%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO406^1 : 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 09:12:35 AM UTC 2026 % Result : Theorem 0.38s 0.61s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO406^1 : 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 : n011.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 00:06:35 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.38/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.61 % SZS status Theorem % 0.38/0.61 % SZS output start Proof % 0.38/0.61 ( % 0.38/0.61 (declare-sort $$unsorted 0) % 0.38/0.61 (declare-sort tptp.mu 0) % 0.38/0.61 (declare-const tptp.rel_k (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.p (-> $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.q (-> $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.38/0.61 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.38/0.61 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.38/0.61 (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)))))) % 0.38/0.61 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.61 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.61 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.38/0.61 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.61 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.38/0.61 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.61 (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))))))) % 0.38/0.61 (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))))))) % 0.38/0.61 (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)))))) % 0.38/0.61 (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)))))) % 0.38/0.61 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.38/0.61 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.38/0.61 (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)))))) % 0.38/0.61 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.38/0.61 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.61 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.61 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.38/0.61 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.38/0.61 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.38/0.61 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.38/0.61 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.38/0.61 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.38/0.61 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.38/0.61 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.61 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.61 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.61 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.61 (define tptp.mbox_k () (let ((_let_1 (@var "V" $$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)))))))) % 0.38/0.61 (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))))) % 0.38/0.61 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mbox_k (_ (_ tptp.mor tptp.p) tptp.q))) (_ (_ tptp.mor (_ tptp.mbox_k tptp.p)) (_ tptp.mdia_k tptp.q)))))) % 0.38/0.61 (define @t2 () (@var "Y" tptp.mu)) % 0.38/0.61 (define @t3 () (@var "X" tptp.mu)) % 0.38/0.61 (define @t4 () (@var "W" $$unsorted)) % 0.38/0.61 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.38/0.61 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.61 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.61 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.38/0.61 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.38/0.61 (define @t10 () (_ @t9 @t4)) % 0.38/0.61 (define @t11 () (not @t10)) % 0.38/0.61 (define @t12 () (@list @t9 @t4)) % 0.38/0.61 (define @t13 () (lambda @t12 @t11)) % 0.38/0.61 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.38/0.61 (define @t15 () (_ @t14 @t4)) % 0.38/0.61 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.38/0.61 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.38/0.61 (define @t18 () (_ tptp.mnot @t14)) % 0.38/0.61 (define @t19 () (_ tptp.mnot @t9)) % 0.38/0.61 (define @t20 () (_ tptp.mor @t19)) % 0.38/0.61 (define @t21 () (@list @t9 @t14 @t17)) % 0.38/0.61 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.38/0.61 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.38/0.61 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.38/0.61 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.38/0.61 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.38/0.61 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.38/0.61 (define @t28 () (_ @t27 @t3)) % 0.38/0.61 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.38/0.61 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.38/0.61 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.38/0.61 (define @t32 () (_ @t31 @t30)) % 0.38/0.61 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.38/0.61 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.38/0.61 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.38/0.61 (define @t36 () (@list @t4)) % 0.38/0.61 (define @t37 () (lambda @t36 true)) % 0.38/0.61 (define @t38 () (@var "V" $$unsorted)) % 0.38/0.61 (define @t39 () (_ @t9 @t38)) % 0.38/0.61 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.38/0.61 (define @t41 () (@list @t38)) % 0.38/0.61 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.38/0.61 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.38/0.61 (define @t44 () (@var "S" $$unsorted)) % 0.38/0.61 (define @t45 () (_ @t40 @t44)) % 0.38/0.61 (define @t46 () (@list @t44)) % 0.38/0.61 (define @t47 () (@list @t40)) % 0.38/0.61 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.38/0.61 (define @t49 () (@var "T" $$unsorted)) % 0.38/0.61 (define @t50 () (_ @t40 @t49)) % 0.38/0.61 (define @t51 () (_ @t45 @t49)) % 0.38/0.61 (define @t52 () (lambda @t47 (forall (@list @t44 @t49) (=> @t51 (_ @t50 @t44))))) % 0.38/0.61 (define @t53 () (@list @t49)) % 0.38/0.61 (define @t54 () (lambda @t47 (forall @t46 (exists @t53 @t51)))) % 0.38/0.61 (define @t55 () (@var "U" $$unsorted)) % 0.38/0.61 (define @t56 () (_ @t45 @t55)) % 0.38/0.61 (define @t57 () (_ @t50 @t55)) % 0.38/0.61 (define @t58 () (@list @t44 @t49 @t55)) % 0.38/0.61 (define @t59 () (lambda @t47 (forall @t58 (=> (and @t51 @t57) @t56)))) % 0.38/0.61 (define @t60 () (and @t51 @t56)) % 0.38/0.61 (define @t61 () (lambda @t47 (forall @t58 (=> @t60 @t57)))) % 0.38/0.61 (define @t62 () (= @t49 @t55)) % 0.38/0.61 (define @t63 () (lambda @t47 (forall @t58 (=> @t60 @t62)))) % 0.38/0.61 (define @t64 () (@list @t55)) % 0.38/0.61 (define @t65 () (lambda @t47 (forall @t46 (exists @t53 (and @t51 (forall @t64 (=> @t56 @t62))))))) % 0.38/0.61 (define @t66 () (_ @t40 @t55)) % 0.38/0.61 (define @t67 () (_ @t66 @t49)) % 0.38/0.61 (define @t68 () (lambda @t47 (forall @t58 (=> @t51 (exists @t64 (and @t56 @t67)))))) % 0.38/0.61 (define @t69 () (lambda @t47 (forall @t58 (=> @t60 (or @t57 @t62 @t67))))) % 0.38/0.61 (define @t70 () (lambda @t47 (forall @t58 (=> @t60 (exists @t41 (and (_ @t50 @t38) (_ @t66 @t38))))))) % 0.38/0.61 (define @t71 () (forall @t36 @t10)) % 0.38/0.61 (define @t72 () (@list @t9)) % 0.38/0.61 (define @t73 () (lambda @t72 @t71)) % 0.38/0.61 (define @t74 () (lambda @t72 (forall @t36 @t11))) % 0.38/0.61 (define @t75 () (lambda @t72 (exists @t36 @t10))) % 0.38/0.61 (define @t76 () (lambda @t72 (exists @t36 @t11))) % 0.38/0.61 (define @t77 () (_ (_ tptp.rel_k @t4) @t38)) % 0.38/0.61 (define @t78 () (not @t77)) % 0.38/0.61 (define @t79 () (or @t78 @t39)) % 0.38/0.61 (define @t80 () (forall @t41 @t79)) % 0.38/0.61 (define @t81 () (lambda @t12 @t80)) % 0.38/0.61 (define @t82 () (@list @t9 @t17)) % 0.38/0.61 (define @t83 () (lambda @t82 (_ (_ tptp.mnot (_ tptp.mbox_k @t19)) @t17))) % 0.38/0.61 (define @t84 () (@var "BOUND_VARIABLE_8482" $$unsorted)) % 0.38/0.61 (define @t85 () (tptp.p @t84)) % 0.38/0.61 (define @t86 () (not (tptp.rel_k @t4 @t84))) % 0.38/0.61 (define @t87 () (tptp.q @t38)) % 0.38/0.61 (define @t88 () (not @t87)) % 0.38/0.61 (define @t89 () (tptp.rel_k @t4 @t38)) % 0.38/0.61 (define @t90 () (not @t89)) % 0.38/0.61 (define @t91 () (not (forall @t41 (or @t90 @t88)))) % 0.38/0.61 (define @t92 () (tptp.p @t38)) % 0.38/0.61 (define @t93 () (forall @t41 (or @t90 @t92 @t87))) % 0.38/0.61 (define @t94 () (not @t93)) % 0.38/0.61 (define @t95 () (or @t94 @t91 @t86 @t85)) % 0.38/0.61 (define @t96 () (or @t86 @t85)) % 0.38/0.61 (define @t97 () (or @t94 @t96 @t91)) % 0.38/0.61 (define @t98 () (@list @t4 @t84)) % 0.38/0.61 (define @t99 () (forall @t98 @t97)) % 0.38/0.61 (define @t100 () (@list @t84)) % 0.38/0.61 (define @t101 () (forall @t100 @t97)) % 0.38/0.61 (define @t102 () (forall @t100 @t96)) % 0.38/0.61 (define @t103 () (or @t94 @t102 @t91)) % 0.38/0.61 (define @t104 () (forall @t41 (or @t90 @t92))) % 0.38/0.61 (define @t105 () (or @t94 @t104 @t91)) % 0.38/0.61 (define @t106 () (not (tptp.rel_k @t17 @t38))) % 0.38/0.61 (define @t107 () (not (forall @t41 (or @t106 @t88)))) % 0.38/0.61 (define @t108 () (forall @t41 (or @t106 @t92))) % 0.38/0.61 (define @t109 () (forall @t41 (or @t106 @t92 @t87))) % 0.38/0.61 (define @t110 () (not @t109)) % 0.38/0.61 (define @t111 () (or @t110 @t108 @t107)) % 0.38/0.61 (define @t112 () (@list @t17)) % 0.38/0.61 (define @t113 () (lambda @t112 @t111)) % 0.38/0.61 (define @t114 () (_ @t113 @t4)) % 0.38/0.61 (define @t115 () (forall @t36 @t114)) % 0.38/0.61 (define @t116 () (_ @t9 @t4)) % 0.38/0.61 (define @t117 () (lambda @t72 (forall @t36 @t116))) % 0.38/0.61 (define @t118 () (or @t108 @t107)) % 0.38/0.61 (define @t119 () (lambda @t36 (or @t104 @t91))) % 0.38/0.61 (define @t120 () (_ @t119 @t17)) % 0.38/0.61 (define @t121 () (or @t110 @t120)) % 0.38/0.61 (define @t122 () (lambda @t112 @t121)) % 0.38/0.61 (define @t123 () (_ @t14 @t17)) % 0.38/0.61 (define @t124 () (@list @t14 @t17)) % 0.38/0.61 (define @t125 () (lambda @t112 @t107)) % 0.38/0.61 (define @t126 () (_ @t125 @t4)) % 0.38/0.61 (define @t127 () (or @t104 @t126)) % 0.38/0.61 (define @t128 () (lambda @t36 @t127)) % 0.38/0.61 (define @t129 () (@list @t14 @t4)) % 0.38/0.61 (define @t130 () (_ @t9 @t38)) % 0.38/0.61 (define @t131 () (not @t130)) % 0.38/0.61 (define @t132 () (not (forall @t41 (or @t106 @t131)))) % 0.38/0.61 (define @t133 () (_ (lambda @t82 @t132) tptp.q)) % 0.38/0.61 (define @t134 () (lambda @t36 @t104)) % 0.38/0.61 (define @t135 () (_ @t134 @t4)) % 0.38/0.61 (define @t136 () (or @t135 @t15)) % 0.38/0.61 (define @t137 () (lambda @t129 @t136)) % 0.38/0.61 (define @t138 () (lambda @t12 (forall @t41 (or @t90 @t130)))) % 0.38/0.61 (define @t139 () (_ @t138 tptp.p)) % 0.38/0.61 (define @t140 () (lambda @t36 @t93)) % 0.38/0.61 (define @t141 () (_ @t140 @t17)) % 0.38/0.61 (define @t142 () (not @t141)) % 0.38/0.61 (define @t143 () (or @t142 @t123)) % 0.38/0.61 (define @t144 () (lambda @t124 @t143)) % 0.38/0.61 (define @t145 () (or (not (_ @t9 @t17)) @t123)) % 0.38/0.61 (define @t146 () (lambda @t21 @t145)) % 0.38/0.61 (define @t147 () (_ tptp.q @t38)) % 0.38/0.61 (define @t148 () (_ tptp.p @t38)) % 0.38/0.61 (define @t149 () (or @t90 @t148 @t147)) % 0.38/0.61 (define @t150 () (or @t148 @t147)) % 0.38/0.61 (define @t151 () (_ tptp.p @t4)) % 0.38/0.61 (define @t152 () (lambda @t36 (or @t151 (_ tptp.q @t4)))) % 0.38/0.61 (define @t153 () (_ @t152 @t38)) % 0.38/0.61 (define @t154 () (or @t90 @t153)) % 0.38/0.61 (define @t155 () (forall @t41 @t154)) % 0.38/0.61 (define @t156 () (lambda @t36 @t155)) % 0.38/0.61 (define @t157 () (lambda @t129 (or @t151 @t15))) % 0.38/0.61 (define @t158 () (_ @t16 tptp.p)) % 0.38/0.61 (define @t159 () (forall @t41 (or @t90 @t131))) % 0.38/0.61 (define @t160 () (lambda @t36 @t159)) % 0.38/0.61 (define @t161 () (_ @t160 @t4)) % 0.38/0.61 (define @t162 () (not @t161)) % 0.38/0.61 (define @t163 () (lambda @t36 @t162)) % 0.38/0.61 (define @t164 () (not @t39)) % 0.38/0.61 (define @t165 () (or @t90 @t164)) % 0.38/0.61 (define @t166 () (lambda @t36 @t11)) % 0.38/0.61 (define @t167 () (_ @t166 @t38)) % 0.38/0.61 (define @t168 () (or @t90 @t167)) % 0.38/0.61 (define @t169 () (forall @t41 @t168)) % 0.38/0.61 (define @t170 () (lambda @t36 @t169)) % 0.38/0.61 (define @t171 () (or @t11 @t15)) % 0.38/0.61 (define @t172 () (lambda @t36 @t171)) % 0.38/0.61 (define @t173 () (_ @t166 @t4)) % 0.38/0.61 (define @t174 () (or @t173 @t15)) % 0.38/0.61 (define @t175 () (lambda @t129 @t174)) % 0.38/0.61 (define @t176 () (forall @t98 @t95)) % 0.38/0.61 (define @t177 () (@quantifiers_skolemize @t176 1)) % 0.38/0.61 (define @t178 () (@quantifiers_skolemize @t176 0)) % 0.38/0.61 (define @t179 () (tptp.rel_k @t178 @t177)) % 0.38/0.61 (define @t180 () (tptp.p @t177)) % 0.38/0.61 (define @t181 () (not @t179)) % 0.38/0.61 (define @t182 () (not (tptp.rel_k @t178 @t38))) % 0.38/0.61 (define @t183 () (forall @t41 (or @t182 @t88))) % 0.38/0.61 (define @t184 () (not @t183)) % 0.38/0.61 (define @t185 () (forall @t41 (or @t182 @t92 @t87))) % 0.38/0.61 (define @t186 () (not @t185)) % 0.38/0.61 (define @t187 () (or @t186 @t184 @t181 @t180)) % 0.38/0.61 (define @t188 () (@list true)) % 0.38/0.61 (define @t189 () (@list @t187)) % 0.38/0.61 (define @t190 () (@list @t177)) % 0.38/0.61 (define @t191 () (tptp.q @t177)) % 0.38/0.61 (define @t192 () (or @t181 @t180 @t191)) % 0.38/0.61 (define @t193 () (not @t191)) % 0.38/0.61 (define @t194 () (or @t181 @t193)) % 0.38/0.61 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.38/0.61 (assume @p2 @t1) % 0.38/0.61 (assume @p3 true) % 0.38/0.61 (step @p4 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.38/0.61 (step @p5 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.38/0.61 (step @p6 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.38/0.61 (step @p7 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.38/0.61 (step @p8 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.38/0.61 (step @p9 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.38/0.61 (step @p10 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.38/0.61 (step @p11 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.38/0.61 (step @p12 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.38/0.61 (step @p13 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.38/0.61 (step @p14 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.38/0.61 (step @p15 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.38/0.61 (step @p16 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.38/0.61 (step @p17 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.38/0.61 (step @p18 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.38/0.61 (step @p19 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.38/0.61 (step @p20 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.38/0.61 (step @p21 (= tptp.msymmetric @t52) :rule refl :args (@t52)) % 0.38/0.61 (step @p22 (= tptp.mserial @t54) :rule refl :args (@t54)) % 0.38/0.61 (step @p23 (= tptp.mtransitive @t59) :rule refl :args (@t59)) % 0.38/0.61 (step @p24 (= tptp.meuclidean @t61) :rule refl :args (@t61)) % 0.38/0.61 (step @p25 (= tptp.mpartially_functional @t63) :rule refl :args (@t63)) % 0.38/0.61 (step @p26 (= tptp.mfunctional @t65) :rule refl :args (@t65)) % 0.38/0.61 (step @p27 (= tptp.mweakly_dense @t68) :rule refl :args (@t68)) % 0.38/0.61 (step @p28 (= tptp.mweakly_connected @t69) :rule refl :args (@t69)) % 0.38/0.61 (step @p29 (= tptp.mweakly_directed @t70) :rule refl :args (@t70)) % 0.38/0.61 (step @p30 (= tptp.mvalid @t73) :rule refl :args (@t73)) % 0.38/0.61 (step @p31 (= tptp.minvalid @t74) :rule refl :args (@t74)) % 0.38/0.61 (step @p32 (= tptp.msatisfiable @t75) :rule refl :args (@t75)) % 0.38/0.61 (step @p33 (= tptp.mcountersatisfiable @t76) :rule refl :args (@t76)) % 0.38/0.61 (step @p34 (= tptp.mbox_k @t81) :rule refl :args (@t81)) % 0.38/0.61 (step @p35 (= tptp.mdia_k @t83) :rule refl :args (@t83)) % 0.38/0.61 (step @p36 :rule aci_norm :args ((= @t97 @t95))) % 0.38/0.61 (step @p37 :rule cong :premises (@p36) :args (@t99)) % 0.38/0.61 (step @p38 :rule quant-merge-prenex :args ((= (forall @t36 @t101) @t99))) % 0.38/0.61 (step @p39 :rule refl :args (@t91)) % 0.38/0.61 (step @p40 :rule alpha_equiv :args (@t102 (@list @t84) (@list @t38))) % 0.38/0.61 (step @p41 :rule refl :args (@t94)) % 0.38/0.61 (step @p42 :rule nary_cong :premises (@p41 @p40 @p39) :args (@t103)) % 0.38/0.61 (step @p43 :rule quant-miniscope-or :args ((= @t101 @t103))) % 0.38/0.61 (step @p44 :rule trans :premises (@p43 @p42)) % 0.38/0.61 (step @p45 :rule symm :premises (@p44)) % 0.38/0.61 (step @p46 :rule cong :premises (@p45) :args ((forall @t36 @t105))) % 0.38/0.61 (step @p47 :rule trans :premises (@p46 @p38)) % 0.38/0.61 (step @p48 :rule trans :premises (@p47 @p37)) % 0.38/0.61 (step @p49 :rule beta-reduce :args ((= @t114 @t105))) % 0.38/0.61 (step @p50 :rule cong :premises (@p49) :args (@t115)) % 0.38/0.61 (step @p51 :rule trans :premises (@p50 @p48)) % 0.38/0.61 (step @p52 :rule beta-reduce :args ((= (_ @t117 @t113) @t115))) % 0.38/0.61 (step @p53 :rule trans :premises (@p52 @p51)) % 0.38/0.61 (step @p54 :rule aci_norm :args ((= (or @t110 @t118) @t111))) % 0.38/0.61 (step @p55 :rule beta-reduce :args ((= @t120 @t118))) % 0.38/0.61 (step @p56 :rule refl :args (@t110)) % 0.38/0.61 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t121)) % 0.38/0.61 (step @p58 :rule trans :premises (@p57 @p54)) % 0.38/0.61 (step @p59 :rule cong :premises (@p58) :args (@t122)) % 0.38/0.61 (step @p60 :rule beta-reduce :args ((= (_ (lambda @t124 (or @t110 @t123)) @t119) @t122))) % 0.38/0.61 (step @p61 :rule trans :premises (@p60 @p59)) % 0.38/0.61 (step @p62 :rule beta-reduce :args ((= @t126 @t91))) % 0.38/0.61 (step @p63 :rule refl :args (@t104)) % 0.38/0.61 (step @p64 :rule nary_cong :premises (@p63 @p62) :args (@t127)) % 0.38/0.61 (step @p65 :rule cong :premises (@p64) :args (@t128)) % 0.38/0.61 (step @p66 :rule beta-reduce :args ((= (_ (lambda @t129 (or @t104 @t15)) @t125) @t128))) % 0.38/0.61 (step @p67 :rule trans :premises (@p66 @p65)) % 0.38/0.61 (step @p68 :rule beta-reduce :args ((= @t133 @t125))) % 0.38/0.61 (step @p69 :rule refl :args (@t15)) % 0.38/0.61 (step @p70 :rule beta-reduce :args ((= @t135 @t104))) % 0.38/0.61 (step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t136)) % 0.38/0.61 (step @p72 :rule cong :premises (@p71) :args (@t137)) % 0.38/0.61 (step @p73 :rule beta-reduce :args ((= (_ @t16 @t134) @t137))) % 0.38/0.61 (step @p74 :rule trans :premises (@p73 @p72)) % 0.38/0.61 (step @p75 :rule beta-reduce :args ((= @t139 @t134))) % 0.38/0.61 (step @p76 :rule refl :args (@t16)) % 0.38/0.61 (step @p77 :rule ho_cong :premises (@p76 @p75)) % 0.38/0.61 (step @p78 :rule trans :premises (@p77 @p74)) % 0.38/0.61 (step @p79 :rule ho_cong :premises (@p78 @p68)) % 0.38/0.61 (step @p80 :rule trans :premises (@p79 @p67)) % 0.38/0.61 (step @p81 :rule refl :args (@t123)) % 0.38/0.61 (step @p82 :rule beta-reduce :args ((= @t141 @t109))) % 0.38/0.61 (step @p83 :rule cong :premises (@p82) :args (@t142)) % 0.38/0.61 (step @p84 :rule nary_cong :premises (@p83 @p81) :args (@t143)) % 0.38/0.61 (step @p85 :rule cong :premises (@p84) :args (@t144)) % 0.38/0.61 (step @p86 :rule beta-reduce :args ((= (_ @t146 @t140) @t144))) % 0.38/0.61 (step @p87 :rule trans :premises (@p86 @p85)) % 0.38/0.61 (step @p88 :rule refl :args (@t87)) % 0.38/0.61 (step @p89 :rule refl :args (@t147)) % 0.38/0.61 (step @p90 :rule cong :premises (@p89 @p88) :args ((= @t147 @t87))) % 0.38/0.61 (step @p91 :rule symm :premises (@p90)) % 0.38/0.61 (step @p92 :rule eq_resolve :premises (@p89 @p91)) % 0.38/0.61 (step @p93 :rule refl :args (@t92)) % 0.38/0.61 (step @p94 :rule refl :args (@t148)) % 0.38/0.61 (step @p95 :rule cong :premises (@p94 @p93) :args ((= @t148 @t92))) % 0.38/0.61 (step @p96 :rule symm :premises (@p95)) % 0.38/0.61 (step @p97 :rule eq_resolve :premises (@p94 @p96)) % 0.38/0.61 (step @p98 :rule refl :args (@t90)) % 0.38/0.61 (step @p99 :rule nary_cong :premises (@p98 @p97 @p92) :args (@t149)) % 0.38/0.61 (step @p100 :rule cong :premises (@p99) :args ((forall @t41 @t149))) % 0.38/0.61 (step @p101 :rule aci_norm :args ((= (or @t90 @t150) @t149))) % 0.38/0.61 (step @p102 :rule beta-reduce :args ((= @t153 @t150))) % 0.38/0.61 (step @p103 :rule refl :args (@t90)) % 0.38/0.61 (step @p104 :rule nary_cong :premises (@p103 @p102) :args (@t154)) % 0.38/0.61 (step @p105 :rule trans :premises (@p104 @p101)) % 0.38/0.61 (step @p106 :rule cong :premises (@p105) :args (@t155)) % 0.38/0.61 (step @p107 :rule trans :premises (@p106 @p100)) % 0.38/0.61 (step @p108 :rule cong :premises (@p107) :args (@t156)) % 0.38/0.61 (step @p109 :rule beta-reduce :args ((= (_ @t138 @t152) @t156))) % 0.38/0.61 (step @p110 :rule trans :premises (@p109 @p108)) % 0.38/0.61 (step @p111 :rule beta-reduce :args ((= (_ @t157 tptp.q) @t152))) % 0.38/0.61 (step @p112 :rule refl :args (tptp.q)) % 0.38/0.61 (step @p113 :rule beta-reduce :args ((= @t158 @t157))) % 0.38/0.61 (step @p114 :rule ho_cong :premises (@p113 @p112)) % 0.38/0.61 (step @p115 :rule trans :premises (@p114 @p111)) % 0.38/0.61 (step @p116 :rule refl :args (@t138)) % 0.38/0.61 (step @p117 :rule ho_cong :premises (@p116 @p115)) % 0.38/0.61 (step @p118 :rule trans :premises (@p117 @p110)) % 0.38/0.61 (step @p119 :rule refl :args (@t146)) % 0.38/0.61 (step @p120 :rule ho_cong :premises (@p119 @p118)) % 0.38/0.61 (step @p121 :rule trans :premises (@p120 @p87)) % 0.38/0.61 (step @p122 :rule ho_cong :premises (@p121 @p80)) % 0.38/0.61 (step @p123 :rule trans :premises (@p122 @p61)) % 0.38/0.61 (step @p124 :rule refl :args (@t117)) % 0.38/0.61 (step @p125 :rule ho_cong :premises (@p124 @p123)) % 0.38/0.61 (step @p126 :rule trans :premises (@p125 @p53)) % 0.38/0.61 (step @p127 :rule cong :premises (@p126) :args ((not (_ @t117 (_ (_ @t146 (_ @t138 (_ @t158 tptp.q))) (_ (_ @t16 @t139) @t133)))))) % 0.38/0.61 (step @p128 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t159)) @t17) @t132))) % 0.38/0.61 (step @p129 :rule refl :args (@t17)) % 0.38/0.61 (step @p130 :rule beta-reduce :args ((= @t161 @t159))) % 0.38/0.61 (step @p131 :rule cong :premises (@p130) :args (@t162)) % 0.38/0.61 (step @p132 :rule cong :premises (@p131) :args (@t163)) % 0.38/0.61 (step @p133 :rule beta-reduce :args ((= (_ @t13 @t160) @t163))) % 0.38/0.61 (step @p134 :rule trans :premises (@p133 @p132)) % 0.38/0.61 (step @p135 :rule refl :args (@t130)) % 0.38/0.61 (step @p136 :rule refl :args (@t39)) % 0.38/0.61 (step @p137 :rule cong :premises (@p136 @p135) :args ((= @t39 @t130))) % 0.38/0.61 (step @p138 :rule symm :premises (@p137)) % 0.38/0.61 (step @p139 :rule eq_resolve :premises (@p136 @p138)) % 0.38/0.61 (step @p140 :rule cong :premises (@p139) :args (@t164)) % 0.38/0.61 (step @p141 :rule nary_cong :premises (@p98 @p140) :args (@t165)) % 0.38/0.61 (step @p142 :rule cong :premises (@p141) :args ((forall @t41 @t165))) % 0.38/0.61 (step @p143 :rule beta-reduce :args ((= @t167 @t164))) % 0.38/0.61 (step @p144 :rule nary_cong :premises (@p103 @p143) :args (@t168)) % 0.38/0.61 (step @p145 :rule cong :premises (@p144) :args (@t169)) % 0.38/0.61 (step @p146 :rule trans :premises (@p145 @p142)) % 0.38/0.61 (step @p147 :rule cong :premises (@p146) :args (@t170)) % 0.38/0.61 (step @p148 :rule beta-reduce :args ((= (_ @t138 @t166) @t170))) % 0.38/0.61 (step @p149 :rule trans :premises (@p148 @p147)) % 0.38/0.61 (step @p150 :rule beta-reduce :args ((= (_ @t13 @t9) @t166))) % 0.38/0.61 (step @p151 :rule ho_cong :premises (@p116 @p150)) % 0.38/0.61 (step @p152 :rule trans :premises (@p151 @p149)) % 0.38/0.61 (step @p153 :rule refl :args (@t13)) % 0.38/0.61 (step @p154 :rule ho_cong :premises (@p153 @p152)) % 0.38/0.61 (step @p155 :rule trans :premises (@p154 @p134)) % 0.38/0.61 (step @p156 :rule ho_cong :premises (@p155 @p129)) % 0.38/0.61 (step @p157 :rule trans :premises (@p156 @p128)) % 0.38/0.61 (step @p158 :rule refl :args (@t9)) % 0.38/0.61 (step @p159 :rule ho_cong :premises (@p6 @p158)) % 0.38/0.61 (step @p160 :rule refl :args (@t89)) % 0.38/0.61 (step @p161 :rule refl :args (@t77)) % 0.38/0.61 (step @p162 :rule cong :premises (@p161 @p160) :args ((= @t77 @t89))) % 0.38/0.61 (step @p163 :rule symm :premises (@p162)) % 0.38/0.61 (step @p164 :rule eq_resolve :premises (@p161 @p163)) % 0.38/0.61 (step @p165 :rule cong :premises (@p164) :args (@t78)) % 0.38/0.61 (step @p166 :rule nary_cong :premises (@p165 @p139) :args (@t79)) % 0.38/0.61 (step @p167 :rule cong :premises (@p166) :args (@t80)) % 0.38/0.61 (step @p168 :rule cong :premises (@p167) :args (@t81)) % 0.38/0.61 (step @p169 :rule trans :premises (@p34 @p168)) % 0.38/0.61 (step @p170 :rule ho_cong :premises (@p169 @p159)) % 0.38/0.61 (step @p171 :rule ho_cong :premises (@p6 @p170)) % 0.38/0.61 (step @p172 :rule ho_cong :premises (@p171 @p129)) % 0.38/0.61 (step @p173 :rule trans :premises (@p172 @p157)) % 0.38/0.61 (step @p174 :rule cong :premises (@p173) :args (@t83)) % 0.38/0.61 (step @p175 :rule trans :premises (@p35 @p174)) % 0.38/0.61 (step @p176 :rule ho_cong :premises (@p175 @p112)) % 0.38/0.61 (step @p177 :rule refl :args (tptp.p)) % 0.38/0.61 (step @p178 :rule ho_cong :premises (@p169 @p177)) % 0.38/0.61 (step @p179 :rule ho_cong :premises (@p7 @p178)) % 0.38/0.61 (step @p180 :rule ho_cong :premises (@p179 @p176)) % 0.38/0.61 (step @p181 :rule ho_cong :premises (@p7 @p177)) % 0.38/0.61 (step @p182 :rule ho_cong :premises (@p181 @p112)) % 0.38/0.61 (step @p183 :rule ho_cong :premises (@p169 @p182)) % 0.38/0.61 (step @p184 :rule beta-reduce :args ((= (_ @t172 @t17) @t145))) % 0.38/0.61 (step @p185 :rule beta-reduce :args ((= (_ (lambda @t129 @t171) @t14) @t172))) % 0.38/0.61 (step @p186 :rule refl :args (@t14)) % 0.38/0.61 (step @p187 :rule beta-reduce :args ((= @t173 @t11))) % 0.38/0.61 (step @p188 :rule nary_cong :premises (@p187 @p69) :args (@t174)) % 0.38/0.61 (step @p189 :rule cong :premises (@p188) :args (@t175)) % 0.38/0.61 (step @p190 :rule beta-reduce :args ((= (_ @t16 @t166) @t175))) % 0.38/0.61 (step @p191 :rule trans :premises (@p190 @p189)) % 0.38/0.61 (step @p192 :rule ho_cong :premises (@p76 @p150)) % 0.38/0.61 (step @p193 :rule trans :premises (@p192 @p191)) % 0.38/0.61 (step @p194 :rule ho_cong :premises (@p193 @p186)) % 0.38/0.61 (step @p195 :rule trans :premises (@p194 @p185)) % 0.38/0.61 (step @p196 :rule ho_cong :premises (@p195 @p129)) % 0.38/0.61 (step @p197 :rule trans :premises (@p196 @p184)) % 0.38/0.61 (step @p198 :rule ho_cong :premises (@p7 @p159)) % 0.38/0.61 (step @p199 :rule ho_cong :premises (@p198 @p186)) % 0.38/0.61 (step @p200 :rule ho_cong :premises (@p199 @p129)) % 0.38/0.61 (step @p201 :rule trans :premises (@p200 @p197)) % 0.38/0.61 (step @p202 :rule cong :premises (@p201) :args (@t23)) % 0.38/0.61 (step @p203 :rule trans :premises (@p9 @p202)) % 0.38/0.61 (step @p204 :rule ho_cong :premises (@p203 @p183)) % 0.38/0.61 (step @p205 :rule ho_cong :premises (@p204 @p180)) % 0.38/0.61 (step @p206 :rule refl :args (@t116)) % 0.38/0.61 (step @p207 :rule refl :args (@t10)) % 0.38/0.61 (step @p208 :rule cong :premises (@p207 @p206) :args ((= @t10 @t116))) % 0.38/0.61 (step @p209 :rule symm :premises (@p208)) % 0.38/0.61 (step @p210 :rule eq_resolve :premises (@p207 @p209)) % 0.38/0.61 (step @p211 :rule cong :premises (@p210) :args (@t71)) % 0.38/0.61 (step @p212 :rule cong :premises (@p211) :args (@t73)) % 0.38/0.61 (step @p213 :rule trans :premises (@p30 @p212)) % 0.38/0.61 (step @p214 :rule ho_cong :premises (@p213 @p205)) % 0.38/0.61 (step @p215 :rule cong :premises (@p214) :args (@t1)) % 0.38/0.61 (step @p216 :rule trans :premises (@p215 @p127)) % 0.38/0.61 (step @p217 :rule eq_resolve :premises (@p2 @p216)) % 0.38/0.61 (step @p218 :rule skolemize :premises (@p217)) % 0.38/0.61 (step @p219 :rule bool-double-not-elim :args (@t179)) % 0.38/0.61 (step @p220 :rule refl :args (@t187)) % 0.38/0.61 (step @p221 :rule nary_cong :premises (@p220 @p219) :args ((or @t187 (not @t181)))) % 0.38/0.61 (step @p222 :rule cnf_or_neg :args (@t187 2)) % 0.38/0.61 (step @p223 :rule eq_resolve :premises (@p222 @p221)) % 0.38/0.61 (step @p224 :rule reordering :premises (@p223) :args ((or @t179 @t187))) % 0.38/0.61 (step @p225 :rule chain_m_resolution :premises (@p224 @p218) :args (@t179 @t188 @t189)) % 0.38/0.61 (step @p226 :rule bool-double-not-elim :args (@t183)) % 0.38/0.61 (step @p227 :rule nary_cong :premises (@p220 @p226) :args ((or @t187 (not @t184)))) % 0.38/0.61 (step @p228 :rule cnf_or_neg :args (@t187 1)) % 0.38/0.61 (step @p229 :rule eq_resolve :premises (@p228 @p227)) % 0.38/0.61 (step @p230 :rule reordering :premises (@p229) :args ((or @t183 @t187))) % 0.38/0.61 (step @p231 :rule chain_m_resolution :premises (@p230 @p218) :args (@t183 @t188 @t189)) % 0.38/0.61 (step @p232 :rule instantiate :premises (@p231) :args (@t190)) % 0.38/0.61 (step @p233 :rule bool-double-not-elim :args (@t185)) % 0.38/0.61 (step @p234 :rule nary_cong :premises (@p220 @p233) :args ((or @t187 (not @t186)))) % 0.38/0.61 (step @p235 :rule cnf_or_neg :args (@t187 0)) % 0.38/0.61 (step @p236 :rule eq_resolve :premises (@p235 @p234)) % 0.38/0.61 (step @p237 :rule reordering :premises (@p236) :args ((or @t185 @t187))) % 0.38/0.61 (step @p238 :rule chain_m_resolution :premises (@p237 @p218) :args (@t185 @t188 @t189)) % 0.38/0.61 (step @p239 :rule instantiate :premises (@p238) :args (@t190)) % 0.38/0.61 (step @p240 :rule cnf_or_neg :args (@t187 3)) % 0.38/0.61 (step @p241 :rule chain_m_resolution :premises (@p240 @p218) :args ((not @t180) @t188 @t189)) % 0.38/0.61 (step @p242 :rule cnf_or_pos :args (@t192)) % 0.38/0.61 (step @p243 :rule reordering :premises (@p242) :args ((or @t181 @t180 @t191 (not @t192)))) % 0.38/0.61 (step @p244 :rule chain_m_resolution :premises (@p243 @p225 @p241 @p239) :args (@t191 (@list false true false) (@list @t179 @t180 @t192))) % 0.38/0.61 (step @p245 :rule cnf_or_pos :args (@t194)) % 0.38/0.61 (step @p246 :rule reordering :premises (@p245) :args ((or @t181 @t193 (not @t194)))) % 0.38/0.61 (step @p247 false :rule chain_m_resolution :premises (@p246 @p244 @p232 @p225) :args (false (@list false false false) (@list @t191 @t194 @t179))) % 0.38/0.61 ) % 0.38/0.61 % SZS output end Proof % 0.38/0.61 % cvc5 exiting %------------------------------------------------------------------------------