%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO396^1 : 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 : n007.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 0.38s 0.60s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO396^1 : 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 % 0.16/0.34 % Computer : n007.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Wed Jun 3 00:05:56 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.51 %----Proving TH0 % 0.38/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.60 % SZS status Theorem % 0.38/0.60 % SZS output start Proof % 0.38/0.60 ( % 0.38/0.60 (declare-sort $$unsorted 0) % 0.38/0.60 (declare-sort tptp.mu 0) % 0.38/0.60 (declare-const tptp.rel_k (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.p (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.38/0.60 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.38/0.60 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.38/0.60 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.38/0.60 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.38/0.60 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.60 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.38/0.60 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.60 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.38/0.60 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.60 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.60 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.38/0.60 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.38/0.60 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.38/0.60 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.38/0.60 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.38/0.60 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.38/0.60 (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)))))))) % 0.38/0.60 (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)))))))) % 0.38/0.60 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.38/0.60 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 0.38/0.60 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.38/0.60 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 0.38/0.60 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.38/0.60 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 0.38/0.60 (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))))))))))))) % 0.38/0.60 (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)))))) % 0.38/0.60 (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))))))) % 0.38/0.60 (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)))))) % 0.38/0.60 (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))))))) % 0.38/0.60 (define tptp.mbox_k () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_k _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.38/0.60 (define tptp.mdia_k () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_k (_ tptp.mnot _let_2))) _let_1))))) % 0.38/0.60 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mequiv (_ tptp.mbox_k (_ (_ tptp.mimplies tptp.p) (_ tptp.mnot tptp.p)))) (_ tptp.mnot (_ tptp.mdia_k tptp.p)))))) % 0.38/0.60 (define @t2 () (@var "Y" tptp.mu)) % 0.38/0.60 (define @t3 () (@var "X" tptp.mu)) % 0.38/0.60 (define @t4 () (@var "W" $$unsorted)) % 0.38/0.60 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.38/0.60 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.60 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.60 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.38/0.60 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.38/0.60 (define @t10 () (_ @t9 @t4)) % 0.38/0.60 (define @t11 () (not @t10)) % 0.38/0.60 (define @t12 () (@list @t9 @t4)) % 0.38/0.60 (define @t13 () (lambda @t12 @t11)) % 0.38/0.60 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.38/0.60 (define @t15 () (_ @t14 @t4)) % 0.38/0.60 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.38/0.60 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.38/0.60 (define @t18 () (_ tptp.mnot @t14)) % 0.38/0.60 (define @t19 () (_ tptp.mnot @t9)) % 0.38/0.60 (define @t20 () (_ tptp.mor @t19)) % 0.38/0.60 (define @t21 () (@list @t9 @t14 @t17)) % 0.38/0.60 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.38/0.60 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.38/0.60 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.38/0.60 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.38/0.60 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.38/0.60 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.38/0.60 (define @t28 () (_ @t27 @t3)) % 0.38/0.60 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.38/0.60 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.38/0.60 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.38/0.60 (define @t32 () (_ @t31 @t30)) % 0.38/0.60 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.38/0.60 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.38/0.60 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.38/0.60 (define @t36 () (@list @t4)) % 0.38/0.60 (define @t37 () (lambda @t36 true)) % 0.38/0.60 (define @t38 () (@var "V" $$unsorted)) % 0.38/0.60 (define @t39 () (_ @t9 @t38)) % 0.38/0.60 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.38/0.60 (define @t41 () (@list @t38)) % 0.38/0.60 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.38/0.60 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.38/0.60 (define @t44 () (@var "S" $$unsorted)) % 0.38/0.60 (define @t45 () (_ @t40 @t44)) % 0.38/0.60 (define @t46 () (@list @t44)) % 0.38/0.60 (define @t47 () (@list @t40)) % 0.38/0.60 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.38/0.60 (define @t49 () (@var "T" $$unsorted)) % 0.38/0.60 (define @t50 () (_ @t40 @t49)) % 0.38/0.60 (define @t51 () (_ @t45 @t49)) % 0.38/0.60 (define @t52 () (lambda @t47 (forall (@list @t44 @t49) (=> @t51 (_ @t50 @t44))))) % 0.38/0.60 (define @t53 () (@list @t49)) % 0.38/0.60 (define @t54 () (lambda @t47 (forall @t46 (exists @t53 @t51)))) % 0.38/0.60 (define @t55 () (@var "U" $$unsorted)) % 0.38/0.60 (define @t56 () (_ @t45 @t55)) % 0.38/0.60 (define @t57 () (_ @t50 @t55)) % 0.38/0.60 (define @t58 () (@list @t44 @t49 @t55)) % 0.38/0.60 (define @t59 () (lambda @t47 (forall @t58 (=> (and @t51 @t57) @t56)))) % 0.38/0.60 (define @t60 () (and @t51 @t56)) % 0.38/0.60 (define @t61 () (lambda @t47 (forall @t58 (=> @t60 @t57)))) % 0.38/0.60 (define @t62 () (= @t49 @t55)) % 0.38/0.60 (define @t63 () (lambda @t47 (forall @t58 (=> @t60 @t62)))) % 0.38/0.60 (define @t64 () (@list @t55)) % 0.38/0.60 (define @t65 () (lambda @t47 (forall @t46 (exists @t53 (and @t51 (forall @t64 (=> @t56 @t62))))))) % 0.38/0.60 (define @t66 () (_ @t40 @t55)) % 0.38/0.60 (define @t67 () (_ @t66 @t49)) % 0.38/0.60 (define @t68 () (lambda @t47 (forall @t58 (=> @t51 (exists @t64 (and @t56 @t67)))))) % 0.38/0.60 (define @t69 () (lambda @t47 (forall @t58 (=> @t60 (or @t57 @t62 @t67))))) % 0.38/0.60 (define @t70 () (lambda @t47 (forall @t58 (=> @t60 (exists @t41 (and (_ @t50 @t38) (_ @t66 @t38))))))) % 0.38/0.60 (define @t71 () (forall @t36 @t10)) % 0.38/0.60 (define @t72 () (@list @t9)) % 0.38/0.60 (define @t73 () (lambda @t72 @t71)) % 0.38/0.60 (define @t74 () (lambda @t72 (forall @t36 @t11))) % 0.38/0.60 (define @t75 () (lambda @t72 (exists @t36 @t10))) % 0.38/0.60 (define @t76 () (lambda @t72 (exists @t36 @t11))) % 0.38/0.60 (define @t77 () (_ (_ tptp.rel_k @t4) @t38)) % 0.38/0.60 (define @t78 () (not @t77)) % 0.38/0.60 (define @t79 () (or @t78 @t39)) % 0.38/0.60 (define @t80 () (forall @t41 @t79)) % 0.38/0.60 (define @t81 () (lambda @t12 @t80)) % 0.38/0.60 (define @t82 () (@list @t9 @t17)) % 0.38/0.60 (define @t83 () (lambda @t82 (_ (_ tptp.mnot (_ tptp.mbox_k @t19)) @t17))) % 0.38/0.60 (define @t84 () (tptp.p @t38)) % 0.38/0.60 (define @t85 () (not @t84)) % 0.38/0.60 (define @t86 () (tptp.rel_k @t4 @t38)) % 0.38/0.60 (define @t87 () (not @t86)) % 0.38/0.60 (define @t88 () (forall @t41 (or @t87 @t85))) % 0.38/0.60 (define @t89 () (not @t88)) % 0.38/0.60 (define @t90 () (or @t89 @t88)) % 0.38/0.60 (define @t91 () (not (tptp.rel_k @t17 @t38))) % 0.38/0.60 (define @t92 () (forall @t41 (or @t91 @t85))) % 0.38/0.60 (define @t93 () (not @t92)) % 0.38/0.60 (define @t94 () (or @t93 @t92)) % 0.38/0.60 (define @t95 () (@list @t17)) % 0.38/0.60 (define @t96 () (lambda @t95 @t94)) % 0.38/0.60 (define @t97 () (_ @t96 @t4)) % 0.38/0.60 (define @t98 () (forall @t36 @t97)) % 0.38/0.60 (define @t99 () (_ @t9 @t4)) % 0.38/0.60 (define @t100 () (lambda @t72 (forall @t36 @t99))) % 0.38/0.60 (define @t101 () (not @t94)) % 0.38/0.60 (define @t102 () (lambda @t36 @t88)) % 0.38/0.60 (define @t103 () (_ @t102 @t17)) % 0.38/0.60 (define @t104 () (not @t103)) % 0.38/0.60 (define @t105 () (or @t104 @t92)) % 0.38/0.60 (define @t106 () (not @t105)) % 0.38/0.60 (define @t107 () (or @t93 @t103)) % 0.38/0.60 (define @t108 () (not @t107)) % 0.38/0.60 (define @t109 () (or @t108 @t106)) % 0.38/0.60 (define @t110 () (not @t109)) % 0.38/0.60 (define @t111 () (lambda @t95 @t110)) % 0.38/0.60 (define @t112 () (_ @t14 @t17)) % 0.38/0.60 (define @t113 () (not @t112)) % 0.38/0.60 (define @t114 () (@list @t14 @t17)) % 0.38/0.60 (define @t115 () (lambda @t95 @t93)) % 0.38/0.60 (define @t116 () (_ @t115 @t4)) % 0.38/0.60 (define @t117 () (not @t116)) % 0.38/0.60 (define @t118 () (lambda @t36 @t117)) % 0.38/0.60 (define @t119 () (_ @t9 @t38)) % 0.38/0.60 (define @t120 () (not @t119)) % 0.38/0.60 (define @t121 () (not (forall @t41 (or @t91 @t120)))) % 0.38/0.60 (define @t122 () (_ (lambda @t82 @t121) tptp.p)) % 0.38/0.60 (define @t123 () (or @t113 @t103)) % 0.38/0.60 (define @t124 () (not @t123)) % 0.38/0.60 (define @t125 () (or @t104 @t112)) % 0.38/0.60 (define @t126 () (not @t125)) % 0.38/0.60 (define @t127 () (or @t126 @t124)) % 0.38/0.60 (define @t128 () (not @t127)) % 0.38/0.60 (define @t129 () (lambda @t114 @t128)) % 0.38/0.60 (define @t130 () (_ @t9 @t17)) % 0.38/0.60 (define @t131 () (or @t113 @t130)) % 0.38/0.60 (define @t132 () (not @t130)) % 0.38/0.60 (define @t133 () (or @t132 @t112)) % 0.38/0.60 (define @t134 () (not @t133)) % 0.38/0.60 (define @t135 () (not (or @t134 (not @t131)))) % 0.38/0.60 (define @t136 () (lambda @t21 @t135)) % 0.38/0.60 (define @t137 () (_ tptp.p @t38)) % 0.38/0.60 (define @t138 () (not @t137)) % 0.38/0.60 (define @t139 () (or @t87 @t138)) % 0.38/0.60 (define @t140 () (not (_ tptp.p @t17))) % 0.38/0.60 (define @t141 () (lambda @t95 @t140)) % 0.38/0.60 (define @t142 () (_ @t141 @t38)) % 0.38/0.60 (define @t143 () (or @t87 @t142)) % 0.38/0.60 (define @t144 () (forall @t41 @t143)) % 0.38/0.60 (define @t145 () (lambda @t36 @t144)) % 0.38/0.60 (define @t146 () (lambda @t12 (forall @t41 (or @t87 @t119)))) % 0.38/0.60 (define @t147 () (lambda @t36 (not (_ tptp.p @t4)))) % 0.38/0.60 (define @t148 () (_ @t147 @t17)) % 0.38/0.60 (define @t149 () (or @t140 @t148)) % 0.38/0.60 (define @t150 () (lambda @t95 @t149)) % 0.38/0.60 (define @t151 () (lambda @t114 (or @t140 @t112))) % 0.38/0.60 (define @t152 () (_ @t13 tptp.p)) % 0.38/0.60 (define @t153 () (lambda @t21 @t133)) % 0.38/0.60 (define @t154 () (_ @t153 tptp.p)) % 0.38/0.60 (define @t155 () (forall @t41 (or @t87 @t120))) % 0.38/0.60 (define @t156 () (lambda @t36 @t155)) % 0.38/0.60 (define @t157 () (_ @t156 @t4)) % 0.38/0.60 (define @t158 () (not @t157)) % 0.38/0.60 (define @t159 () (lambda @t36 @t158)) % 0.38/0.60 (define @t160 () (not @t39)) % 0.38/0.60 (define @t161 () (or @t87 @t160)) % 0.38/0.60 (define @t162 () (lambda @t36 @t11)) % 0.38/0.60 (define @t163 () (_ @t162 @t38)) % 0.38/0.60 (define @t164 () (or @t87 @t163)) % 0.38/0.60 (define @t165 () (forall @t41 @t164)) % 0.38/0.60 (define @t166 () (lambda @t36 @t165)) % 0.38/0.60 (define @t167 () (or @t11 @t15)) % 0.38/0.60 (define @t168 () (lambda @t36 @t167)) % 0.38/0.60 (define @t169 () (@list @t14 @t4)) % 0.38/0.60 (define @t170 () (lambda @t169 @t167)) % 0.38/0.60 (define @t171 () (_ @t162 @t4)) % 0.38/0.60 (define @t172 () (or @t171 @t15)) % 0.38/0.60 (define @t173 () (lambda @t169 @t172)) % 0.38/0.60 (define @t174 () (lambda @t95 @t131)) % 0.38/0.60 (define @t175 () (_ @t174 @t17)) % 0.38/0.60 (define @t176 () (not @t175)) % 0.38/0.60 (define @t177 () (or @t134 @t176)) % 0.38/0.60 (define @t178 () (not @t177)) % 0.38/0.60 (define @t179 () (lambda @t95 @t178)) % 0.38/0.60 (define @t180 () (@var "BOUND_VARIABLE_7581" (-> $$unsorted Bool))) % 0.38/0.60 (define @t181 () (not (_ @t180 @t17))) % 0.38/0.60 (define @t182 () (@list @t180 @t17)) % 0.38/0.60 (define @t183 () (@var "BOUND_VARIABLE_7601" (-> $$unsorted Bool))) % 0.38/0.60 (define @t184 () (_ @t183 @t17)) % 0.38/0.60 (define @t185 () (lambda (@list @t183 @t17) (or @t113 @t184))) % 0.38/0.60 (define @t186 () (@list @t14)) % 0.38/0.60 (define @t187 () (lambda @t95 @t133)) % 0.38/0.60 (define @t188 () (_ @t187 @t17)) % 0.38/0.60 (define @t189 () (not @t188)) % 0.38/0.60 (define @t190 () (or @t189 @t181)) % 0.38/0.60 (define @t191 () (not @t190)) % 0.38/0.60 (define @t192 () (lambda @t182 @t191)) % 0.38/0.60 (define @t193 () (not (or @t132 @t113))) % 0.38/0.60 (define @t194 () (lambda @t21 @t193)) % 0.38/0.60 (define @t195 () (lambda @t114 @t133)) % 0.38/0.60 (define @t196 () (not @t15)) % 0.38/0.60 (define @t197 () (or @t11 @t196)) % 0.38/0.60 (define @t198 () (lambda @t36 @t197)) % 0.38/0.60 (define @t199 () (_ @t198 @t4)) % 0.38/0.60 (define @t200 () (not @t199)) % 0.38/0.60 (define @t201 () (lambda @t36 @t200)) % 0.38/0.60 (define @t202 () (lambda @t36 @t196)) % 0.38/0.60 (define @t203 () (_ @t202 @t4)) % 0.38/0.60 (define @t204 () (or @t11 @t203)) % 0.38/0.60 (define @t205 () (lambda @t36 @t204)) % 0.38/0.60 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.38/0.60 (assume @p2 @t1) % 0.38/0.60 (assume @p3 true) % 0.38/0.60 (step @p4 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.38/0.60 (step @p5 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.38/0.60 (step @p6 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.38/0.60 (step @p7 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.38/0.60 (step @p8 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.38/0.60 (step @p9 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.38/0.60 (step @p10 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.38/0.60 (step @p11 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.38/0.60 (step @p12 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.38/0.60 (step @p13 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.38/0.60 (step @p14 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.38/0.60 (step @p15 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.38/0.60 (step @p16 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.38/0.60 (step @p17 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.38/0.60 (step @p18 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.38/0.60 (step @p19 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.38/0.60 (step @p20 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.38/0.60 (step @p21 (= tptp.msymmetric @t52) :rule refl :args (@t52)) % 0.38/0.60 (step @p22 (= tptp.mserial @t54) :rule refl :args (@t54)) % 0.38/0.60 (step @p23 (= tptp.mtransitive @t59) :rule refl :args (@t59)) % 0.38/0.60 (step @p24 (= tptp.meuclidean @t61) :rule refl :args (@t61)) % 0.38/0.60 (step @p25 (= tptp.mpartially_functional @t63) :rule refl :args (@t63)) % 0.38/0.60 (step @p26 (= tptp.mfunctional @t65) :rule refl :args (@t65)) % 0.38/0.60 (step @p27 (= tptp.mweakly_dense @t68) :rule refl :args (@t68)) % 0.38/0.60 (step @p28 (= tptp.mweakly_connected @t69) :rule refl :args (@t69)) % 0.38/0.60 (step @p29 (= tptp.mweakly_directed @t70) :rule refl :args (@t70)) % 0.38/0.60 (step @p30 (= tptp.mvalid @t73) :rule refl :args (@t73)) % 0.38/0.60 (step @p31 (= tptp.minvalid @t74) :rule refl :args (@t74)) % 0.38/0.60 (step @p32 (= tptp.msatisfiable @t75) :rule refl :args (@t75)) % 0.38/0.60 (step @p33 (= tptp.mcountersatisfiable @t76) :rule refl :args (@t76)) % 0.38/0.60 (step @p34 (= tptp.mbox_k @t81) :rule refl :args (@t81)) % 0.38/0.60 (step @p35 (= tptp.mdia_k @t83) :rule refl :args (@t83)) % 0.38/0.60 (step @p36 :rule evaluate :args ((not true))) % 0.38/0.60 (step @p37 :rule quant-unused-vars :args ((= (forall @t36 true) true))) % 0.38/0.60 (step @p38 :rule bool-or-taut2 :args (false @t88 false false)) % 0.38/0.60 (step @p39 :rule cong :premises (@p38) :args ((forall @t36 @t90))) % 0.38/0.60 (step @p40 :rule trans :premises (@p39 @p37)) % 0.38/0.60 (step @p41 :rule beta-reduce :args ((= @t97 @t90))) % 0.38/0.60 (step @p42 :rule cong :premises (@p41) :args (@t98)) % 0.38/0.60 (step @p43 :rule trans :premises (@p42 @p40)) % 0.38/0.60 (step @p44 :rule beta-reduce :args ((= (_ @t100 @t96) @t98))) % 0.38/0.60 (step @p45 :rule trans :premises (@p44 @p43)) % 0.38/0.60 (step @p46 :rule bool-double-not-elim :args (@t94)) % 0.38/0.60 (step @p47 :rule aci_norm :args ((= (or @t101 @t101) @t101))) % 0.38/0.60 (step @p48 :rule refl :args (@t92)) % 0.38/0.60 (step @p49 :rule beta-reduce :args ((= @t103 @t92))) % 0.38/0.60 (step @p50 :rule cong :premises (@p49) :args (@t104)) % 0.38/0.60 (step @p51 :rule nary_cong :premises (@p50 @p48) :args (@t105)) % 0.38/0.60 (step @p52 :rule cong :premises (@p51) :args (@t106)) % 0.38/0.60 (step @p53 :rule refl :args (@t93)) % 0.38/0.60 (step @p54 :rule nary_cong :premises (@p53 @p49) :args (@t107)) % 0.38/0.60 (step @p55 :rule cong :premises (@p54) :args (@t108)) % 0.38/0.60 (step @p56 :rule nary_cong :premises (@p55 @p52) :args (@t109)) % 0.38/0.60 (step @p57 :rule trans :premises (@p56 @p47)) % 0.38/0.60 (step @p58 :rule cong :premises (@p57) :args (@t110)) % 0.38/0.60 (step @p59 :rule trans :premises (@p58 @p46)) % 0.38/0.60 (step @p60 :rule cong :premises (@p59) :args (@t111)) % 0.38/0.60 (step @p61 :rule beta-reduce :args ((= (_ (lambda @t114 (not (or (not (or @t93 @t112)) (not (or @t113 @t92))))) @t102) @t111))) % 0.38/0.60 (step @p62 :rule trans :premises (@p61 @p60)) % 0.38/0.60 (step @p63 :rule bool-double-not-elim :args (@t88)) % 0.38/0.60 (step @p64 :rule beta-reduce :args ((= @t116 @t89))) % 0.38/0.60 (step @p65 :rule cong :premises (@p64) :args (@t117)) % 0.38/0.60 (step @p66 :rule trans :premises (@p65 @p63)) % 0.38/0.60 (step @p67 :rule cong :premises (@p66) :args (@t118)) % 0.38/0.60 (step @p68 :rule beta-reduce :args ((= (_ @t13 @t115) @t118))) % 0.38/0.60 (step @p69 :rule trans :premises (@p68 @p67)) % 0.38/0.60 (step @p70 :rule beta-reduce :args ((= @t122 @t115))) % 0.38/0.60 (step @p71 :rule refl :args (@t13)) % 0.38/0.60 (step @p72 :rule ho_cong :premises (@p71 @p70)) % 0.38/0.60 (step @p73 :rule trans :premises (@p72 @p69)) % 0.38/0.60 (step @p74 :rule refl :args (@t113)) % 0.38/0.60 (step @p75 :rule nary_cong :premises (@p74 @p49) :args (@t123)) % 0.38/0.60 (step @p76 :rule cong :premises (@p75) :args (@t124)) % 0.38/0.60 (step @p77 :rule refl :args (@t112)) % 0.38/0.60 (step @p78 :rule nary_cong :premises (@p50 @p77) :args (@t125)) % 0.38/0.60 (step @p79 :rule cong :premises (@p78) :args (@t126)) % 0.38/0.60 (step @p80 :rule nary_cong :premises (@p79 @p76) :args (@t127)) % 0.38/0.60 (step @p81 :rule cong :premises (@p80) :args (@t128)) % 0.38/0.60 (step @p82 :rule cong :premises (@p81) :args (@t129)) % 0.38/0.60 (step @p83 :rule beta-reduce :args ((= (_ @t136 @t102) @t129))) % 0.38/0.60 (step @p84 :rule trans :premises (@p83 @p82)) % 0.38/0.60 (step @p85 :rule refl :args (@t84)) % 0.38/0.60 (step @p86 :rule refl :args (@t137)) % 0.38/0.60 (step @p87 :rule cong :premises (@p86 @p85) :args ((= @t137 @t84))) % 0.38/0.60 (step @p88 :rule symm :premises (@p87)) % 0.38/0.60 (step @p89 :rule eq_resolve :premises (@p86 @p88)) % 0.38/0.60 (step @p90 :rule cong :premises (@p89) :args (@t138)) % 0.38/0.60 (step @p91 :rule refl :args (@t87)) % 0.38/0.60 (step @p92 :rule nary_cong :premises (@p91 @p90) :args (@t139)) % 0.38/0.60 (step @p93 :rule cong :premises (@p92) :args ((forall @t41 @t139))) % 0.38/0.60 (step @p94 :rule beta-reduce :args ((= @t142 @t138))) % 0.38/0.60 (step @p95 :rule refl :args (@t87)) % 0.38/0.60 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t143)) % 0.38/0.60 (step @p97 :rule cong :premises (@p96) :args (@t144)) % 0.38/0.60 (step @p98 :rule trans :premises (@p97 @p93)) % 0.38/0.60 (step @p99 :rule cong :premises (@p98) :args (@t145)) % 0.38/0.60 (step @p100 :rule beta-reduce :args ((= (_ @t146 @t141) @t145))) % 0.38/0.60 (step @p101 :rule trans :premises (@p100 @p99)) % 0.38/0.60 (step @p102 :rule aci_norm :args ((= (or @t140 @t140) @t140))) % 0.38/0.60 (step @p103 :rule beta-reduce :args ((= @t148 @t140))) % 0.38/0.60 (step @p104 :rule refl :args (@t140)) % 0.38/0.60 (step @p105 :rule nary_cong :premises (@p104 @p103) :args (@t149)) % 0.38/0.60 (step @p106 :rule trans :premises (@p105 @p102)) % 0.38/0.60 (step @p107 :rule cong :premises (@p106) :args (@t150)) % 0.38/0.60 (step @p108 :rule beta-reduce :args ((= (_ @t151 @t147) @t150))) % 0.38/0.60 (step @p109 :rule trans :premises (@p108 @p107)) % 0.38/0.60 (step @p110 :rule beta-reduce :args ((= @t152 @t147))) % 0.38/0.60 (step @p111 :rule beta-reduce :args ((= @t154 @t151))) % 0.38/0.60 (step @p112 :rule ho_cong :premises (@p111 @p110)) % 0.38/0.60 (step @p113 :rule trans :premises (@p112 @p109)) % 0.38/0.60 (step @p114 :rule refl :args (@t146)) % 0.38/0.60 (step @p115 :rule ho_cong :premises (@p114 @p113)) % 0.38/0.60 (step @p116 :rule trans :premises (@p115 @p101)) % 0.38/0.60 (step @p117 :rule refl :args (@t136)) % 0.38/0.60 (step @p118 :rule ho_cong :premises (@p117 @p116)) % 0.38/0.60 (step @p119 :rule trans :premises (@p118 @p84)) % 0.38/0.60 (step @p120 :rule ho_cong :premises (@p119 @p73)) % 0.38/0.60 (step @p121 :rule trans :premises (@p120 @p62)) % 0.38/0.60 (step @p122 :rule refl :args (@t100)) % 0.38/0.60 (step @p123 :rule ho_cong :premises (@p122 @p121)) % 0.38/0.60 (step @p124 :rule trans :premises (@p123 @p45)) % 0.38/0.60 (step @p125 :rule cong :premises (@p124) :args ((not (_ @t100 (_ (_ @t136 (_ @t146 (_ @t154 @t152))) (_ @t13 @t122)))))) % 0.38/0.60 (step @p126 :rule trans :premises (@p125 @p36)) % 0.38/0.60 (step @p127 :rule refl :args (tptp.p)) % 0.38/0.60 (step @p128 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t155)) @t17) @t121))) % 0.38/0.60 (step @p129 :rule refl :args (@t17)) % 0.38/0.60 (step @p130 :rule beta-reduce :args ((= @t157 @t155))) % 0.38/0.60 (step @p131 :rule cong :premises (@p130) :args (@t158)) % 0.38/0.60 (step @p132 :rule cong :premises (@p131) :args (@t159)) % 0.38/0.60 (step @p133 :rule beta-reduce :args ((= (_ @t13 @t156) @t159))) % 0.38/0.60 (step @p134 :rule trans :premises (@p133 @p132)) % 0.38/0.60 (step @p135 :rule refl :args (@t119)) % 0.38/0.60 (step @p136 :rule refl :args (@t39)) % 0.38/0.60 (step @p137 :rule cong :premises (@p136 @p135) :args ((= @t39 @t119))) % 0.38/0.60 (step @p138 :rule symm :premises (@p137)) % 0.38/0.60 (step @p139 :rule eq_resolve :premises (@p136 @p138)) % 0.38/0.60 (step @p140 :rule cong :premises (@p139) :args (@t160)) % 0.38/0.60 (step @p141 :rule nary_cong :premises (@p91 @p140) :args (@t161)) % 0.38/0.60 (step @p142 :rule cong :premises (@p141) :args ((forall @t41 @t161))) % 0.38/0.60 (step @p143 :rule beta-reduce :args ((= @t163 @t160))) % 0.38/0.60 (step @p144 :rule nary_cong :premises (@p95 @p143) :args (@t164)) % 0.38/0.60 (step @p145 :rule cong :premises (@p144) :args (@t165)) % 0.38/0.60 (step @p146 :rule trans :premises (@p145 @p142)) % 0.38/0.60 (step @p147 :rule cong :premises (@p146) :args (@t166)) % 0.38/0.60 (step @p148 :rule beta-reduce :args ((= (_ @t146 @t162) @t166))) % 0.38/0.60 (step @p149 :rule trans :premises (@p148 @p147)) % 0.38/0.60 (step @p150 :rule beta-reduce :args ((= (_ @t13 @t9) @t162))) % 0.38/0.60 (step @p151 :rule ho_cong :premises (@p114 @p150)) % 0.38/0.60 (step @p152 :rule trans :premises (@p151 @p149)) % 0.38/0.60 (step @p153 :rule ho_cong :premises (@p71 @p152)) % 0.38/0.60 (step @p154 :rule trans :premises (@p153 @p134)) % 0.38/0.60 (step @p155 :rule ho_cong :premises (@p154 @p129)) % 0.38/0.60 (step @p156 :rule trans :premises (@p155 @p128)) % 0.38/0.60 (step @p157 :rule refl :args (@t9)) % 0.38/0.60 (step @p158 :rule ho_cong :premises (@p6 @p157)) % 0.38/0.60 (step @p159 :rule refl :args (@t86)) % 0.38/0.60 (step @p160 :rule refl :args (@t77)) % 0.38/0.60 (step @p161 :rule cong :premises (@p160 @p159) :args ((= @t77 @t86))) % 0.38/0.60 (step @p162 :rule symm :premises (@p161)) % 0.38/0.60 (step @p163 :rule eq_resolve :premises (@p160 @p162)) % 0.38/0.60 (step @p164 :rule cong :premises (@p163) :args (@t78)) % 0.38/0.60 (step @p165 :rule nary_cong :premises (@p164 @p139) :args (@t79)) % 0.38/0.60 (step @p166 :rule cong :premises (@p165) :args (@t80)) % 0.38/0.60 (step @p167 :rule cong :premises (@p166) :args (@t81)) % 0.38/0.60 (step @p168 :rule trans :premises (@p34 @p167)) % 0.38/0.60 (step @p169 :rule ho_cong :premises (@p168 @p158)) % 0.38/0.60 (step @p170 :rule ho_cong :premises (@p6 @p169)) % 0.38/0.60 (step @p171 :rule ho_cong :premises (@p170 @p129)) % 0.38/0.60 (step @p172 :rule trans :premises (@p171 @p156)) % 0.38/0.60 (step @p173 :rule cong :premises (@p172) :args (@t83)) % 0.38/0.60 (step @p174 :rule trans :premises (@p35 @p173)) % 0.38/0.60 (step @p175 :rule ho_cong :premises (@p174 @p127)) % 0.38/0.60 (step @p176 :rule ho_cong :premises (@p6 @p175)) % 0.38/0.60 (step @p177 :rule ho_cong :premises (@p6 @p127)) % 0.38/0.60 (step @p178 :rule beta-reduce :args ((= (_ @t168 @t17) @t133))) % 0.38/0.60 (step @p179 :rule beta-reduce :args ((= (_ @t170 @t14) @t168))) % 0.38/0.60 (step @p180 :rule refl :args (@t14)) % 0.38/0.60 (step @p181 :rule refl :args (@t15)) % 0.38/0.60 (step @p182 :rule beta-reduce :args ((= @t171 @t11))) % 0.38/0.60 (step @p183 :rule nary_cong :premises (@p182 @p181) :args (@t172)) % 0.38/0.60 (step @p184 :rule cong :premises (@p183) :args (@t173)) % 0.38/0.60 (step @p185 :rule beta-reduce :args ((= (_ @t16 @t162) @t173))) % 0.38/0.60 (step @p186 :rule trans :premises (@p185 @p184)) % 0.38/0.60 (step @p187 :rule refl :args (@t16)) % 0.38/0.60 (step @p188 :rule ho_cong :premises (@p187 @p150)) % 0.38/0.60 (step @p189 :rule trans :premises (@p188 @p186)) % 0.38/0.60 (step @p190 :rule ho_cong :premises (@p189 @p180)) % 0.38/0.60 (step @p191 :rule trans :premises (@p190 @p179)) % 0.38/0.60 (step @p192 :rule ho_cong :premises (@p191 @p129)) % 0.38/0.60 (step @p193 :rule trans :premises (@p192 @p178)) % 0.38/0.60 (step @p194 :rule ho_cong :premises (@p7 @p158)) % 0.38/0.60 (step @p195 :rule ho_cong :premises (@p194 @p180)) % 0.38/0.60 (step @p196 :rule ho_cong :premises (@p195 @p129)) % 0.38/0.60 (step @p197 :rule trans :premises (@p196 @p193)) % 0.38/0.60 (step @p198 :rule cong :premises (@p197) :args (@t23)) % 0.38/0.60 (step @p199 :rule trans :premises (@p9 @p198)) % 0.38/0.60 (step @p200 :rule ho_cong :premises (@p199 @p127)) % 0.38/0.60 (step @p201 :rule ho_cong :premises (@p200 @p177)) % 0.38/0.60 (step @p202 :rule ho_cong :premises (@p168 @p201)) % 0.38/0.60 (step @p203 :rule beta-reduce :args ((= (_ (lambda @t95 @t135) @t17) @t135))) % 0.38/0.60 (step @p204 :rule beta-reduce :args ((= @t175 @t131))) % 0.38/0.60 (step @p205 :rule cong :premises (@p204) :args (@t176)) % 0.38/0.60 (step @p206 :rule refl :args (@t134)) % 0.38/0.60 (step @p207 :rule nary_cong :premises (@p206 @p205) :args (@t177)) % 0.38/0.60 (step @p208 :rule cong :premises (@p207) :args (@t178)) % 0.38/0.60 (step @p209 :rule cong :premises (@p208) :args (@t179)) % 0.38/0.60 (step @p210 :rule beta-reduce :args ((= (_ (lambda @t182 (not (or @t134 @t181))) @t174) @t179))) % 0.38/0.60 (step @p211 :rule trans :premises (@p210 @p209)) % 0.38/0.60 (step @p212 :rule beta-reduce :args ((= (_ @t185 @t9) @t174))) % 0.38/0.60 (step @p213 :rule beta-reduce :args ((= (_ (lambda (@list @t9 @t183 @t17) (or @t132 @t184)) @t14) @t185))) % 0.38/0.60 (step @p214 :rule refl :args (@t14)) % 0.38/0.60 (step @p215 :rule alpha_equiv :args (@t153 @t186 (@list @t183))) % 0.38/0.60 (step @p216 :rule ho_cong :premises (@p215 @p214)) % 0.38/0.60 (step @p217 :rule trans :premises (@p216 @p213)) % 0.38/0.60 (step @p218 :rule ho_cong :premises (@p217 @p157)) % 0.38/0.60 (step @p219 :rule trans :premises (@p218 @p212)) % 0.38/0.60 (step @p220 :rule refl :args (@t181)) % 0.38/0.60 (step @p221 :rule beta-reduce :args ((= @t188 @t133))) % 0.38/0.60 (step @p222 :rule cong :premises (@p221) :args (@t189)) % 0.38/0.60 (step @p223 :rule nary_cong :premises (@p222 @p220) :args (@t190)) % 0.38/0.60 (step @p224 :rule cong :premises (@p223) :args (@t191)) % 0.38/0.60 (step @p225 :rule cong :premises (@p224) :args (@t192)) % 0.38/0.60 (step @p226 :rule beta-reduce :args ((= (_ (lambda (@list @t9 @t180 @t17) (not (or @t132 @t181))) @t187) @t192))) % 0.38/0.60 (step @p227 :rule trans :premises (@p226 @p225)) % 0.38/0.60 (step @p228 :rule refl :args (@t187)) % 0.38/0.60 (step @p229 :rule alpha_equiv :args (@t194 @t186 (@list @t180))) % 0.38/0.60 (step @p230 :rule ho_cong :premises (@p229 @p228)) % 0.38/0.60 (step @p231 :rule trans :premises (@p230 @p227)) % 0.38/0.60 (step @p232 :rule beta-reduce :args ((= (_ @t195 @t14) @t187))) % 0.38/0.60 (step @p233 :rule beta-reduce :args ((= (_ @t153 @t9) @t195))) % 0.38/0.60 (step @p234 :rule ho_cong :premises (@p233 @p180)) % 0.38/0.60 (step @p235 :rule trans :premises (@p234 @p232)) % 0.38/0.60 (step @p236 :rule refl :args (@t194)) % 0.38/0.60 (step @p237 :rule ho_cong :premises (@p236 @p235)) % 0.38/0.60 (step @p238 :rule trans :premises (@p237 @p231)) % 0.38/0.60 (step @p239 :rule ho_cong :premises (@p238 @p219)) % 0.38/0.60 (step @p240 :rule trans :premises (@p239 @p211)) % 0.38/0.60 (step @p241 :rule ho_cong :premises (@p240 @p129)) % 0.38/0.60 (step @p242 :rule trans :premises (@p241 @p203)) % 0.38/0.60 (step @p243 :rule ho_cong :premises (@p199 @p180)) % 0.38/0.60 (step @p244 :rule ho_cong :premises (@p243 @p157)) % 0.38/0.60 (step @p245 :rule ho_cong :premises (@p199 @p157)) % 0.38/0.60 (step @p246 :rule ho_cong :premises (@p245 @p180)) % 0.38/0.60 (step @p247 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t197)) @t17) @t193))) % 0.38/0.60 (step @p248 :rule beta-reduce :args ((= @t199 @t197))) % 0.38/0.60 (step @p249 :rule cong :premises (@p248) :args (@t200)) % 0.38/0.60 (step @p250 :rule cong :premises (@p249) :args (@t201)) % 0.38/0.60 (step @p251 :rule beta-reduce :args ((= (_ @t13 @t198) @t201))) % 0.38/0.60 (step @p252 :rule trans :premises (@p251 @p250)) % 0.38/0.60 (step @p253 :rule beta-reduce :args ((= @t203 @t196))) % 0.38/0.60 (step @p254 :rule refl :args (@t11)) % 0.38/0.60 (step @p255 :rule nary_cong :premises (@p254 @p253) :args (@t204)) % 0.38/0.60 (step @p256 :rule cong :premises (@p255) :args (@t205)) % 0.38/0.60 (step @p257 :rule beta-reduce :args ((= (_ @t170 @t202) @t205))) % 0.38/0.60 (step @p258 :rule trans :premises (@p257 @p256)) % 0.38/0.60 (step @p259 :rule beta-reduce :args ((= (_ @t13 @t14) @t202))) % 0.38/0.60 (step @p260 :rule ho_cong :premises (@p189 @p259)) % 0.38/0.60 (step @p261 :rule trans :premises (@p260 @p258)) % 0.38/0.60 (step @p262 :rule ho_cong :premises (@p71 @p261)) % 0.38/0.60 (step @p263 :rule trans :premises (@p262 @p252)) % 0.38/0.60 (step @p264 :rule ho_cong :premises (@p263 @p129)) % 0.38/0.60 (step @p265 :rule trans :premises (@p264 @p247)) % 0.38/0.60 (step @p266 :rule ho_cong :premises (@p6 @p180)) % 0.38/0.60 (step @p267 :rule ho_cong :premises (@p194 @p266)) % 0.38/0.60 (step @p268 :rule ho_cong :premises (@p6 @p267)) % 0.38/0.60 (step @p269 :rule ho_cong :premises (@p268 @p129)) % 0.38/0.61 (step @p270 :rule trans :premises (@p269 @p265)) % 0.38/0.61 (step @p271 :rule cong :premises (@p270) :args (@t22)) % 0.38/0.61 (step @p272 :rule trans :premises (@p8 @p271)) % 0.38/0.61 (step @p273 :rule ho_cong :premises (@p272 @p246)) % 0.38/0.61 (step @p274 :rule ho_cong :premises (@p273 @p244)) % 0.38/0.61 (step @p275 :rule ho_cong :premises (@p274 @p129)) % 0.38/0.61 (step @p276 :rule trans :premises (@p275 @p242)) % 0.38/0.61 (step @p277 :rule cong :premises (@p276) :args (@t25)) % 0.38/0.61 (step @p278 :rule trans :premises (@p11 @p277)) % 0.38/0.61 (step @p279 :rule ho_cong :premises (@p278 @p202)) % 0.38/0.61 (step @p280 :rule ho_cong :premises (@p279 @p176)) % 0.38/0.61 (step @p281 :rule refl :args (@t99)) % 0.38/0.61 (step @p282 :rule refl :args (@t10)) % 0.38/0.61 (step @p283 :rule cong :premises (@p282 @p281) :args ((= @t10 @t99))) % 0.38/0.61 (step @p284 :rule symm :premises (@p283)) % 0.38/0.61 (step @p285 :rule eq_resolve :premises (@p282 @p284)) % 0.38/0.61 (step @p286 :rule cong :premises (@p285) :args (@t71)) % 0.38/0.61 (step @p287 :rule cong :premises (@p286) :args (@t73)) % 0.38/0.61 (step @p288 :rule trans :premises (@p30 @p287)) % 0.38/0.61 (step @p289 :rule ho_cong :premises (@p288 @p280)) % 0.38/0.61 (step @p290 :rule cong :premises (@p289) :args (@t1)) % 0.38/0.61 (step @p291 :rule trans :premises (@p290 @p126)) % 0.38/0.61 (step @p292 false :rule eq_resolve :premises (@p2 @p291)) % 0.38/0.61 ) % 0.38/0.61 % SZS output end Proof % 0.38/0.61 % cvc5 exiting %------------------------------------------------------------------------------