%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO412^1 : 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 : n011.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 09:12:36 AM UTC 2026 % Result : Theorem 0.38s 0.62s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO412^1 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n011.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 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Jun 3 00:06:50 EDT 2026 % 0.17/0.35 % CPUTime : % 0.31/0.51 %----Proving TH0 % 0.38/0.62 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.62 % SZS status Theorem % 0.38/0.62 % SZS output start Proof % 0.38/0.62 ( % 0.38/0.62 (declare-sort $$unsorted 0) % 0.38/0.62 (declare-sort tptp.mu 0) % 0.38/0.62 (declare-const tptp.rel_k (-> $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.p (-> $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.q (-> $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.38/0.62 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.38/0.62 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.38/0.62 (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)))))) % 0.38/0.62 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.62 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.62 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.38/0.62 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.62 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.38/0.62 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.62 (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))))))) % 0.38/0.62 (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))))))) % 0.38/0.62 (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)))))) % 0.38/0.62 (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)))))) % 0.38/0.62 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.38/0.62 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.38/0.62 (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)))))) % 0.38/0.62 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.38/0.62 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.62 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.62 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.38/0.62 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.38/0.62 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.38/0.62 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.38/0.62 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.38/0.62 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.38/0.62 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.38/0.62 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.62 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.62 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.62 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.62 (define tptp.mbox_k () (let ((_let_1 (@var "V" $$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)))))))) % 0.38/0.62 (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))))) % 0.38/0.62 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mequiv (_ tptp.mdia_k (_ (_ tptp.mimplies tptp.p) tptp.q))) (_ (_ tptp.mimplies (_ tptp.mbox_k tptp.p)) (_ tptp.mdia_k tptp.q)))))) % 0.38/0.62 (define @t2 () (@var "Y" tptp.mu)) % 0.38/0.62 (define @t3 () (@var "X" tptp.mu)) % 0.38/0.62 (define @t4 () (@var "W" $$unsorted)) % 0.38/0.62 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.38/0.62 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.62 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.62 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.38/0.62 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.38/0.62 (define @t10 () (_ @t9 @t4)) % 0.38/0.62 (define @t11 () (not @t10)) % 0.38/0.62 (define @t12 () (@list @t9 @t4)) % 0.38/0.62 (define @t13 () (lambda @t12 @t11)) % 0.38/0.62 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.38/0.62 (define @t15 () (_ @t14 @t4)) % 0.38/0.62 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.38/0.62 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.38/0.62 (define @t18 () (_ tptp.mnot @t14)) % 0.38/0.62 (define @t19 () (_ tptp.mnot @t9)) % 0.38/0.62 (define @t20 () (_ tptp.mor @t19)) % 0.38/0.62 (define @t21 () (@list @t9 @t14 @t17)) % 0.38/0.62 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.38/0.62 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.38/0.62 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.38/0.62 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.38/0.62 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.38/0.62 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.38/0.62 (define @t28 () (_ @t27 @t3)) % 0.38/0.62 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.38/0.62 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.38/0.62 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.38/0.62 (define @t32 () (_ @t31 @t30)) % 0.38/0.62 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.38/0.62 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.38/0.62 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.38/0.62 (define @t36 () (@list @t4)) % 0.38/0.62 (define @t37 () (lambda @t36 true)) % 0.38/0.62 (define @t38 () (@var "V" $$unsorted)) % 0.38/0.62 (define @t39 () (_ @t9 @t38)) % 0.38/0.62 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.38/0.62 (define @t41 () (@list @t38)) % 0.38/0.62 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.38/0.62 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.38/0.62 (define @t44 () (@var "S" $$unsorted)) % 0.38/0.62 (define @t45 () (_ @t40 @t44)) % 0.38/0.62 (define @t46 () (@list @t44)) % 0.38/0.62 (define @t47 () (@list @t40)) % 0.38/0.62 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.38/0.62 (define @t49 () (@var "T" $$unsorted)) % 0.38/0.62 (define @t50 () (_ @t40 @t49)) % 0.38/0.62 (define @t51 () (_ @t45 @t49)) % 0.38/0.62 (define @t52 () (lambda @t47 (forall (@list @t44 @t49) (=> @t51 (_ @t50 @t44))))) % 0.38/0.62 (define @t53 () (@list @t49)) % 0.38/0.62 (define @t54 () (lambda @t47 (forall @t46 (exists @t53 @t51)))) % 0.38/0.62 (define @t55 () (@var "U" $$unsorted)) % 0.38/0.62 (define @t56 () (_ @t45 @t55)) % 0.38/0.62 (define @t57 () (_ @t50 @t55)) % 0.38/0.62 (define @t58 () (@list @t44 @t49 @t55)) % 0.38/0.62 (define @t59 () (lambda @t47 (forall @t58 (=> (and @t51 @t57) @t56)))) % 0.38/0.62 (define @t60 () (and @t51 @t56)) % 0.38/0.62 (define @t61 () (lambda @t47 (forall @t58 (=> @t60 @t57)))) % 0.38/0.62 (define @t62 () (= @t49 @t55)) % 0.38/0.62 (define @t63 () (lambda @t47 (forall @t58 (=> @t60 @t62)))) % 0.38/0.62 (define @t64 () (@list @t55)) % 0.38/0.62 (define @t65 () (lambda @t47 (forall @t46 (exists @t53 (and @t51 (forall @t64 (=> @t56 @t62))))))) % 0.38/0.62 (define @t66 () (_ @t40 @t55)) % 0.38/0.62 (define @t67 () (_ @t66 @t49)) % 0.38/0.62 (define @t68 () (lambda @t47 (forall @t58 (=> @t51 (exists @t64 (and @t56 @t67)))))) % 0.38/0.62 (define @t69 () (lambda @t47 (forall @t58 (=> @t60 (or @t57 @t62 @t67))))) % 0.38/0.62 (define @t70 () (lambda @t47 (forall @t58 (=> @t60 (exists @t41 (and (_ @t50 @t38) (_ @t66 @t38))))))) % 0.38/0.62 (define @t71 () (forall @t36 @t10)) % 0.38/0.62 (define @t72 () (@list @t9)) % 0.38/0.62 (define @t73 () (lambda @t72 @t71)) % 0.38/0.62 (define @t74 () (lambda @t72 (forall @t36 @t11))) % 0.38/0.62 (define @t75 () (lambda @t72 (exists @t36 @t10))) % 0.38/0.62 (define @t76 () (lambda @t72 (exists @t36 @t11))) % 0.38/0.62 (define @t77 () (_ (_ tptp.rel_k @t4) @t38)) % 0.38/0.62 (define @t78 () (not @t77)) % 0.38/0.62 (define @t79 () (or @t78 @t39)) % 0.38/0.62 (define @t80 () (forall @t41 @t79)) % 0.38/0.62 (define @t81 () (lambda @t12 @t80)) % 0.38/0.62 (define @t82 () (@list @t9 @t17)) % 0.38/0.62 (define @t83 () (lambda @t82 (_ (_ tptp.mnot (_ tptp.mbox_k @t19)) @t17))) % 0.38/0.62 (define @t84 () (tptp.q @t38)) % 0.38/0.62 (define @t85 () (not @t84)) % 0.38/0.62 (define @t86 () (tptp.p @t38)) % 0.38/0.62 (define @t87 () (and @t86 @t85)) % 0.38/0.62 (define @t88 () (@var "BOUND_VARIABLE_8542" $$unsorted)) % 0.38/0.62 (define @t89 () (not (tptp.rel_k @t88 @t38))) % 0.38/0.62 (define @t90 () (not (forall @t41 (or @t89 @t87)))) % 0.38/0.62 (define @t91 () (@var "BOUND_VARIABLE_8578" $$unsorted)) % 0.38/0.62 (define @t92 () (or (not (tptp.rel_k @t88 @t91)) (not (tptp.q @t91)))) % 0.38/0.62 (define @t93 () (@var "BOUND_VARIABLE_8572" $$unsorted)) % 0.38/0.62 (define @t94 () (or (not (tptp.rel_k @t88 @t93)) (tptp.p @t93))) % 0.38/0.62 (define @t95 () (and @t94 @t92)) % 0.38/0.62 (define @t96 () (or @t95 @t90)) % 0.38/0.62 (define @t97 () (forall (@list @t88 @t93 @t91) @t96)) % 0.38/0.62 (define @t98 () (@quantifiers_skolemize @t97 2)) % 0.38/0.62 (define @t99 () (@quantifiers_skolemize @t97 0)) % 0.38/0.62 (define @t100 () (tptp.rel_k @t99 @t98)) % 0.38/0.62 (define @t101 () (tptp.q @t98)) % 0.38/0.62 (define @t102 () (not @t101)) % 0.38/0.62 (define @t103 () (not @t100)) % 0.38/0.62 (define @t104 () (or @t103 @t102)) % 0.38/0.62 (define @t105 () (@var "BOUND_VARIABLE_8558" $$unsorted)) % 0.38/0.62 (define @t106 () (and (tptp.p @t105) (not (tptp.q @t105)))) % 0.38/0.62 (define @t107 () (@var "BOUND_VARIABLE_8527" $$unsorted)) % 0.38/0.62 (define @t108 () (not (tptp.rel_k @t107 @t105))) % 0.38/0.62 (define @t109 () (not (tptp.rel_k @t107 @t38))) % 0.38/0.62 (define @t110 () (not (forall @t41 (or @t109 @t85)))) % 0.38/0.62 (define @t111 () (not (forall @t41 (or @t109 @t86)))) % 0.38/0.62 (define @t112 () (or @t111 @t110 @t108 @t106)) % 0.38/0.62 (define @t113 () (@list @t107 @t105)) % 0.38/0.62 (define @t114 () (forall @t113 @t112)) % 0.38/0.62 (define @t115 () (@quantifiers_skolemize @t114 0)) % 0.38/0.62 (define @t116 () (not (tptp.rel_k @t115 @t38))) % 0.38/0.62 (define @t117 () (forall @t41 (or @t116 @t86))) % 0.38/0.62 (define @t118 () (@quantifiers_skolemize @t114 1)) % 0.38/0.62 (define @t119 () (tptp.q @t118)) % 0.38/0.62 (define @t120 () (not @t119)) % 0.38/0.62 (define @t121 () (tptp.p @t118)) % 0.38/0.62 (define @t122 () (and @t121 @t120)) % 0.38/0.62 (define @t123 () (tptp.rel_k @t115 @t118)) % 0.38/0.62 (define @t124 () (not @t123)) % 0.38/0.62 (define @t125 () (forall @t41 (or @t116 @t85))) % 0.38/0.62 (define @t126 () (not @t125)) % 0.38/0.62 (define @t127 () (not @t117)) % 0.38/0.62 (define @t128 () (or @t127 @t126 @t124 @t122)) % 0.38/0.62 (define @t129 () (@list @t118)) % 0.38/0.62 (define @t130 () (or @t124 @t121)) % 0.38/0.62 (define @t131 () (not @t121)) % 0.38/0.62 (define @t132 () (or @t124 @t120)) % 0.38/0.62 (define @t133 () (not @t128)) % 0.38/0.62 (define @t134 () (not @t114)) % 0.38/0.62 (define @t135 () (@list false)) % 0.38/0.62 (define @t136 () (@list @t93 @t91)) % 0.38/0.62 (define @t137 () (forall @t136 @t96)) % 0.38/0.62 (define @t138 () (@list @t88)) % 0.38/0.62 (define @t139 () (forall (@list @t91) @t92)) % 0.38/0.62 (define @t140 () (@list @t38)) % 0.38/0.62 (define @t141 () (forall @t136 @t92)) % 0.38/0.62 (define @t142 () (forall (@list @t93) @t94)) % 0.38/0.62 (define @t143 () (forall @t136 @t94)) % 0.38/0.62 (define @t144 () (and @t143 @t141)) % 0.38/0.62 (define @t145 () (forall @t136 @t95)) % 0.38/0.62 (define @t146 () (or @t145 @t90)) % 0.38/0.62 (define @t147 () (forall @t138 (or (and (forall @t41 (or @t89 @t86)) (forall @t41 (or @t89 @t85))) @t90))) % 0.38/0.62 (define @t148 () (or @t108 @t106)) % 0.38/0.62 (define @t149 () (or @t148 @t111 @t110)) % 0.38/0.62 (define @t150 () (forall @t113 @t149)) % 0.38/0.62 (define @t151 () (@list @t105)) % 0.38/0.62 (define @t152 () (forall @t151 @t149)) % 0.38/0.62 (define @t153 () (@list @t107)) % 0.38/0.62 (define @t154 () (forall @t151 @t148)) % 0.38/0.62 (define @t155 () (or @t154 @t111 @t110)) % 0.38/0.62 (define @t156 () (forall @t153 (or (forall @t41 (or @t109 @t87)) @t111 @t110))) % 0.38/0.62 (define @t157 () (tptp.rel_k @t4 @t38)) % 0.38/0.62 (define @t158 () (not @t157)) % 0.38/0.62 (define @t159 () (forall @t41 (or @t158 @t87))) % 0.38/0.62 (define @t160 () (not @t159)) % 0.38/0.62 (define @t161 () (forall @t41 (or @t158 @t85))) % 0.38/0.62 (define @t162 () (forall @t41 (or @t158 @t86))) % 0.38/0.62 (define @t163 () (or (and @t162 @t161) @t160)) % 0.38/0.62 (define @t164 () (forall @t36 @t163)) % 0.38/0.62 (define @t165 () (@list @t4)) % 0.38/0.62 (define @t166 () (not @t161)) % 0.38/0.62 (define @t167 () (not @t162)) % 0.38/0.62 (define @t168 () (or @t159 @t167 @t166)) % 0.38/0.62 (define @t169 () (forall @t36 @t168)) % 0.38/0.62 (define @t170 () (and @t169 @t164)) % 0.38/0.62 (define @t171 () (or (not (or @t167 @t166)) @t160)) % 0.38/0.62 (define @t172 () (not @t171)) % 0.38/0.62 (define @t173 () (not @t168)) % 0.38/0.62 (define @t174 () (not (or @t173 @t172))) % 0.38/0.62 (define @t175 () (not (tptp.rel_k @t17 @t38))) % 0.38/0.62 (define @t176 () (forall @t41 (or @t175 @t87))) % 0.38/0.62 (define @t177 () (not @t176)) % 0.38/0.62 (define @t178 () (not (forall @t41 (or @t175 @t85)))) % 0.38/0.62 (define @t179 () (forall @t41 (or @t175 @t86))) % 0.38/0.62 (define @t180 () (not @t179)) % 0.38/0.62 (define @t181 () (or @t180 @t178)) % 0.38/0.62 (define @t182 () (or @t176 @t180 @t178)) % 0.38/0.62 (define @t183 () (@list @t17)) % 0.38/0.62 (define @t184 () (lambda @t183 (not (or (not @t182) (not (or (not @t181) @t177)))))) % 0.38/0.62 (define @t185 () (_ @t184 @t4)) % 0.38/0.62 (define @t186 () (forall @t36 @t185)) % 0.38/0.62 (define @t187 () (_ @t9 @t4)) % 0.38/0.62 (define @t188 () (lambda @t72 (forall @t36 @t187))) % 0.38/0.62 (define @t189 () (lambda @t183 @t181)) % 0.38/0.62 (define @t190 () (_ @t189 @t17)) % 0.38/0.62 (define @t191 () (not @t190)) % 0.38/0.62 (define @t192 () (or @t191 @t177)) % 0.38/0.62 (define @t193 () (not @t192)) % 0.38/0.62 (define @t194 () (or @t176 @t190)) % 0.38/0.62 (define @t195 () (not @t194)) % 0.38/0.62 (define @t196 () (or @t195 @t193)) % 0.38/0.62 (define @t197 () (not @t196)) % 0.38/0.62 (define @t198 () (lambda @t183 @t197)) % 0.38/0.62 (define @t199 () (_ @t14 @t17)) % 0.38/0.62 (define @t200 () (not @t199)) % 0.38/0.62 (define @t201 () (@list @t14 @t17)) % 0.38/0.62 (define @t202 () (lambda @t183 @t178)) % 0.38/0.62 (define @t203 () (_ @t202 @t17)) % 0.38/0.62 (define @t204 () (or @t180 @t203)) % 0.38/0.62 (define @t205 () (lambda @t183 @t204)) % 0.38/0.62 (define @t206 () (_ @t9 @t38)) % 0.38/0.62 (define @t207 () (not @t206)) % 0.38/0.62 (define @t208 () (not (forall @t41 (or @t175 @t207)))) % 0.38/0.62 (define @t209 () (lambda @t82 @t208)) % 0.38/0.62 (define @t210 () (_ @t209 tptp.q)) % 0.38/0.62 (define @t211 () (lambda @t36 @t162)) % 0.38/0.62 (define @t212 () (_ @t211 @t17)) % 0.38/0.62 (define @t213 () (not @t212)) % 0.38/0.62 (define @t214 () (or @t213 @t199)) % 0.38/0.62 (define @t215 () (lambda @t201 @t214)) % 0.38/0.62 (define @t216 () (_ @t9 @t17)) % 0.38/0.62 (define @t217 () (not @t216)) % 0.38/0.62 (define @t218 () (or @t217 @t199)) % 0.38/0.62 (define @t219 () (lambda @t21 @t218)) % 0.38/0.62 (define @t220 () (lambda @t12 (forall @t41 (or @t158 @t206)))) % 0.38/0.62 (define @t221 () (_ @t220 tptp.p)) % 0.38/0.62 (define @t222 () (lambda @t183 @t177)) % 0.38/0.62 (define @t223 () (_ @t222 @t17)) % 0.38/0.62 (define @t224 () (or @t200 @t223)) % 0.38/0.62 (define @t225 () (not @t224)) % 0.38/0.62 (define @t226 () (not @t223)) % 0.38/0.62 (define @t227 () (or @t226 @t199)) % 0.38/0.62 (define @t228 () (not @t227)) % 0.38/0.62 (define @t229 () (or @t228 @t225)) % 0.38/0.62 (define @t230 () (not @t229)) % 0.38/0.62 (define @t231 () (lambda @t201 @t230)) % 0.38/0.62 (define @t232 () (or @t200 @t216)) % 0.38/0.62 (define @t233 () (not @t218)) % 0.38/0.62 (define @t234 () (not (or @t233 (not @t232)))) % 0.38/0.62 (define @t235 () (lambda @t21 @t234)) % 0.38/0.62 (define @t236 () (_ tptp.q @t38)) % 0.38/0.62 (define @t237 () (not @t236)) % 0.38/0.62 (define @t238 () (_ tptp.p @t38)) % 0.38/0.62 (define @t239 () (and @t238 @t237)) % 0.38/0.62 (define @t240 () (or @t175 @t239)) % 0.38/0.62 (define @t241 () (not @t238)) % 0.38/0.62 (define @t242 () (or @t241 @t236)) % 0.38/0.62 (define @t243 () (or @t175 (not @t242))) % 0.38/0.62 (define @t244 () (not (_ tptp.p @t17))) % 0.38/0.62 (define @t245 () (lambda @t183 (or @t244 (_ tptp.q @t17)))) % 0.38/0.62 (define @t246 () (_ @t245 @t38)) % 0.38/0.62 (define @t247 () (not @t246)) % 0.38/0.62 (define @t248 () (or @t175 @t247)) % 0.38/0.62 (define @t249 () (forall @t41 @t248)) % 0.38/0.62 (define @t250 () (not @t249)) % 0.38/0.62 (define @t251 () (lambda @t183 @t250)) % 0.38/0.62 (define @t252 () (lambda @t201 (or @t244 @t199))) % 0.38/0.62 (define @t253 () (_ @t219 tptp.p)) % 0.38/0.62 (define @t254 () (forall @t41 (or @t158 @t207))) % 0.38/0.62 (define @t255 () (lambda @t36 @t254)) % 0.38/0.62 (define @t256 () (_ @t255 @t4)) % 0.38/0.62 (define @t257 () (not @t256)) % 0.38/0.62 (define @t258 () (lambda @t36 @t257)) % 0.38/0.62 (define @t259 () (not @t39)) % 0.38/0.62 (define @t260 () (or @t158 @t259)) % 0.38/0.62 (define @t261 () (lambda @t36 @t11)) % 0.38/0.62 (define @t262 () (_ @t261 @t38)) % 0.38/0.62 (define @t263 () (or @t158 @t262)) % 0.38/0.62 (define @t264 () (forall @t41 @t263)) % 0.38/0.62 (define @t265 () (lambda @t36 @t264)) % 0.38/0.62 (define @t266 () (or @t11 @t15)) % 0.38/0.62 (define @t267 () (lambda @t36 @t266)) % 0.38/0.62 (define @t268 () (@list @t14 @t4)) % 0.38/0.62 (define @t269 () (lambda @t268 @t266)) % 0.38/0.62 (define @t270 () (_ @t261 @t4)) % 0.38/0.62 (define @t271 () (or @t270 @t15)) % 0.38/0.62 (define @t272 () (lambda @t268 @t271)) % 0.38/0.62 (define @t273 () (lambda @t183 @t232)) % 0.38/0.62 (define @t274 () (_ @t273 @t17)) % 0.38/0.62 (define @t275 () (not @t274)) % 0.38/0.62 (define @t276 () (or @t233 @t275)) % 0.38/0.62 (define @t277 () (not @t276)) % 0.38/0.62 (define @t278 () (lambda @t183 @t277)) % 0.38/0.62 (define @t279 () (@var "BOUND_VARIABLE_7581" (-> $$unsorted Bool))) % 0.38/0.62 (define @t280 () (not (_ @t279 @t17))) % 0.38/0.62 (define @t281 () (@list @t279 @t17)) % 0.38/0.62 (define @t282 () (@var "BOUND_VARIABLE_7601" (-> $$unsorted Bool))) % 0.38/0.62 (define @t283 () (_ @t282 @t17)) % 0.38/0.62 (define @t284 () (lambda (@list @t282 @t17) (or @t200 @t283))) % 0.38/0.62 (define @t285 () (@list @t14)) % 0.38/0.62 (define @t286 () (lambda @t183 @t218)) % 0.38/0.62 (define @t287 () (_ @t286 @t17)) % 0.38/0.62 (define @t288 () (not @t287)) % 0.38/0.62 (define @t289 () (or @t288 @t280)) % 0.38/0.62 (define @t290 () (not @t289)) % 0.38/0.62 (define @t291 () (lambda @t281 @t290)) % 0.38/0.62 (define @t292 () (not (or @t217 @t200))) % 0.38/0.62 (define @t293 () (lambda @t21 @t292)) % 0.38/0.62 (define @t294 () (lambda @t201 @t218)) % 0.38/0.62 (define @t295 () (not @t15)) % 0.38/0.62 (define @t296 () (or @t11 @t295)) % 0.38/0.62 (define @t297 () (lambda @t36 @t296)) % 0.38/0.62 (define @t298 () (_ @t297 @t4)) % 0.38/0.62 (define @t299 () (not @t298)) % 0.38/0.62 (define @t300 () (lambda @t36 @t299)) % 0.38/0.62 (define @t301 () (lambda @t36 @t295)) % 0.38/0.62 (define @t302 () (_ @t301 @t4)) % 0.38/0.62 (define @t303 () (or @t11 @t302)) % 0.38/0.62 (define @t304 () (lambda @t36 @t303)) % 0.38/0.62 (define @t305 () (not @t97)) % 0.38/0.62 (define @t306 () (forall @t41 (or (not (tptp.rel_k @t99 @t38)) @t87))) % 0.38/0.62 (define @t307 () (not @t306)) % 0.38/0.62 (define @t308 () (@quantifiers_skolemize @t97 1)) % 0.38/0.62 (define @t309 () (tptp.p @t308)) % 0.38/0.62 (define @t310 () (tptp.rel_k @t99 @t308)) % 0.38/0.62 (define @t311 () (not @t310)) % 0.38/0.62 (define @t312 () (or @t311 @t309)) % 0.38/0.62 (define @t313 () (and @t312 @t104)) % 0.38/0.62 (define @t314 () (or @t313 @t307)) % 0.38/0.62 (define @t315 () (not @t314)) % 0.38/0.62 (define @t316 () (@list true)) % 0.38/0.62 (define @t317 () (@list @t314)) % 0.38/0.62 (define @t318 () (and (tptp.p @t98) @t102)) % 0.38/0.62 (define @t319 () (or @t103 @t318)) % 0.38/0.62 (define @t320 () (@list @t306)) % 0.38/0.62 (define @t321 () (@list @t312)) % 0.38/0.62 (define @t322 () (and @t309 (not (tptp.q @t308)))) % 0.38/0.62 (define @t323 () (or @t311 @t322)) % 0.38/0.62 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.38/0.62 (assume @p2 @t1) % 0.38/0.62 (assume @p3 true) % 0.38/0.62 (step @p4 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.38/0.62 (step @p5 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.38/0.62 (step @p6 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.38/0.62 (step @p7 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.38/0.62 (step @p8 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.38/0.62 (step @p9 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.38/0.62 (step @p10 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.38/0.62 (step @p11 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.38/0.62 (step @p12 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.38/0.62 (step @p13 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.38/0.62 (step @p14 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.38/0.62 (step @p15 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.38/0.62 (step @p16 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.38/0.62 (step @p17 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.38/0.62 (step @p18 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.38/0.62 (step @p19 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.38/0.62 (step @p20 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.38/0.62 (step @p21 (= tptp.msymmetric @t52) :rule refl :args (@t52)) % 0.38/0.62 (step @p22 (= tptp.mserial @t54) :rule refl :args (@t54)) % 0.38/0.62 (step @p23 (= tptp.mtransitive @t59) :rule refl :args (@t59)) % 0.38/0.62 (step @p24 (= tptp.meuclidean @t61) :rule refl :args (@t61)) % 0.38/0.62 (step @p25 (= tptp.mpartially_functional @t63) :rule refl :args (@t63)) % 0.38/0.62 (step @p26 (= tptp.mfunctional @t65) :rule refl :args (@t65)) % 0.38/0.62 (step @p27 (= tptp.mweakly_dense @t68) :rule refl :args (@t68)) % 0.38/0.62 (step @p28 (= tptp.mweakly_connected @t69) :rule refl :args (@t69)) % 0.38/0.62 (step @p29 (= tptp.mweakly_directed @t70) :rule refl :args (@t70)) % 0.38/0.62 (step @p30 (= tptp.mvalid @t73) :rule refl :args (@t73)) % 0.38/0.62 (step @p31 (= tptp.minvalid @t74) :rule refl :args (@t74)) % 0.38/0.62 (step @p32 (= tptp.msatisfiable @t75) :rule refl :args (@t75)) % 0.38/0.62 (step @p33 (= tptp.mcountersatisfiable @t76) :rule refl :args (@t76)) % 0.38/0.62 (step @p34 (= tptp.mbox_k @t81) :rule refl :args (@t81)) % 0.38/0.62 (step @p35 (= tptp.mdia_k @t83) :rule refl :args (@t83)) % 0.38/0.62 (step @p36 :rule bool-double-not-elim :args (@t100)) % 0.38/0.62 (step @p37 :rule refl :args (@t104)) % 0.38/0.62 (step @p38 :rule nary_cong :premises (@p37 @p36) :args ((or @t104 (not @t103)))) % 0.38/0.62 (step @p39 :rule cnf_or_neg :args (@t104 0)) % 0.38/0.62 (step @p40 :rule eq_resolve :premises (@p39 @p38)) % 0.38/0.62 (step @p41 :rule reordering :premises (@p40) :args ((or @t100 @t104))) % 0.38/0.62 (step @p42 :rule bool-double-not-elim :args (@t101)) % 0.38/0.62 (step @p43 :rule nary_cong :premises (@p37 @p42) :args ((or @t104 (not @t102)))) % 0.38/0.62 (step @p44 :rule cnf_or_neg :args (@t104 1)) % 0.38/0.62 (step @p45 :rule eq_resolve :premises (@p44 @p43)) % 0.38/0.62 (step @p46 :rule reordering :premises (@p45) :args ((or @t101 @t104))) % 0.38/0.62 (step @p47 :rule bool-double-not-elim :args (@t117)) % 0.38/0.62 (step @p48 :rule refl :args (@t128)) % 0.38/0.62 (step @p49 :rule nary_cong :premises (@p48 @p47) :args ((or @t128 (not @t127)))) % 0.38/0.62 (step @p50 :rule cnf_or_neg :args (@t128 0)) % 0.38/0.62 (step @p51 :rule eq_resolve :premises (@p50 @p49)) % 0.38/0.62 (step @p52 :rule reordering :premises (@p51) :args ((or @t117 @t128))) % 0.38/0.62 (step @p53 :rule bool-double-not-elim :args (@t125)) % 0.38/0.62 (step @p54 :rule nary_cong :premises (@p48 @p53) :args ((or @t128 (not @t126)))) % 0.38/0.62 (step @p55 :rule cnf_or_neg :args (@t128 1)) % 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0.38/0.63 (step @p479 false :rule chain_m_resolution :premises (@p478 @p476 @p460) :args (false (@list false true) (@list @t322 @t309))) % 0.38/0.63 ) % 0.38/0.63 % SZS output end Proof % 0.38/0.63 % cvc5 exiting %------------------------------------------------------------------------------