neg :args (@t159 0)) % 0.36/0.61 (step @p173 :rule eq_resolve :premises (@p172 @p171)) % 0.36/0.61 (step @p174 :rule reordering :premises (@p173) :args ((or @t153 @t159))) % 0.36/0.61 (step @p175 :rule chain_m_resolution :premises (@p174 @p168) :args (@t153 @t160 @t161)) % 0.36/0.61 (step @p176 :rule cnf_or_neg :args (@t159 3)) % 0.36/0.61 (step @p177 :rule chain_m_resolution :premises (@p176 @p168) :args ((not @t155) @t160 @t161)) % 0.36/0.61 (step @p178 :rule bool-double-not-elim :args (@t156)) % 0.36/0.61 (step @p179 :rule nary_cong :premises (@p170 @p178) :args ((or @t159 (not @t157)))) % 0.36/0.61 (step @p180 :rule cnf_or_neg :args (@t159 1)) % 0.36/0.61 (step @p181 :rule eq_resolve :premises (@p180 @p179)) % 0.36/0.61 (step @p182 :rule reordering :premises (@p181) :args ((or @t156 @t159))) % 0.36/0.61 (step @p183 :rule chain_m_resolution :premises (@p182 @p168) :args (@t156 @t160 @t161)) % 0.36/0.61 (step @p184 :rule cnf_or_pos :args (@t162)) % 0.36/0.61 (step @p185 :rule reordering :premises (@p184) :args ((or @t157 @t155 @t163))) % 0.36/0.61 (step @p186 :rule chain_m_resolution :premises (@p185 @p183 @p177) :args (@t163 (@list false true) (@list @t156 @t155))) % 0.36/0.61 (assume-push @p193 @t153) % 0.36/0.61 (step @p188 :rule instantiate :premises (@p175) :args ((@list @t154))) % 0.36/0.61 (step-pop @p194 :rule scope :premises (@p188)) % 0.36/0.61 (step @p189 :rule process_scope :premises (@p194) :args (@t162)) % 0.36/0.61 (step @p191 :rule implies_elim :premises (@p189)) % 0.36/0.61 (step @p192 false :rule chain_m_resolution :premises (@p191 @p186 @p175) :args (false (@list true false) (@list @t162 @t153))) % 0.36/0.61 ) % 0.36/0.61 % SZS output end Proof % 0.36/0.61 % cvc5 exiting %------------------------------------------------------------------------------