%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO392^1 : 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 09:12:33 AM UTC 2026 % Result : Theorem 0.40s 0.61s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO392^1 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.33 % Computer : n011.cluster.edu % 0.17/0.33 % Model : x86_64 x86_64 % 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.33 % Memory : 8042.1875MB % 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.33 % CPULimit : 300 % 0.17/0.33 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Jun 3 00:06:05 EDT 2026 % 0.17/0.34 % CPUTime : % 0.33/0.49 %----Proving TH0 % 0.40/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.61 % SZS status Theorem % 0.40/0.61 % SZS output start Proof % 0.40/0.61 ( % 0.40/0.61 (declare-sort $$unsorted 0) % 0.40/0.61 (declare-sort tptp.mu 0) % 0.40/0.61 (declare-const tptp.rel_k (-> $$unsorted $$unsorted Bool)) % 0.40/0.61 (declare-const tptp.p (-> $$unsorted Bool)) % 0.40/0.61 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.40/0.61 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.40/0.61 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.40/0.61 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.40/0.61 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.40/0.61 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.40/0.61 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.40/0.61 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.40/0.61 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.40/0.61 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.40/0.61 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.40/0.61 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.40/0.61 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.40/0.61 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.40/0.61 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.40/0.61 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.40/0.61 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.40/0.61 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.40/0.61 (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)))))))) % 0.40/0.61 (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)))))))) % 0.40/0.61 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.40/0.61 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 0.40/0.61 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.40/0.61 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 0.40/0.61 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.40/0.61 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 0.40/0.61 (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))))))))))))) % 0.40/0.61 (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)))))) % 0.40/0.61 (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))))))) % 0.40/0.61 (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)))))) % 0.40/0.61 (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))))))) % 0.40/0.61 (define tptp.mbox_k () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_k _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.40/0.61 (define tptp.mdia_k () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_k (_ tptp.mnot _let_2))) _let_1))))) % 0.40/0.61 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mequiv (_ tptp.mnot (_ tptp.mbox_k (_ tptp.mdia_k (_ tptp.mbox_k tptp.p))))) (_ tptp.mdia_k (_ tptp.mbox_k (_ tptp.mdia_k (_ tptp.mnot tptp.p)))))))) % 0.40/0.61 (define @t2 () (@var "Y" tptp.mu)) % 0.40/0.61 (define @t3 () (@var "X" tptp.mu)) % 0.40/0.61 (define @t4 () (@var "W" $$unsorted)) % 0.40/0.61 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.40/0.61 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.40/0.61 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.40/0.61 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.40/0.61 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.40/0.61 (define @t10 () (_ @t9 @t4)) % 0.40/0.61 (define @t11 () (not @t10)) % 0.40/0.61 (define @t12 () (@list @t9 @t4)) % 0.40/0.61 (define @t13 () (lambda @t12 @t11)) % 0.40/0.61 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.40/0.61 (define @t15 () (_ @t14 @t4)) % 0.40/0.61 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.40/0.61 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.40/0.61 (define @t18 () (_ tptp.mnot @t14)) % 0.40/0.61 (define @t19 () (_ tptp.mnot @t9)) % 0.40/0.61 (define @t20 () (_ tptp.mor @t19)) % 0.40/0.61 (define @t21 () (@list @t9 @t14 @t17)) % 0.40/0.61 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.40/0.61 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.40/0.61 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.40/0.61 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.40/0.61 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.40/0.61 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.40/0.61 (define @t28 () (_ @t27 @t3)) % 0.40/0.61 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.40/0.61 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.40/0.61 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.40/0.61 (define @t32 () (_ @t31 @t30)) % 0.40/0.61 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.40/0.61 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.40/0.61 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.40/0.61 (define @t36 () (@list @t4)) % 0.40/0.61 (define @t37 () (lambda @t36 true)) % 0.40/0.61 (define @t38 () (@var "V" $$unsorted)) % 0.40/0.61 (define @t39 () (_ @t9 @t38)) % 0.40/0.61 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.40/0.61 (define @t41 () (@list @t38)) % 0.40/0.61 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.40/0.61 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.40/0.61 (define @t44 () (@var "S" $$unsorted)) % 0.40/0.61 (define @t45 () (_ @t40 @t44)) % 0.40/0.61 (define @t46 () (@list @t44)) % 0.40/0.61 (define @t47 () (@list @t40)) % 0.40/0.61 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.40/0.61 (define @t49 () (@var "T" $$unsorted)) % 0.40/0.61 (define @t50 () (_ @t40 @t49)) % 0.40/0.61 (define @t51 () (_ @t45 @t49)) % 0.40/0.61 (define @t52 () (lambda @t47 (forall (@list @t44 @t49) (=> @t51 (_ @t50 @t44))))) % 0.40/0.61 (define @t53 () (@list @t49)) % 0.40/0.61 (define @t54 () (lambda @t47 (forall @t46 (exists @t53 @t51)))) % 0.40/0.61 (define @t55 () (@var "U" $$unsorted)) % 0.40/0.61 (define @t56 () (_ @t45 @t55)) % 0.40/0.61 (define @t57 () (_ @t50 @t55)) % 0.40/0.61 (define @t58 () (@list @t44 @t49 @t55)) % 0.40/0.61 (define @t59 () (lambda @t47 (forall @t58 (=> (and @t51 @t57) @t56)))) % 0.40/0.61 (define @t60 () (and @t51 @t56)) % 0.40/0.61 (define @t61 () (lambda @t47 (forall @t58 (=> @t60 @t57)))) % 0.40/0.61 (define @t62 () (= @t49 @t55)) % 0.40/0.61 (define @t63 () (lambda @t47 (forall @t58 (=> @t60 @t62)))) % 0.40/0.61 (define @t64 () (@list @t55)) % 0.40/0.61 (define @t65 () (lambda @t47 (forall @t46 (exists @t53 (and @t51 (forall @t64 (=> @t56 @t62))))))) % 0.40/0.61 (define @t66 () (_ @t40 @t55)) % 0.40/0.61 (define @t67 () (_ @t66 @t49)) % 0.40/0.61 (define @t68 () (lambda @t47 (forall @t58 (=> @t51 (exists @t64 (and @t56 @t67)))))) % 0.40/0.61 (define @t69 () (lambda @t47 (forall @t58 (=> @t60 (or @t57 @t62 @t67))))) % 0.40/0.61 (define @t70 () (lambda @t47 (forall @t58 (=> @t60 (exists @t41 (and (_ @t50 @t38) (_ @t66 @t38))))))) % 0.40/0.61 (define @t71 () (forall @t36 @t10)) % 0.40/0.61 (define @t72 () (@list @t9)) % 0.40/0.61 (define @t73 () (lambda @t72 @t71)) % 0.40/0.61 (define @t74 () (lambda @t72 (forall @t36 @t11))) % 0.40/0.61 (define @t75 () (lambda @t72 (exists @t36 @t10))) % 0.40/0.61 (define @t76 () (lambda @t72 (exists @t36 @t11))) % 0.40/0.61 (define @t77 () (_ (_ tptp.rel_k @t4) @t38)) % 0.40/0.61 (define @t78 () (not @t77)) % 0.40/0.61 (define @t79 () (or @t78 @t39)) % 0.40/0.61 (define @t80 () (forall @t41 @t79)) % 0.40/0.61 (define @t81 () (lambda @t12 @t80)) % 0.40/0.61 (define @t82 () (@list @t9 @t17)) % 0.40/0.61 (define @t83 () (lambda @t82 (_ (_ tptp.mnot (_ tptp.mbox_k @t19)) @t17))) % 0.40/0.61 (define @t84 () (@var "BOUND_VARIABLE_8517" $$unsorted)) % 0.40/0.61 (define @t85 () (tptp.p @t84)) % 0.40/0.61 (define @t86 () (@var "BOUND_VARIABLE_8543" $$unsorted)) % 0.40/0.61 (define @t87 () (@list @t84)) % 0.40/0.61 (define @t88 () (not (forall @t87 (or (not (tptp.rel_k @t86 @t84)) @t85)))) % 0.40/0.61 (define @t89 () (@list @t86)) % 0.40/0.61 (define @t90 () (forall @t89 (or (not (tptp.rel_k @t38 @t86)) @t88))) % 0.40/0.61 (define @t91 () (not @t90)) % 0.40/0.61 (define @t92 () (@var "BOUND_VARIABLE_8419" $$unsorted)) % 0.40/0.61 (define @t93 () (tptp.p @t92)) % 0.40/0.61 (define @t94 () (@var "BOUND_VARIABLE_8443" $$unsorted)) % 0.40/0.61 (define @t95 () (@list @t92)) % 0.40/0.61 (define @t96 () (not (forall @t95 (or (not (tptp.rel_k @t94 @t92)) @t93)))) % 0.40/0.61 (define @t97 () (@var "BOUND_VARIABLE_8625" $$unsorted)) % 0.40/0.61 (define @t98 () (@list @t94)) % 0.40/0.61 (define @t99 () (not (forall @t98 (or (not (tptp.rel_k @t97 @t94)) @t96)))) % 0.40/0.61 (define @t100 () (@var "BOUND_VARIABLE_8600" $$unsorted)) % 0.40/0.61 (define @t101 () (not (tptp.rel_k @t100 @t97))) % 0.40/0.61 (define @t102 () (not (tptp.rel_k @t100 @t38))) % 0.40/0.61 (define @t103 () (not (forall @t41 (or @t102 @t91)))) % 0.40/0.61 (define @t104 () (or @t103 @t101 @t99)) % 0.40/0.61 (define @t105 () (@list @t100 @t97)) % 0.40/0.61 (define @t106 () (forall @t105 @t104)) % 0.40/0.61 (define @t107 () (@quantifiers_skolemize @t106 0)) % 0.40/0.61 (define @t108 () (forall @t41 (or (not (tptp.rel_k @t107 @t38)) @t91))) % 0.40/0.61 (define @t109 () (@quantifiers_skolemize @t106 1)) % 0.40/0.61 (define @t110 () (forall @t98 (or (not (tptp.rel_k @t109 @t94)) @t96))) % 0.40/0.61 (define @t111 () (not @t110)) % 0.40/0.61 (define @t112 () (tptp.rel_k @t107 @t109)) % 0.40/0.61 (define @t113 () (not @t112)) % 0.40/0.61 (define @t114 () (not @t108)) % 0.40/0.61 (define @t115 () (or @t114 @t113 @t111)) % 0.40/0.61 (define @t116 () (forall @t89 (or (not (tptp.rel_k @t109 @t86)) @t88))) % 0.40/0.61 (define @t117 () (not @t116)) % 0.40/0.61 (define @t118 () (or @t113 @t117)) % 0.40/0.61 (define @t119 () (not @t115)) % 0.40/0.61 (define @t120 () (not @t106)) % 0.40/0.61 (define @t121 () (@list false)) % 0.40/0.61 (define @t122 () (@var "BOUND_VARIABLE_8722" $$unsorted)) % 0.40/0.61 (define @t123 () (@var "BOUND_VARIABLE_8721" $$unsorted)) % 0.40/0.61 (define @t124 () (@var "BOUND_VARIABLE_8717" $$unsorted)) % 0.40/0.61 (define @t125 () (@var "BOUND_VARIABLE_8716" $$unsorted)) % 0.40/0.61 (define @t126 () (@var "BOUND_VARIABLE_8720" $$unsorted)) % 0.40/0.61 (define @t127 () (@var "BOUND_VARIABLE_8719" $$unsorted)) % 0.40/0.61 (define @t128 () (@var "BOUND_VARIABLE_8718" $$unsorted)) % 0.40/0.61 (define @t129 () (@list @t125 @t124 @t128 @t127 @t126 @t123 @t122)) % 0.40/0.61 (define @t130 () (@var "BOUND_VARIABLE_8640" $$unsorted)) % 0.40/0.61 (define @t131 () (@var "BOUND_VARIABLE_8612" $$unsorted)) % 0.40/0.61 (define @t132 () (not (forall @t89 (or (not (tptp.rel_k @t130 @t86)) @t88)))) % 0.40/0.61 (define @t133 () (not (tptp.rel_k @t131 @t130))) % 0.40/0.61 (define @t134 () (not (forall @t98 (or (not (tptp.rel_k @t38 @t94)) @t96)))) % 0.40/0.61 (define @t135 () (not (tptp.rel_k @t131 @t38))) % 0.40/0.61 (define @t136 () (not (forall @t41 (or @t135 @t134)))) % 0.40/0.61 (define @t137 () (or @t136 @t133 @t132)) % 0.40/0.61 (define @t138 () (@list @t131 @t130)) % 0.40/0.61 (define @t139 () (forall @t138 @t137)) % 0.40/0.61 (define @t140 () (or @t133 @t132)) % 0.40/0.61 (define @t141 () (or @t140 @t136)) % 0.40/0.61 (define @t142 () (forall @t138 @t141)) % 0.40/0.61 (define @t143 () (@list @t130)) % 0.40/0.61 (define @t144 () (forall @t143 @t141)) % 0.40/0.61 (define @t145 () (@list @t131)) % 0.40/0.61 (define @t146 () (forall @t143 @t140)) % 0.40/0.61 (define @t147 () (@list @t38)) % 0.40/0.61 (define @t148 () (or @t146 @t136)) % 0.40/0.61 (define @t149 () (forall @t145 (or (forall @t41 (or @t135 @t91)) @t136))) % 0.40/0.61 (define @t150 () (or @t101 @t99)) % 0.40/0.61 (define @t151 () (or @t150 @t103)) % 0.40/0.61 (define @t152 () (forall @t105 @t151)) % 0.40/0.61 (define @t153 () (@list @t97)) % 0.40/0.61 (define @t154 () (forall @t153 @t151)) % 0.40/0.61 (define @t155 () (@list @t100)) % 0.40/0.61 (define @t156 () (forall @t153 @t150)) % 0.40/0.61 (define @t157 () (or @t156 @t103)) % 0.40/0.61 (define @t158 () (forall @t155 (or (forall @t41 (or @t102 @t134)) @t103))) % 0.40/0.61 (define @t159 () (tptp.rel_k @t4 @t38)) % 0.40/0.61 (define @t160 () (not @t159)) % 0.40/0.61 (define @t161 () (forall @t41 (or @t160 @t134))) % 0.40/0.61 (define @t162 () (not @t161)) % 0.40/0.61 (define @t163 () (forall @t41 (or @t160 @t91))) % 0.40/0.61 (define @t164 () (or @t163 @t162)) % 0.40/0.61 (define @t165 () (forall @t36 @t164)) % 0.40/0.61 (define @t166 () (@list @t4)) % 0.40/0.61 (define @t167 () (or @t161 (not @t163))) % 0.40/0.61 (define @t168 () (forall @t36 @t167)) % 0.40/0.61 (define @t169 () (and @t168 @t165)) % 0.40/0.61 (define @t170 () (not @t164)) % 0.40/0.61 (define @t171 () (not @t167)) % 0.40/0.61 (define @t172 () (not (or @t171 @t170))) % 0.40/0.61 (define @t173 () (not (tptp.rel_k @t17 @t38))) % 0.40/0.61 (define @t174 () (forall @t41 (or @t173 @t134))) % 0.40/0.61 (define @t175 () (not @t174)) % 0.40/0.61 (define @t176 () (forall @t41 (or @t173 @t91))) % 0.40/0.61 (define @t177 () (not @t176)) % 0.40/0.61 (define @t178 () (@list @t17)) % 0.40/0.61 (define @t179 () (lambda @t178 (not (or (not (or @t174 @t177)) (not (or @t176 @t175)))))) % 0.40/0.61 (define @t180 () (_ @t179 @t4)) % 0.40/0.61 (define @t181 () (forall @t36 @t180)) % 0.40/0.61 (define @t182 () (_ @t9 @t4)) % 0.40/0.61 (define @t183 () (lambda @t72 (forall @t36 @t182))) % 0.40/0.61 (define @t184 () (lambda @t178 @t177)) % 0.40/0.61 (define @t185 () (_ @t184 @t17)) % 0.40/0.61 (define @t186 () (not @t185)) % 0.40/0.61 (define @t187 () (or @t186 @t175)) % 0.40/0.61 (define @t188 () (not @t187)) % 0.40/0.61 (define @t189 () (or @t174 @t185)) % 0.40/0.61 (define @t190 () (not @t189)) % 0.40/0.61 (define @t191 () (or @t190 @t188)) % 0.40/0.61 (define @t192 () (not @t191)) % 0.40/0.61 (define @t193 () (lambda @t178 @t192)) % 0.40/0.61 (define @t194 () (_ @t14 @t17)) % 0.40/0.61 (define @t195 () (not @t194)) % 0.40/0.61 (define @t196 () (@list @t14 @t17)) % 0.40/0.61 (define @t197 () (not (forall @t87 (or (not (tptp.rel_k @t38 @t84)) @t85)))) % 0.40/0.61 (define @t198 () (forall @t41 (or @t160 @t197))) % 0.40/0.61 (define @t199 () (lambda @t36 @t198)) % 0.40/0.61 (define @t200 () (not (_ @t199 @t38))) % 0.40/0.61 (define @t201 () (or @t173 @t200)) % 0.40/0.61 (define @t202 () (forall @t41 @t201)) % 0.40/0.61 (define @t203 () (not @t202)) % 0.40/0.61 (define @t204 () (lambda @t178 @t203)) % 0.40/0.61 (define @t205 () (_ @t9 @t38)) % 0.40/0.61 (define @t206 () (not @t205)) % 0.40/0.61 (define @t207 () (not (forall @t41 (or @t173 @t206)))) % 0.40/0.61 (define @t208 () (lambda @t82 @t207)) % 0.40/0.61 (define @t209 () (tptp.p @t38)) % 0.40/0.61 (define @t210 () (forall @t41 (or @t173 @t209))) % 0.40/0.61 (define @t211 () (not @t210)) % 0.40/0.61 (define @t212 () (lambda @t178 @t211)) % 0.40/0.61 (define @t213 () (or @t160 (_ @t212 @t38))) % 0.40/0.61 (define @t214 () (forall @t41 @t213)) % 0.40/0.61 (define @t215 () (lambda @t36 @t214)) % 0.40/0.61 (define @t216 () (lambda @t12 (forall @t41 (or @t160 @t205)))) % 0.40/0.61 (define @t217 () (_ tptp.p @t38)) % 0.40/0.61 (define @t218 () (or @t173 @t217)) % 0.40/0.61 (define @t219 () (lambda @t36 (not (_ tptp.p @t4)))) % 0.40/0.61 (define @t220 () (_ @t219 @t38)) % 0.40/0.61 (define @t221 () (not @t220)) % 0.40/0.61 (define @t222 () (or @t173 @t221)) % 0.40/0.61 (define @t223 () (forall @t41 @t222)) % 0.40/0.61 (define @t224 () (not @t223)) % 0.40/0.61 (define @t225 () (lambda @t178 @t224)) % 0.40/0.61 (define @t226 () (_ @t13 tptp.p)) % 0.40/0.61 (define @t227 () (lambda @t36 @t162)) % 0.40/0.61 (define @t228 () (_ @t227 @t17)) % 0.40/0.61 (define @t229 () (or @t195 @t228)) % 0.40/0.61 (define @t230 () (not @t229)) % 0.40/0.61 (define @t231 () (not @t228)) % 0.40/0.61 (define @t232 () (or @t231 @t194)) % 0.40/0.61 (define @t233 () (not @t232)) % 0.40/0.61 (define @t234 () (or @t233 @t230)) % 0.40/0.61 (define @t235 () (not @t234)) % 0.40/0.61 (define @t236 () (lambda @t196 @t235)) % 0.40/0.61 (define @t237 () (_ @t9 @t17)) % 0.40/0.61 (define @t238 () (or @t195 @t237)) % 0.40/0.61 (define @t239 () (not @t237)) % 0.40/0.61 (define @t240 () (or @t239 @t194)) % 0.40/0.61 (define @t241 () (not @t240)) % 0.40/0.61 (define @t242 () (not (or @t241 (not @t238)))) % 0.40/0.61 (define @t243 () (lambda @t21 @t242)) % 0.40/0.61 (define @t244 () (lambda @t36 @t161)) % 0.40/0.61 (define @t245 () (_ @t244 @t4)) % 0.40/0.61 (define @t246 () (not @t245)) % 0.40/0.61 (define @t247 () (lambda @t36 @t246)) % 0.40/0.61 (define @t248 () (forall @t95 (or (not (tptp.rel_k @t38 @t92)) @t93))) % 0.40/0.61 (define @t249 () (forall @t41 (or @t173 (not @t248)))) % 0.40/0.61 (define @t250 () (not @t249)) % 0.40/0.61 (define @t251 () (lambda @t178 @t250)) % 0.40/0.61 (define @t252 () (or @t160 (_ @t251 @t38))) % 0.40/0.61 (define @t253 () (forall @t41 @t252)) % 0.40/0.61 (define @t254 () (lambda @t36 @t253)) % 0.40/0.61 (define @t255 () (forall @t41 (or @t160 @t209))) % 0.40/0.61 (define @t256 () (lambda @t36 @t255)) % 0.40/0.61 (define @t257 () (not (_ @t256 @t38))) % 0.40/0.61 (define @t258 () (or @t173 @t257)) % 0.40/0.61 (define @t259 () (forall @t41 @t258)) % 0.40/0.61 (define @t260 () (not @t259)) % 0.40/0.61 (define @t261 () (lambda @t178 @t260)) % 0.40/0.61 (define @t262 () (_ @t216 tptp.p)) % 0.40/0.61 (define @t263 () (forall @t41 (or @t160 @t206))) % 0.40/0.61 (define @t264 () (lambda @t36 @t263)) % 0.40/0.61 (define @t265 () (_ @t264 @t4)) % 0.40/0.61 (define @t266 () (not @t265)) % 0.40/0.61 (define @t267 () (lambda @t36 @t266)) % 0.40/0.61 (define @t268 () (not @t39)) % 0.40/0.61 (define @t269 () (or @t160 @t268)) % 0.40/0.61 (define @t270 () (lambda @t36 @t11)) % 0.40/0.61 (define @t271 () (_ @t270 @t38)) % 0.40/0.61 (define @t272 () (or @t160 @t271)) % 0.40/0.61 (define @t273 () (forall @t41 @t272)) % 0.40/0.61 (define @t274 () (lambda @t36 @t273)) % 0.40/0.61 (define @t275 () (lambda @t178 @t238)) % 0.40/0.61 (define @t276 () (_ @t275 @t17)) % 0.40/0.61 (define @t277 () (not @t276)) % 0.40/0.61 (define @t278 () (or @t241 @t277)) % 0.40/0.61 (define @t279 () (not @t278)) % 0.40/0.61 (define @t280 () (lambda @t178 @t279)) % 0.40/0.61 (define @t281 () (@var "BOUND_VARIABLE_7581" (-> $$unsorted Bool))) % 0.40/0.61 (define @t282 () (not (_ @t281 @t17))) % 0.40/0.61 (define @t283 () (@list @t281 @t17)) % 0.40/0.61 (define @t284 () (@var "BOUND_VARIABLE_7601" (-> $$unsorted Bool))) % 0.40/0.61 (define @t285 () (_ @t284 @t17)) % 0.40/0.61 (define @t286 () (lambda (@list @t284 @t17) (or @t195 @t285))) % 0.40/0.61 (define @t287 () (lambda @t21 @t240)) % 0.40/0.61 (define @t288 () (@list @t14)) % 0.40/0.61 (define @t289 () (lambda @t178 @t240)) % 0.40/0.61 (define @t290 () (_ @t289 @t17)) % 0.40/0.61 (define @t291 () (not @t290)) % 0.40/0.61 (define @t292 () (or @t291 @t282)) % 0.40/0.61 (define @t293 () (not @t292)) % 0.40/0.61 (define @t294 () (lambda @t283 @t293)) % 0.40/0.61 (define @t295 () (not (or @t239 @t195))) % 0.40/0.61 (define @t296 () (lambda @t21 @t295)) % 0.40/0.61 (define @t297 () (lambda @t196 @t240)) % 0.40/0.61 (define @t298 () (or @t11 @t15)) % 0.40/0.61 (define @t299 () (lambda @t36 @t298)) % 0.40/0.61 (define @t300 () (@list @t14 @t4)) % 0.40/0.61 (define @t301 () (lambda @t300 @t298)) % 0.40/0.61 (define @t302 () (_ @t270 @t4)) % 0.40/0.61 (define @t303 () (or @t302 @t15)) % 0.40/0.61 (define @t304 () (lambda @t300 @t303)) % 0.40/0.61 (define @t305 () (not @t15)) % 0.40/0.61 (define @t306 () (or @t11 @t305)) % 0.40/0.61 (define @t307 () (lambda @t36 @t306)) % 0.40/0.61 (define @t308 () (_ @t307 @t4)) % 0.40/0.61 (define @t309 () (not @t308)) % 0.40/0.61 (define @t310 () (lambda @t36 @t309)) % 0.40/0.61 (define @t311 () (lambda @t36 @t305)) % 0.40/0.61 (define @t312 () (_ @t311 @t4)) % 0.40/0.61 (define @t313 () (or @t11 @t312)) % 0.40/0.61 (define @t314 () (lambda @t36 @t313)) % 0.40/0.61 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.40/0.61 (assume @p2 @t1) % 0.40/0.61 (assume @p3 true) % 0.40/0.61 (step @p4 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.40/0.61 (step @p5 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.40/0.61 (step @p6 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.40/0.61 (step @p7 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.40/0.61 (step @p8 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.40/0.61 (step @p9 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.40/0.61 (step @p10 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.40/0.61 (step @p11 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.40/0.61 (step @p12 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.40/0.61 (step @p13 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.40/0.61 (step @p14 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.40/0.61 (step @p15 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.40/0.61 (step @p16 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.40/0.61 (step @p17 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.40/0.61 (step @p18 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.40/0.61 (step @p19 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.40/0.61 (step @p20 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.40/0.61 (step @p21 (= tptp.msymmetric @t52) :rule refl :args (@t52)) % 0.40/0.61 (step @p22 (= tptp.mserial @t54) :rule refl :args (@t54)) % 0.40/0.61 (step @p23 (= tptp.mtransitive @t59) :rule refl :args (@t59)) % 0.40/0.61 (step @p24 (= tptp.meuclidean @t61) :rule refl :args (@t61)) % 0.40/0.61 (step @p25 (= tptp.mpartially_functional @t63) :rule refl :args (@t63)) % 0.40/0.61 (step @p26 (= tptp.mfunctional @t65) :rule refl :args (@t65)) % 0.40/0.61 (step @p27 (= tptp.mweakly_dense @t68) :rule refl :args (@t68)) % 0.40/0.61 (step @p28 (= tptp.mweakly_connected @t69) :rule refl :args (@t69)) % 0.40/0.61 (step @p29 (= tptp.mweakly_directed @t70) :rule refl :args (@t70)) % 0.40/0.61 (step @p30 (= tptp.mvalid @t73) :rule refl :args (@t73)) % 0.40/0.61 (step @p31 (= tptp.minvalid @t74) :rule refl :args (@t74)) % 0.40/0.61 (step @p32 (= tptp.msatisfiable @t75) :rule refl :args (@t75)) % 0.40/0.61 (step @p33 (= tptp.mcountersatisfiable @t76) :rule refl :args (@t76)) % 0.40/0.61 (step @p34 (= tptp.mbox_k @t81) :rule refl :args (@t81)) % 0.40/0.61 (step @p35 (= tptp.mdia_k @t83) :rule refl :args (@t83)) % 0.40/0.61 (step @p36 :rule bool-double-not-elim :args (@t108)) % 0.40/0.61 (step @p37 :rule refl :args (@t115)) % 0.40/0.61 (step @p38 :rule nary_cong :premises (@p37 @p36) :args ((or @t115 (not @t114)))) % 0.40/0.61 (step @p39 :rule cnf_or_neg :args (@t115 0)) % 0.40/0.61 (step @p40 :rule eq_resolve :premises (@p39 @p38)) % 0.40/0.61 (step @p41 :rule reordering :premises (@p40) :args ((or @t108 @t115))) % 0.40/0.61 (step @p42 :rule bool-double-not-elim :args (@t112)) % 0.40/0.61 (step @p43 :rule nary_cong :premises (@p37 @p42) :args ((or @t115 (not @t113)))) % 0.40/0.61 (step @p44 :rule cnf_or_neg :args (@t115 1)) % 0.40/0.61 (step @p45 :rule eq_resolve :premises (@p44 @p43)) % 0.40/0.61 (step @p46 :rule reordering :premises (@p45) :args ((or @t112 @t115))) % 0.40/0.61 (step @p47 :rule bool-double-not-elim :args (@t110)) % 0.40/0.61 (step @p48 :rule nary_cong :premises (@p37 @p47) :args ((or @t115 (not @t111)))) % 0.40/0.61 (step @p49 :rule cnf_or_neg :args (@t115 2)) % 0.40/0.61 (step @p50 :rule eq_resolve :premises (@p49 @p48)) % 0.40/0.61 (step @p51 :rule reordering :premises (@p50) :args ((or @t110 @t115))) % 0.40/0.61 (step @p52 :rule alpha_equiv :args (@t110 (@list @t94 @t92) (@list @t86 @t84))) % 0.40/0.61 (step @p53 :rule equiv_elim1 :premises (@p52)) % 0.40/0.61 (assume-push @p421 @t108) % 0.40/0.61 (step @p55 :rule instantiate :premises (@p421) :args ((@list @t109))) % 0.40/0.61 (step-pop @p422 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@t262)))) (_ @t208 (_ @t216 (_ @t208 @t226)))))))) % 0.40/0.61 (step @p250 :rule refl :args (tptp.p)) % 0.40/0.61 (step @p251 :rule ho_cong :premises (@p6 @p250)) % 0.40/0.61 (step @p252 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t263)) @t17) @t207))) % 0.40/0.61 (step @p253 :rule refl :args (@t17)) % 0.40/0.61 (step @p254 :rule beta-reduce :args ((= @t265 @t263))) % 0.40/0.61 (step @p255 :rule cong :premises (@p254) :args (@t266)) % 0.40/0.61 (step @p256 :rule cong :premises (@p255) :args (@t267)) % 0.40/0.61 (step @p257 :rule beta-reduce :args ((= (_ @t13 @t264) @t267))) % 0.40/0.61 (step @p258 :rule trans :premises (@p257 @p256)) % 0.40/0.61 (step @p259 :rule refl :args (@t205)) % 0.40/0.61 (step @p260 :rule refl :args (@t39)) % 0.40/0.61 (step @p261 :rule cong :premises (@p260 @p259) :args ((= @t39 @t205))) % 0.40/0.61 (step @p262 :rule symm :premises (@p261)) % 0.40/0.61 (step @p263 :rule eq_resolve :premises (@p260 @p262)) % 0.40/0.61 (step @p264 :rule cong :premises (@p263) :args (@t268)) % 0.40/0.61 (step @p265 :rule refl :args (@t160)) % 0.40/0.61 (step @p266 :rule nary_cong :premises (@p265 @p264) :args (@t269)) % 0.40/0.61 (step @p267 :rule cong :premises (@p266) :args ((forall @t41 @t269))) % 0.40/0.61 (step @p268 :rule beta-reduce :args ((= @t271 @t268))) % 0.40/0.61 (step @p269 :rule nary_cong :premises (@p156 @p268) :args (@t272)) % 0.40/0.61 (step @p270 :rule cong :premises (@p269) :args (@t273)) % 0.40/0.61 (step @p271 :rule trans :premises (@p270 @p267)) % 0.40/0.61 (step @p272 :rule cong :premises (@p271) :args (@t274)) % 0.40/0.61 (step @p273 :rule beta-reduce :args ((= (_ @t216 @t270) @t274))) % 0.40/0.61 (step @p274 :rule trans :premises (@p273 @p272)) % 0.40/0.61 (step @p275 :rule beta-reduce :args ((= (_ @t13 @t9) @t270))) % 0.40/0.61 (step @p276 :rule ho_cong :premises (@p185 @p275)) % 0.40/0.61 (step @p277 :rule trans :premises (@p276 @p274)) % 0.40/0.61 (step @p278 :rule ho_cong :premises (@p238 @p277)) % 0.40/0.61 (step @p279 :rule trans :premises (@p278 @p258)) % 0.40/0.61 (step @p280 :rule ho_cong :premises (@p279 @p253)) % 0.40/0.61 (step @p281 :rule trans :premises (@p280 @p252)) % 0.40/0.61 (step @p282 :rule refl :args (@t9)) % 0.40/0.61 (step @p283 :rule ho_cong :premises (@p6 @p282)) % 0.40/0.61 (step @p284 :rule refl :args (@t159)) % 0.40/0.61 (step @p285 :rule refl :args (@t77)) % 0.40/0.61 (step @p286 :rule cong :premises (@p285 @p284) :args ((= @t77 @t159))) % 0.40/0.61 (step @p287 :rule symm :premises (@p286)) % 0.40/0.61 (step @p288 :rule eq_resolve :premises (@p285 @p287)) % 0.40/0.61 (step @p289 :rule cong :premises (@p288) :args (@t78)) % 0.40/0.61 (step @p290 :rule nary_cong :premises (@p289 @p263) :args (@t79)) % 0.40/0.61 (step @p291 :rule cong :premises (@p290) :args (@t80)) % 0.40/0.61 (step @p292 :rule cong :premises (@p291) :args (@t81)) % 0.40/0.61 (step @p293 :rule trans :premises (@p34 @p292)) % 0.40/0.61 (step @p294 :rule ho_cong :premises (@p293 @p283)) % 0.40/0.61 (step @p295 :rule ho_cong :premises (@p6 @p294)) % 0.40/0.61 (step @p296 :rule ho_cong :premises (@p295 @p253)) % 0.40/0.61 (step @p297 :rule trans :premises (@p296 @p281)) % 0.40/0.61 (step @p298 :rule cong :premises (@p297) :args (@t83)) % 0.40/0.61 (step @p299 :rule trans :premises (@p35 @p298)) % 0.40/0.61 (step @p300 :rule ho_cong :premises (@p299 @p251)) % 0.40/0.61 (step @p301 :rule ho_cong :premises (@p293 @p300)) % 0.40/0.61 (step @p302 :rule ho_cong :premises (@p299 @p301)) % 0.40/0.61 (step @p303 :rule ho_cong :premises (@p293 @p250)) % 0.40/0.61 (step @p304 :rule ho_cong :premises (@p299 @p303)) % 0.40/0.61 (step @p305 :rule ho_cong :premises (@p293 @p304)) % 0.40/0.61 (step @p306 :rule ho_cong :premises (@p6 @p305)) % 0.40/0.61 (step @p307 :rule beta-reduce :args ((= (_ (lambda @t178 @t242) @t17) @t242))) % 0.40/0.61 (step @p308 :rule beta-reduce :args ((= @t276 @t238))) % 0.40/0.61 (step @p309 :rule cong :premises (@p308) :args (@t277)) % 0.40/0.61 (step @p310 :rule refl :args (@t241)) % 0.40/0.61 (step @p311 :rule nary_cong :premises (@p310 @p309) :args (@t278)) % 0.40/0.61 (step @p312 :rule cong :premises (@p311) :args (@t279)) % 0.40/0.61 (step @p313 :rule cong :premises (@p312) :args (@t280)) % 0.40/0.61 (step @p314 :rule beta-reduce :args ((= (_ (lambda @t283 (not (or @t241 @t282))) @t275) @t280))) % 0.40/0.61 (step @p315 :rule trans :premises (@p314 @p313)) % 0.40/0.61 (step @p316 :rule beta-reduce :args ((= (_ @t286 @t9) @t275))) % 0.40/0.61 (step @p317 :rule beta-reduce :args ((= (_ (lambda (@list @t9 @t284 @t17) (or @t239 @t285)) @t14) @t286))) % 0.40/0.61 (step @p318 :rule refl :args (@t14)) % 0.40/0.61 (step @p319 :rule alpha_equiv :args (@t287 @t288 (@list @t284))) % 0.40/0.61 (step @p320 :rule ho_cong :premises (@p319 @p318)) % 0.40/0.61 (step @p321 :rule trans :premises (@p320 @p317)) % 0.40/0.61 (step @p322 :rule ho_cong :premises (@p321 @p282)) % 0.40/0.61 (step @p323 :rule trans :premises (@p322 @p316)) % 0.40/0.61 (step @p324 :rule refl :args (@t282)) % 0.40/0.61 (step @p325 :rule beta-reduce :args ((= @t290 @t240))) % 0.40/0.61 (step @p326 :rule cong :premises (@p325) :args (@t291)) % 0.40/0.61 (step @p327 :rule nary_cong :premises (@p326 @p324) :args (@t292)) % 0.40/0.61 (step @p328 :rule cong :premises (@p327) :args (@t293)) % 0.40/0.61 (step @p329 :rule cong :premises (@p328) :args (@t294)) % 0.40/0.61 (step @p330 :rule beta-reduce :args ((= (_ (lambda (@list @t9 @t281 @t17) (not (or @t239 @t282))) @t289) @t294))) % 0.40/0.61 (step @p331 :rule trans :premises (@p330 @p329)) % 0.40/0.61 (step @p332 :rule refl :args (@t289)) % 0.40/0.61 (step @p333 :rule alpha_equiv :args (@t296 @t288 (@list @t281))) % 0.40/0.61 (step @p334 :rule ho_cong :premises (@p333 @p332)) % 0.40/0.61 (step @p335 :rule trans :premises (@p334 @p331)) % 0.40/0.61 (step @p336 :rule beta-reduce :args ((= (_ @t297 @t14) @t289))) % 0.40/0.61 (step @p337 :rule refl :args (@t14)) % 0.40/0.61 (step @p338 :rule beta-reduce :args ((= (_ @t287 @t9) @t297))) % 0.40/0.61 (step @p339 :rule ho_cong :premises (@p338 @p337)) % 0.40/0.61 (step @p340 :rule trans :premises (@p339 @p336)) % 0.40/0.61 (step @p341 :rule refl :args (@t296)) % 0.40/0.61 (step @p342 :rule ho_cong :premises (@p341 @p340)) % 0.40/0.61 (step @p343 :rule trans :premises (@p342 @p335)) % 0.40/0.61 (step @p344 :rule ho_cong :premises (@p343 @p323)) % 0.40/0.61 (step @p345 :rule trans :premises (@p344 @p315)) % 0.40/0.61 (step @p346 :rule ho_cong :premises (@p345 @p253)) % 0.40/0.61 (step @p347 :rule trans :premises (@p346 @p307)) % 0.40/0.61 (step @p348 :rule beta-reduce :args ((= (_ @t299 @t17) @t240))) % 0.40/0.61 (step @p349 :rule beta-reduce :args ((= (_ @t301 @t14) @t299))) % 0.40/0.61 (step @p350 :rule refl :args (@t15)) % 0.40/0.61 (step @p351 :rule beta-reduce :args ((= @t302 @t11))) % 0.40/0.61 (step @p352 :rule nary_cong :premises (@p351 @p350) :args (@t303)) % 0.40/0.61 (step @p353 :rule cong :premises (@p352) :args (@t304)) % 0.40/0.61 (step @p354 :rule beta-reduce :args ((= (_ @t16 @t270) @t304))) % 0.40/0.61 (step @p355 :rule trans :premises (@p354 @p353)) % 0.40/0.61 (step @p356 :rule refl :args (@t16)) % 0.40/0.61 (step @p357 :rule ho_cong :premises (@p356 @p275)) % 0.40/0.61 (step @p358 :rule trans :premises (@p357 @p355)) % 0.40/0.61 (step @p359 :rule ho_cong :premises (@p358 @p337)) % 0.40/0.61 (step @p360 :rule trans :premises (@p359 @p349)) % 0.40/0.61 (step @p361 :rule ho_cong :premises (@p360 @p253)) % 0.40/0.61 (step @p362 :rule trans :premises (@p361 @p348)) % 0.40/0.61 (step @p363 :rule ho_cong :premises (@p7 @p283)) % 0.40/0.61 (step @p364 :rule ho_cong :premises (@p363 @p337)) % 0.40/0.61 (step @p365 :rule ho_cong :premises (@p364 @p253)) % 0.40/0.61 (step @p366 :rule trans :premises (@p365 @p362)) % 0.40/0.61 (step @p367 :rule cong :premises (@p366) :args (@t23)) % 0.40/0.61 (step @p368 :rule trans :premises (@p9 @p367)) % 0.40/0.61 (step @p369 :rule ho_cong :premises (@p368 @p337)) % 0.40/0.61 (step @p370 :rule ho_cong :premises (@p369 @p282)) % 0.40/0.61 (step @p371 :rule ho_cong :premises (@p368 @p282)) % 0.40/0.61 (step @p372 :rule ho_cong :premises (@p371 @p337)) % 0.40/0.61 (step @p373 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t306)) @t17) @t295))) % 0.40/0.61 (step @p374 :rule beta-reduce :args ((= @t308 @t306))) % 0.40/0.61 (step @p375 :rule cong :premises (@p374) :args (@t309)) % 0.40/0.61 (step @p376 :rule cong :premises (@p375) :args (@t310)) % 0.40/0.61 (step @p377 :rule beta-reduce :args ((= (_ @t13 @t307) @t310))) % 0.40/0.61 (step @p378 :rule trans :premises (@p377 @p376)) % 0.40/0.61 (step @p379 :rule beta-reduce :args ((= @t312 @t305))) % 0.40/0.61 (step @p380 :rule refl :args (@t11)) % 0.40/0.61 (step @p381 :rule nary_cong :premises (@p380 @p379) :args (@t313)) % 0.40/0.61 (step @p382 :rule cong :premises (@p381) :args (@t314)) % 0.40/0.61 (step @p383 :rule beta-reduce :args ((= (_ @t301 @t311) @t314))) % 0.40/0.61 (step @p384 :rule trans :premises (@p383 @p382)) % 0.40/0.61 (step @p385 :rule beta-reduce :args ((= (_ @t13 @t14) @t311))) % 0.40/0.61 (step @p386 :rule ho_cong :premises (@p358 @p385)) % 0.40/0.61 (step @p387 :rule trans :premises (@p386 @p384)) % 0.40/0.61 (step @p388 :rule ho_cong :premises (@p238 @p387)) % 0.40/0.61 (step @p389 :rule trans :premises (@p388 @p378)) % 0.40/0.61 (step @p390 :rule ho_cong :premises (@p389 @p253)) % 0.40/0.61 (step @p391 :rule trans :premises (@p390 @p373)) % 0.40/0.61 (step @p392 :rule ho_cong :premises (@p6 @p337)) % 0.40/0.61 (step @p393 :rule ho_cong :premises (@p363 @p392)) % 0.40/0.61 (step @p394 :rule ho_cong :premises (@p6 @p393)) % 0.40/0.61 (step @p395 :rule ho_cong :premises (@p394 @p253)) % 0.40/0.61 (step @p396 :rule trans :premises (@p395 @p391)) % 0.40/0.61 (step @p397 :rule cong :premises (@p396) :args (@t22)) % 0.40/0.61 (step @p398 :rule trans :premises (@p8 @p397)) % 0.40/0.61 (step @p399 :rule ho_cong :premises (@p398 @p372)) % 0.40/0.61 (step @p400 :rule ho_cong :premises (@p399 @p370)) % 0.40/0.61 (step @p401 :rule ho_cong :premises (@p400 @p253)) % 0.40/0.61 (step @p402 :rule trans :premises (@p401 @p347)) % 0.40/0.61 (step @p403 :rule cong :premises (@p402) :args (@t25)) % 0.40/0.61 (step @p404 :rule trans :premises (@p11 @p403)) % 0.40/0.61 (step @p405 :rule ho_cong :premises (@p404 @p306)) % 0.40/0.61 (step @p406 :rule ho_cong :premises (@p405 @p302)) % 0.40/0.61 (step @p407 :rule refl :args (@t182)) % 0.40/0.61 (step @p408 :rule refl :args (@t10)) % 0.40/0.61 (step @p409 :rule cong :premises (@p408 @p407) :args ((= @t10 @t182))) % 0.40/0.61 (step @p410 :rule symm :premises (@p409)) % 0.40/0.61 (step @p411 :rule eq_resolve :premises (@p408 @p410)) % 0.40/0.61 (step @p412 :rule cong :premises (@p411) :args (@t71)) % 0.40/0.61 (step @p413 :rule cong :premises (@p412) :args (@t73)) % 0.40/0.61 (step @p414 :rule trans :premises (@p30 @p413)) % 0.40/0.61 (step @p415 :rule ho_cong :premises (@p414 @p406)) % 0.40/0.61 (step @p416 :rule cong :premises (@p415) :args (@t1)) % 0.40/0.61 (step @p417 :rule trans :premises (@p416 @p249)) % 0.40/0.61 (step @p418 :rule eq_resolve :premises (@p2 @p417)) % 0.40/0.61 (step @p419 :rule not_and :premises (@p418)) % 0.40/0.61 (step @p420 false :rule chain_m_resolution :premises (@p419 @p77 @p71) :args (false (@list false false) (@list @t139 @t106))) % 0.40/0.61 ) % 0.40/0.61 % SZS output end Proof % 0.40/0.61 % cvc5 exiting %------------------------------------------------------------------------------