%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO410^1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n024.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:12:36 AM UTC 2026 % Result : Theorem 0.14s 0.38s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SYO410^1 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n024.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 19:07:00 EDT 2026 % 0.07/0.25 % CPUTime : % 0.14/0.33 %----Proving TH0 % 0.14/0.38 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.14/0.38 % SZS status Theorem % 0.14/0.38 % SZS output start Proof % 0.14/0.38 ( % 0.14/0.38 (declare-sort $$unsorted 0) % 0.14/0.38 (declare-sort tptp.mu 0) % 0.14/0.38 (declare-const tptp.rel_k (-> $$unsorted $$unsorted Bool)) % 0.14/0.38 (declare-const tptp.p (-> $$unsorted Bool)) % 0.14/0.38 (declare-const tptp.q (-> $$unsorted Bool)) % 0.14/0.38 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.14/0.38 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.14/0.38 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.14/0.38 (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)))))) % 0.14/0.38 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.14/0.38 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.14/0.38 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.14/0.38 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.14/0.38 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.14/0.38 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.14/0.38 (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))))))) % 0.14/0.38 (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))))))) % 0.14/0.38 (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)))))) % 0.14/0.38 (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)))))) % 0.14/0.38 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.14/0.38 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.14/0.38 (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)))))) % 0.14/0.38 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.14/0.38 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.14/0.38 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.14/0.38 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.14/0.38 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.14/0.38 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.14/0.38 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.14/0.38 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.14/0.38 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.14/0.38 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.14/0.38 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.14/0.38 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.14/0.38 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.14/0.38 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.14/0.38 (define tptp.mbox_k () (let ((_let_1 (@var "V" $$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)))))))) % 0.14/0.38 (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))))) % 0.14/0.38 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ (_ tptp.mand (_ tptp.mdia_k tptp.p)) (_ tptp.mbox_k tptp.q))) (_ tptp.mdia_k (_ (_ tptp.mand tptp.p) tptp.q)))))) % 0.14/0.38 (define @t2 () (@var "Y" tptp.mu)) % 0.14/0.38 (define @t3 () (@var "X" tptp.mu)) % 0.14/0.38 (define @t4 () (@var "W" $$unsorted)) % 0.14/0.38 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.14/0.38 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.14/0.38 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.14/0.38 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.14/0.38 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.14/0.38 (define @t10 () (_ @t9 @t4)) % 0.14/0.38 (define @t11 () (not @t10)) % 0.14/0.38 (define @t12 () (@list @t9 @t4)) % 0.14/0.38 (define @t13 () (lambda @t12 @t11)) % 0.14/0.38 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.14/0.38 (define @t15 () (_ @t14 @t4)) % 0.14/0.38 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.14/0.38 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.14/0.38 (define @t18 () (_ tptp.mnot @t14)) % 0.14/0.38 (define @t19 () (_ tptp.mnot @t9)) % 0.14/0.38 (define @t20 () (_ tptp.mor @t19)) % 0.14/0.38 (define @t21 () (@list @t9 @t14 @t17)) % 0.14/0.38 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.14/0.38 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.14/0.38 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.14/0.38 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.14/0.38 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.14/0.38 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.14/0.38 (define @t28 () (_ @t27 @t3)) % 0.14/0.38 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.14/0.38 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.14/0.38 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.14/0.38 (define @t32 () (_ @t31 @t30)) % 0.14/0.38 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.14/0.38 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.14/0.38 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.14/0.38 (define @t36 () (@list @t4)) % 0.14/0.38 (define @t37 () (lambda @t36 true)) % 0.14/0.38 (define @t38 () (@var "V" $$unsorted)) % 0.14/0.38 (define @t39 () (_ @t9 @t38)) % 0.14/0.38 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.14/0.38 (define @t41 () (@list @t38)) % 0.14/0.38 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.14/0.38 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.14/0.38 (define @t44 () (@var "S" $$unsorted)) % 0.14/0.38 (define @t45 () (_ @t40 @t44)) % 0.14/0.38 (define @t46 () (@list @t44)) % 0.14/0.38 (define @t47 () (@list @t40)) % 0.14/0.38 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.14/0.38 (define @t49 () (@var "T" $$unsorted)) % 0.14/0.38 (define @t50 () (_ @t40 @t49)) % 0.14/0.38 (define @t51 () (_ @t45 @t49)) % 0.14/0.38 (define @t52 () (lambda @t47 (forall (@list @t44 @t49) (=> @t51 (_ @t50 @t44))))) % 0.14/0.38 (define @t53 () (@list @t49)) % 0.14/0.38 (define @t54 () (lambda @t47 (forall @t46 (exists @t53 @t51)))) % 0.14/0.38 (define @t55 () (@var "U" $$unsorted)) % 0.14/0.38 (define @t56 () (_ @t45 @t55)) % 0.14/0.38 (define @t57 () (_ @t50 @t55)) % 0.14/0.38 (define @t58 () (@list @t44 @t49 @t55)) % 0.14/0.38 (define @t59 () (lambda @t47 (forall @t58 (=> (and @t51 @t57) @t56)))) % 0.14/0.38 (define @t60 () (and @t51 @t56)) % 0.14/0.38 (define @t61 () (lambda @t47 (forall @t58 (=> @t60 @t57)))) % 0.14/0.38 (define @t62 () (= @t49 @t55)) % 0.14/0.38 (define @t63 () (lambda @t47 (forall @t58 (=> @t60 @t62)))) % 0.14/0.38 (define @t64 () (@list @t55)) % 0.14/0.38 (define @t65 () (lambda @t47 (forall @t46 (exists @t53 (and @t51 (forall @t64 (=> @t56 @t62))))))) % 0.14/0.38 (define @t66 () (_ @t40 @t55)) % 0.14/0.38 (define @t67 () (_ @t66 @t49)) % 0.14/0.38 (define @t68 () (lambda @t47 (forall @t58 (=> @t51 (exists @t64 (and @t56 @t67)))))) % 0.14/0.38 (define @t69 () (lambda @t47 (forall @t58 (=> @t60 (or @t57 @t62 @t67))))) % 0.14/0.38 (define @t70 () (lambda @t47 (forall @t58 (=> @t60 (exists @t41 (and (_ @t50 @t38) (_ @t66 @t38))))))) % 0.14/0.38 (define @t71 () (forall @t36 @t10)) % 0.14/0.38 (define @t72 () (@list @t9)) % 0.14/0.38 (define @t73 () (lambda @t72 @t71)) % 0.14/0.38 (define @t74 () (lambda @t72 (forall @t36 @t11))) % 0.14/0.38 (define @t75 () (lambda @t72 (exists @t36 @t10))) % 0.14/0.38 (define @t76 () (lambda @t72 (exists @t36 @t11))) % 0.14/0.38 (define @t77 () (_ (_ tptp.rel_k @t4) @t38)) % 0.14/0.38 (define @t78 () (not @t77)) % 0.14/0.38 (define @t79 () (or @t78 @t39)) % 0.14/0.38 (define @t80 () (forall @t41 @t79)) % 0.14/0.38 (define @t81 () (lambda @t12 @t80)) % 0.14/0.38 (define @t82 () (@list @t9 @t17)) % 0.14/0.38 (define @t83 () (lambda @t82 (_ (_ tptp.mnot (_ tptp.mbox_k @t19)) @t17))) % 0.14/0.38 (define @t84 () (@var "BOUND_VARIABLE_8501" $$unsorted)) % 0.14/0.38 (define @t85 () (not (tptp.p @t84))) % 0.14/0.38 (define @t86 () (not (tptp.rel_k @t4 @t84))) % 0.14/0.38 (define @t87 () (tptp.q @t38)) % 0.14/0.38 (define @t88 () (tptp.rel_k @t4 @t38)) % 0.14/0.38 (define @t89 () (not @t88)) % 0.14/0.38 (define @t90 () (forall @t41 (or @t89 @t87))) % 0.14/0.38 (define @t91 () (not @t90)) % 0.14/0.38 (define @t92 () (not @t87)) % 0.14/0.38 (define @t93 () (tptp.p @t38)) % 0.14/0.38 (define @t94 () (not @t93)) % 0.14/0.38 (define @t95 () (not (forall @t41 (or @t89 @t94 @t92)))) % 0.14/0.38 (define @t96 () (or @t95 @t91 @t86 @t85)) % 0.14/0.38 (define @t97 () (or @t86 @t85)) % 0.14/0.38 (define @t98 () (or @t95 @t97 @t91)) % 0.14/0.38 (define @t99 () (@list @t4 @t84)) % 0.14/0.38 (define @t100 () (forall @t99 @t98)) % 0.14/0.38 (define @t101 () (@list @t84)) % 0.14/0.38 (define @t102 () (forall @t101 @t98)) % 0.14/0.38 (define @t103 () (forall @t101 @t97)) % 0.14/0.38 (define @t104 () (or @t95 @t103 @t91)) % 0.14/0.38 (define @t105 () (or @t95 (forall @t41 (or @t89 @t94)) @t91)) % 0.14/0.38 (define @t106 () (not (tptp.rel_k @t17 @t38))) % 0.14/0.38 (define @t107 () (forall @t41 (or @t106 @t87))) % 0.14/0.38 (define @t108 () (not @t107)) % 0.14/0.38 (define @t109 () (forall @t41 (or @t106 @t94))) % 0.14/0.38 (define @t110 () (not (forall @t41 (or @t106 @t94 @t92)))) % 0.14/0.38 (define @t111 () (@list @t17)) % 0.14/0.38 (define @t112 () (lambda @t111 (or @t110 @t109 @t108))) % 0.14/0.38 (define @t113 () (_ @t112 @t4)) % 0.14/0.38 (define @t114 () (forall @t36 @t113)) % 0.14/0.38 (define @t115 () (_ @t9 @t4)) % 0.14/0.38 (define @t116 () (lambda @t72 (forall @t36 @t115))) % 0.14/0.38 (define @t117 () (lambda @t111 @t110)) % 0.14/0.38 (define @t118 () (_ @t117 @t17)) % 0.14/0.38 (define @t119 () (or @t118 @t109 @t108)) % 0.14/0.38 (define @t120 () (lambda @t111 @t119)) % 0.14/0.38 (define @t121 () (_ @t14 @t17)) % 0.14/0.38 (define @t122 () (or @t121 @t109 @t108)) % 0.14/0.38 (define @t123 () (@list @t14 @t17)) % 0.14/0.38 (define @t124 () (_ tptp.q @t38)) % 0.14/0.38 (define @t125 () (not @t124)) % 0.14/0.38 (define @t126 () (_ tptp.p @t38)) % 0.14/0.38 (define @t127 () (not @t126)) % 0.14/0.38 (define @t128 () (or @t106 @t127 @t125)) % 0.14/0.38 (define @t129 () (or @t127 @t125)) % 0.14/0.38 (define @t130 () (not (_ tptp.p @t17))) % 0.14/0.38 (define @t131 () (lambda @t111 (not (or @t130 (not (_ tptp.q @t17)))))) % 0.14/0.38 (define @t132 () (_ @t131 @t38)) % 0.14/0.38 (define @t133 () (not @t132)) % 0.14/0.38 (define @t134 () (or @t106 @t133)) % 0.14/0.38 (define @t135 () (forall @t41 @t134)) % 0.14/0.38 (define @t136 () (not @t135)) % 0.14/0.38 (define @t137 () (lambda @t111 @t136)) % 0.14/0.38 (define @t138 () (_ @t9 @t38)) % 0.14/0.38 (define @t139 () (not @t138)) % 0.14/0.38 (define @t140 () (not (forall @t41 (or @t106 @t139)))) % 0.14/0.38 (define @t141 () (lambda @t82 @t140)) % 0.14/0.38 (define @t142 () (not @t121)) % 0.14/0.38 (define @t143 () (lambda @t123 (not (or @t130 @t142)))) % 0.14/0.38 (define @t144 () (not (_ @t9 @t17))) % 0.14/0.38 (define @t145 () (not (or @t144 @t142))) % 0.14/0.38 (define @t146 () (lambda @t21 @t145)) % 0.14/0.38 (define @t147 () (_ @t146 tptp.p)) % 0.14/0.38 (define @t148 () (or @t109 @t108)) % 0.14/0.38 (define @t149 () (not @t148)) % 0.14/0.38 (define @t150 () (lambda @t111 @t149)) % 0.14/0.38 (define @t151 () (_ @t150 @t17)) % 0.14/0.38 (define @t152 () (not @t151)) % 0.14/0.38 (define @t153 () (or @t152 @t121)) % 0.14/0.38 (define @t154 () (lambda @t123 @t153)) % 0.14/0.38 (define @t155 () (or @t144 @t121)) % 0.14/0.38 (define @t156 () (lambda @t21 @t155)) % 0.14/0.38 (define @t157 () (lambda @t36 @t90)) % 0.14/0.38 (define @t158 () (_ @t157 @t17)) % 0.14/0.38 (define @t159 () (not @t158)) % 0.14/0.38 (define @t160 () (or @t109 @t159)) % 0.14/0.38 (define @t161 () (not @t160)) % 0.14/0.38 (define @t162 () (lambda @t111 @t161)) % 0.14/0.38 (define @t163 () (lambda @t12 (forall @t41 (or @t89 @t138)))) % 0.14/0.38 (define @t164 () (_ @t163 tptp.q)) % 0.14/0.38 (define @t165 () (not @t109)) % 0.14/0.38 (define @t166 () (lambda @t111 @t165)) % 0.14/0.38 (define @t167 () (_ @t166 @t17)) % 0.14/0.38 (define @t168 () (not @t167)) % 0.14/0.38 (define @t169 () (or @t168 @t142)) % 0.14/0.38 (define @t170 () (not @t169)) % 0.14/0.38 (define @t171 () (lambda @t123 @t170)) % 0.14/0.38 (define @t172 () (_ @t141 tptp.p)) % 0.14/0.38 (define @t173 () (not @t15)) % 0.14/0.38 (define @t174 () (or @t11 @t173)) % 0.14/0.38 (define @t175 () (lambda @t36 @t174)) % 0.14/0.38 (define @t176 () (_ @t175 @t4)) % 0.14/0.38 (define @t177 () (not @t176)) % 0.14/0.38 (define @t178 () (lambda @t36 @t177)) % 0.14/0.38 (define @t179 () (lambda @t36 @t173)) % 0.14/0.38 (define @t180 () (_ @t179 @t4)) % 0.14/0.38 (define @t181 () (or @t11 @t180)) % 0.14/0.38 (define @t182 () (lambda @t36 @t181)) % 0.14/0.38 (define @t183 () (or @t11 @t15)) % 0.14/0.38 (define @t184 () (@list @t14 @t4)) % 0.14/0.38 (define @t185 () (lambda @t184 @t183)) % 0.14/0.38 (define @t186 () (lambda @t36 @t11)) % 0.14/0.38 (define @t187 () (_ @t186 @t4)) % 0.14/0.38 (define @t188 () (or @t187 @t15)) % 0.14/0.38 (define @t189 () (lambda @t184 @t188)) % 0.14/0.38 (define @t190 () (forall @t41 (or @t89 @t139))) % 0.14/0.38 (define @t191 () (lambda @t36 @t190)) % 0.14/0.38 (define @t192 () (_ @t191 @t4)) % 0.14/0.38 (define @t193 () (not @t192)) % 0.14/0.38 (define @t194 () (lambda @t36 @t193)) % 0.14/0.38 (define @t195 () (not @t39)) % 0.14/0.38 (define @t196 () (or @t89 @t195)) % 0.14/0.38 (define @t197 () (_ @t186 @t38)) % 0.14/0.38 (define @t198 () (or @t89 @t197)) % 0.14/0.38 (define @t199 () (forall @t41 @t198)) % 0.14/0.38 (define @t200 () (lambda @t36 @t199)) % 0.14/0.38 (define @t201 () (lambda @t36 @t183)) % 0.14/0.38 (define @t202 () (forall @t99 @t96)) % 0.14/0.38 (define @t203 () (@quantifiers_skolemize @t202 1)) % 0.14/0.38 (define @t204 () (@quantifiers_skolemize @t202 0)) % 0.14/0.38 (define @t205 () (tptp.rel_k @t204 @t203)) % 0.14/0.38 (define @t206 () (tptp.p @t203)) % 0.14/0.38 (define @t207 () (not @t206)) % 0.14/0.38 (define @t208 () (not @t205)) % 0.14/0.38 (define @t209 () (not (tptp.rel_k @t204 @t38))) % 0.14/0.38 (define @t210 () (forall @t41 (or @t209 @t87))) % 0.14/0.38 (define @t211 () (not @t210)) % 0.14/0.38 (define @t212 () (forall @t41 (or @t209 @t94 @t92))) % 0.14/0.38 (define @t213 () (not @t212)) % 0.14/0.38 (define @t214 () (or @t213 @t211 @t208 @t207)) % 0.14/0.38 (define @t215 () (@list true)) % 0.14/0.38 (define @t216 () (@list @t214)) % 0.14/0.38 (define @t217 () (@list @t203)) % 0.14/0.38 (define @t218 () (tptp.q @t203)) % 0.14/0.38 (define @t219 () (not @t218)) % 0.14/0.38 (define @t220 () (or @t208 @t207 @t219)) % 0.14/0.38 (define @t221 () (or @t208 @t218)) % 0.14/0.38 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.14/0.38 (assume @p2 @t1) % 0.14/0.38 (assume @p3 true) % 0.14/0.38 (step @p4 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.14/0.38 (step @p5 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.14/0.38 (step @p6 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.14/0.38 (step @p7 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.14/0.38 (step @p8 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.14/0.38 (step @p9 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.14/0.38 (step @p10 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.14/0.38 (step @p11 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.14/0.38 (step @p12 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.14/0.38 (step @p13 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.14/0.38 (step @p14 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.14/0.38 (step @p15 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.14/0.38 (step @p16 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.14/0.38 (step @p17 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.14/0.38 (step @p18 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.14/0.38 (step @p19 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.14/0.38 (step @p20 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.14/0.38 (step @p21 (= tptp.msymmetric @t52) :rule refl :args (@t52)) % 0.14/0.38 (step @p22 (= tptp.mserial @t54) :rule refl :args (@t54)) % 0.14/0.38 (step @p23 (= tptp.mtransitive @t59) :rule refl :args (@t59)) % 0.14/0.38 (step @p24 (= tptp.meuclidean @t61) :rule refl :args (@t61)) % 0.14/0.38 (step @p25 (= tptp.mpartially_functional @t63) :rule refl :args (@t63)) % 0.14/0.38 (step @p26 (= tptp.mfunctional @t65) :rule refl :args (@t65)) % 0.14/0.38 (step @p27 (= tptp.mweakly_dense @t68) :rule refl :args (@t68)) % 0.14/0.38 (step @p28 (= tptp.mweakly_connected @t69) :rule refl :args (@t69)) % 0.14/0.38 (step @p29 (= tptp.mweakly_directed @t70) :rule refl :args (@t70)) % 0.14/0.38 (step @p30 (= tptp.mvalid @t73) :rule refl :args (@t73)) % 0.14/0.38 (step @p31 (= tptp.minvalid @t74) :rule refl :args (@t74)) % 0.14/0.38 (step @p32 (= tptp.msatisfiable @t75) :rule refl :args (@t75)) % 0.14/0.38 (step @p33 (= tptp.mcountersatisfiable @t76) :rule refl :args (@t76)) % 0.14/0.38 (step @p34 (= tptp.mbox_k @t81) :rule refl :args (@t81)) % 0.14/0.38 (step @p35 (= tptp.mdia_k @t83) :rule refl :args (@t83)) % 0.14/0.38 (step @p36 :rule aci_norm :args ((= @t98 @t96))) % 0.14/0.38 (step @p37 :rule cong :premises (@p36) :args (@t100)) % 0.14/0.38 (step @p38 :rule quant-merge-prenex :args ((= (forall @t36 @t102) @t100))) % 0.14/0.38 (step @p39 :rule refl :args (@t91)) % 0.14/0.38 (step @p40 :rule alpha_equiv :args (@t103 (@list @t84) (@list @t38))) % 0.14/0.38 (step @p41 :rule refl :args (@t95)) % 0.14/0.38 (step @p42 :rule nary_cong :premises (@p41 @p40 @p39) :args (@t104)) % 0.14/0.38 (step @p43 :rule quant-miniscope-or :args ((= @t102 @t104))) % 0.14/0.38 (step @p44 :rule trans :premises (@p43 @p42)) % 0.14/0.38 (step @p45 :rule symm :premises (@p44)) % 0.14/0.38 (step @p46 :rule cong :premises (@p45) :args ((forall @t36 @t105))) % 0.14/0.38 (step @p47 :rule trans :premises (@p46 @p38)) % 0.14/0.38 (step @p48 :rule trans :premises (@p47 @p37)) % 0.14/0.38 (step @p49 :rule beta-reduce :args ((= @t113 @t105))) % 0.14/0.38 (step @p50 :rule cong :premises (@p49) :args (@t114)) % 0.14/0.38 (step @p51 :rule trans :premises (@p50 @p48)) % 0.14/0.38 (step @p52 :rule beta-reduce :args ((= (_ @t116 @t112) @t114))) % 0.14/0.38 (step @p53 :rule trans :premises (@p52 @p51)) % 0.14/0.38 (step @p54 :rule refl :args (@t108)) % 0.14/0.38 (step @p55 :rule refl :args (@t109)) % 0.14/0.38 (step @p56 :rule beta-reduce :args ((= @t118 @t110))) % 0.14/0.38 (step @p57 :rule nary_cong :premises (@p56 @p55 @p54) :args (@t119)) % 0.14/0.38 (step @p58 :rule cong :premises (@p57) :args (@t120)) % 0.14/0.38 (step @p59 :rule beta-reduce :args ((= (_ (lambda @t123 @t122) @t117) @t120))) % 0.14/0.38 (step @p60 :rule trans :premises (@p59 @p58)) % 0.14/0.38 (step @p61 :rule refl :args (@t87)) % 0.14/0.38 (step @p62 :rule refl :args (@t124)) % 0.14/0.38 (step @p63 :rule cong :premises (@p62 @p61) :args ((= @t124 @t87))) % 0.14/0.38 (step @p64 :rule symm :premises (@p63)) % 0.14/0.38 (step @p65 :rule eq_resolve :premises (@p62 @p64)) % 0.14/0.38 (step @p66 :rule cong :premises (@p65) :args (@t125)) % 0.14/0.38 (step @p67 :rule refl :args (@t93)) % 0.14/0.38 (step @p68 :rule refl :args (@t126)) % 0.14/0.38 (step @p69 :rule cong :premises (@p68 @p67) :args ((= @t126 @t93))) % 0.14/0.38 (step @p70 :rule symm :premises (@p69)) % 0.14/0.38 (step @p71 :rule eq_resolve :premises (@p68 @p70)) % 0.14/0.38 (step @p72 :rule cong :premises (@p71) :args (@t127)) % 0.14/0.38 (step @p73 :rule refl :args (@t106)) % 0.14/0.38 (step @p74 :rule nary_cong :premises (@p73 @p72 @p66) :args (@t128)) % 0.14/0.38 (step @p75 :rule cong :premises (@p74) :args ((forall @t41 @t128))) % 0.14/0.38 (step @p76 :rule aci_norm :args ((= (or @t106 @t129) @t128))) % 0.14/0.38 (step @p77 :rule bool-double-not-elim :args (@t129)) % 0.14/0.38 (step @p78 :rule beta-reduce :args ((= @t132 (not @t129)))) % 0.14/0.38 (step @p79 :rule cong :premises (@p78) :args (@t133)) % 0.14/0.38 (step @p80 :rule trans :premises (@p79 @p77)) % 0.14/0.38 (step @p81 :rule refl :args (@t106)) % 0.14/0.38 (step @p82 :rule nary_cong :premises (@p81 @p80) :args (@t134)) % 0.14/0.38 (step @p83 :rule trans :premises (@p82 @p76)) % 0.14/0.38 (step @p84 :rule cong :premises (@p83) :args (@t135)) % 0.14/0.38 (step @p85 :rule trans :premises (@p84 @p75)) % 0.14/0.38 (step @p86 :rule cong :premises (@p85) :args (@t136)) % 0.14/0.38 (step @p87 :rule cong :premises (@p86) :args (@t137)) % 0.14/0.38 (step @p88 :rule beta-reduce :args ((= (_ @t141 @t131) @t137))) % 0.14/0.38 (step @p89 :rule trans :premises (@p88 @p87)) % 0.14/0.38 (step @p90 :rule beta-reduce :args ((= (_ @t143 tptp.q) @t131))) % 0.14/0.38 (step @p91 :rule refl :args (tptp.q)) % 0.14/0.38 (step @p92 :rule beta-reduce :args ((= @t147 @t143))) % 0.14/0.38 (step @p93 :rule ho_cong :premises (@p92 @p91)) % 0.14/0.38 (step @p94 :rule trans :premises (@p93 @p90)) % 0.14/0.38 (step @p95 :rule refl :args (@t141)) % 0.14/0.38 (step @p96 :rule ho_cong :premises (@p95 @p94)) % 0.14/0.38 (step @p97 :rule trans :premises (@p96 @p89)) % 0.14/0.38 (step @p98 :rule aci_norm :args ((= (or @t148 @t121) @t122))) % 0.14/0.38 (step @p99 :rule refl :args (@t121)) % 0.14/0.38 (step @p100 :rule bool-double-not-elim :args (@t148)) % 0.14/0.38 (step @p101 :rule beta-reduce :args ((= @t151 @t149))) % 0.14/0.38 (step @p102 :rule cong :premises (@p101) :args (@t152)) % 0.14/0.38 (step @p103 :rule trans :premises (@p102 @p100)) % 0.14/0.38 (step @p104 :rule nary_cong :premises (@p103 @p99) :args (@t153)) % 0.14/0.38 (step @p105 :rule trans :premises (@p104 @p98)) % 0.14/0.38 (step @p106 :rule cong :premises (@p105) :args (@t154)) % 0.14/0.38 (step @p107 :rule beta-reduce :args ((= (_ @t156 @t150) @t154))) % 0.14/0.38 (step @p108 :rule trans :premises (@p107 @p106)) % 0.14/0.38 (step @p109 :rule beta-reduce :args ((= @t158 @t107))) % 0.14/0.38 (step @p110 :rule cong :premises (@p109) :args (@t159)) % 0.14/0.38 (step @p111 :rule nary_cong :premises (@p55 @p110) :args (@t160)) % 0.14/0.38 (step @p112 :rule cong :premises (@p111) :args (@t161)) % 0.14/0.38 (step @p113 :rule cong :premises (@p112) :args (@t162)) % 0.14/0.38 (step @p114 :rule beta-reduce :args ((= (_ (lambda @t123 (not (or @t109 @t142))) @t157) @t162))) % 0.14/0.38 (step @p115 :rule trans :premises (@p114 @p113)) % 0.14/0.38 (step @p116 :rule beta-reduce :args ((= @t164 @t157))) % 0.14/0.38 (step @p117 :rule refl :args (@t142)) % 0.14/0.38 (step @p118 :rule bool-double-not-elim :args (@t109)) % 0.14/0.38 (step @p119 :rule beta-reduce :args ((= @t167 @t165))) % 0.14/0.38 (step @p120 :rule cong :premises (@p119) :args (@t168)) % 0.14/0.38 (step @p121 :rule trans :premises (@p120 @p118)) % 0.14/0.38 (step @p122 :rule nary_cong :premises (@p121 @p117) :args (@t169)) % 0.14/0.38 (step @p123 :rule cong :premises (@p122) :args (@t170)) % 0.14/0.38 (step @p124 :rule cong :premises (@p123) :args (@t171)) % 0.14/0.38 (step @p125 :rule beta-reduce :args ((= (_ @t146 @t166) @t171))) % 0.14/0.38 (step @p126 :rule trans :premises (@p125 @p124)) % 0.14/0.38 (step @p127 :rule beta-reduce :args ((= @t172 @t166))) % 0.14/0.38 (step @p128 :rule refl :args (@t146)) % 0.14/0.38 (step @p129 :rule ho_cong :premises (@p128 @p127)) % 0.14/0.38 (step @p130 :rule trans :premises (@p129 @p126)) % 0.14/0.38 (step @p131 :rule ho_cong :premises (@p130 @p116)) % 0.14/0.38 (step @p132 :rule trans :premises (@p131 @p115)) % 0.14/0.38 (step @p133 :rule refl :args (@t156)) % 0.14/0.38 (step @p134 :rule ho_cong :premises (@p133 @p132)) % 0.14/0.38 (step @p135 :rule trans :premises (@p134 @p108)) % 0.14/0.38 (step @p136 :rule ho_cong :premises (@p135 @p97)) % 0.14/0.38 (step @p137 :rule trans :premises (@p136 @p60)) % 0.14/0.38 (step @p138 :rule refl :args (@t116)) % 0.14/0.38 (step @p139 :rule ho_cong :premises (@p138 @p137)) % 0.14/0.38 (step @p140 :rule trans :premises (@p139 @p53)) % 0.14/0.38 (step @p141 :rule cong :premises (@p140) :args ((not (_ @t116 (_ (_ @t156 (_ (_ @t146 @t172) @t164)) (_ @t141 (_ @t147 tptp.q))))))) % 0.14/0.38 (step @p142 :rule refl :args (tptp.p)) % 0.14/0.38 (step @p143 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t174)) @t17) @t145))) % 0.14/0.38 (step @p144 :rule refl :args (@t17)) % 0.14/0.38 (step @p145 :rule beta-reduce :args ((= @t176 @t174))) % 0.14/0.38 (step @p146 :rule cong :premises (@p145) :args (@t177)) % 0.14/0.38 (step @p147 :rule cong :premises (@p146) :args (@t178)) % 0.14/0.38 (step @p148 :rule beta-reduce :args ((= (_ @t13 @t175) @t178))) % 0.14/0.38 (step @p149 :rule trans :premises (@p148 @p147)) % 0.14/0.38 (step @p150 :rule beta-reduce :args ((= @t180 @t173))) % 0.14/0.38 (step @p151 :rule refl :args (@t11)) % 0.14/0.38 (step @p152 :rule nary_cong :premises (@p151 @p150) :args (@t181)) % 0.14/0.38 (step @p153 :rule cong :premises (@p152) :args (@t182)) % 0.14/0.38 (step @p154 :rule beta-reduce :args ((= (_ @t185 @t179) @t182))) % 0.14/0.38 (step @p155 :rule 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(step @p171 :rule trans :premises (@p170 @p149)) % 0.14/0.38 (step @p172 :rule ho_cong :premises (@p171 @p144)) % 0.14/0.38 (step @p173 :rule trans :premises (@p172 @p143)) % 0.14/0.38 (step @p174 :rule refl :args (@t14)) % 0.14/0.38 (step @p175 :rule ho_cong :premises (@p6 @p174)) % 0.14/0.38 (step @p176 :rule refl :args (@t9)) % 0.14/0.38 (step @p177 :rule ho_cong :premises (@p6 @p176)) % 0.14/0.38 (step @p178 :rule ho_cong :premises (@p7 @p177)) % 0.14/0.38 (step @p179 :rule ho_cong :premises (@p178 @p175)) % 0.14/0.38 (step @p180 :rule ho_cong :premises (@p6 @p179)) % 0.14/0.38 (step @p181 :rule ho_cong :premises (@p180 @p144)) % 0.14/0.38 (step @p182 :rule trans :premises (@p181 @p173)) % 0.14/0.38 (step @p183 :rule cong :premises (@p182) :args (@t22)) % 0.14/0.38 (step @p184 :rule trans :premises (@p8 @p183)) % 0.14/0.38 (step @p185 :rule ho_cong :premises (@p184 @p142)) % 0.14/0.38 (step @p186 :rule ho_cong :premises (@p185 @p91)) % 0.14/0.38 (step @p187 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t190)) @t17) @t140))) % 0.14/0.38 (step @p188 :rule beta-reduce :args ((= @t192 @t190))) % 0.14/0.38 (step @p189 :rule cong :premises (@p188) :args (@t193)) % 0.14/0.38 (step @p190 :rule cong :premises (@p189) :args (@t194)) % 0.14/0.38 (step @p191 :rule beta-reduce :args ((= (_ @t13 @t191) @t194))) % 0.14/0.38 (step @p192 :rule trans :premises (@p191 @p190)) % 0.14/0.38 (step @p193 :rule refl :args (@t138)) % 0.14/0.38 (step @p194 :rule refl :args (@t39)) % 0.14/0.38 (step @p195 :rule cong :premises (@p194 @p193) :args ((= @t39 @t138))) % 0.14/0.38 (step @p196 :rule symm :premises (@p195)) % 0.14/0.38 (step @p197 :rule eq_resolve :premises (@p194 @p196)) % 0.14/0.38 (step @p198 :rule cong :premises (@p197) :args (@t195)) % 0.14/0.38 (step @p199 :rule refl :args (@t89)) % 0.14/0.38 (step @p200 :rule nary_cong :premises (@p199 @p198) :args (@t196)) % 0.14/0.38 (step @p201 :rule cong :premises (@p200) :args ((forall @t41 @t196))) % 0.14/0.38 (step @p202 :rule beta-reduce :args ((= @t197 @t195))) % 0.14/0.38 (step @p203 :rule refl :args (@t89)) % 0.14/0.38 (step @p204 :rule nary_cong :premises (@p203 @p202) :args (@t198)) % 0.14/0.38 (step @p205 :rule cong :premises (@p204) :args (@t199)) % 0.14/0.38 (step @p206 :rule trans :premises (@p205 @p201)) % 0.14/0.38 (step @p207 :rule cong :premises (@p206) :args (@t200)) % 0.14/0.38 (step @p208 :rule beta-reduce :args ((= (_ @t163 @t186) @t200))) % 0.14/0.38 (step @p209 :rule trans :premises (@p208 @p207)) % 0.14/0.38 (step @p210 :rule refl :args (@t163)) % 0.14/0.38 (step @p211 :rule ho_cong :premises (@p210 @p163)) % 0.14/0.38 (step @p212 :rule trans :premises (@p211 @p209)) % 0.14/0.38 (step @p213 :rule ho_cong :premises (@p169 @p212)) % 0.14/0.38 (step @p214 :rule trans :premises (@p213 @p192)) % 0.14/0.38 (step @p215 :rule ho_cong :premises (@p214 @p144)) % 0.14/0.38 (step @p216 :rule trans :premises (@p215 @p187)) % 0.14/0.38 (step @p217 :rule refl :args (@t88)) % 0.14/0.38 (step @p218 :rule refl :args (@t77)) % 0.14/0.38 (step @p219 :rule cong :premises (@p218 @p217) :args ((= @t77 @t88))) % 0.14/0.38 (step @p220 :rule symm :premises (@p219)) % 0.14/0.38 (step @p221 :rule eq_resolve :premises (@p218 @p220)) % 0.14/0.38 (step @p222 :rule cong :premises (@p221) :args (@t78)) % 0.14/0.38 (step @p223 :rule nary_cong :premises (@p222 @p197) :args (@t79)) % 0.14/0.38 (step @p224 :rule cong :premises (@p223) :args (@t80)) % 0.14/0.38 (step @p225 :rule cong :premises (@p224) :args (@t81)) % 0.14/0.38 (step @p226 :rule trans :premises (@p34 @p225)) % 0.14/0.38 (step @p227 :rule ho_cong :premises (@p226 @p177)) % 0.14/0.38 (step @p228 :rule ho_cong :premises (@p6 @p227)) % 0.14/0.38 (step @p229 :rule ho_cong :premises (@p228 @p144)) % 0.14/0.38 (step @p230 :rule trans :premises (@p229 @p216)) % 0.14/0.38 (step @p231 :rule cong :premises (@p230) :args (@t83)) % 0.14/0.38 (step @p232 :rule trans :premises (@p35 @p231)) % 0.14/0.38 (step @p233 :rule ho_cong :premises (@p232 @p186)) % 0.14/0.38 (step @p234 :rule ho_cong :premises (@p226 @p91)) % 0.14/0.38 (step @p235 :rule ho_cong :premises (@p232 @p142)) % 0.14/0.38 (step @p236 :rule ho_cong :premises (@p184 @p235)) % 0.14/0.38 (step @p237 :rule ho_cong :premises (@p236 @p234)) % 0.14/0.38 (step @p238 :rule beta-reduce :args ((= (_ @t201 @t17) @t155))) % 0.14/0.38 (step @p239 :rule beta-reduce :args ((= (_ @t185 @t14) @t201))) % 0.14/0.38 (step @p240 :rule ho_cong :premises (@p166 @p174)) % 0.14/0.38 (step @p241 :rule trans :premises (@p240 @p239)) % 0.14/0.38 (step @p242 :rule ho_cong :premises (@p241 @p144)) % 0.14/0.38 (step @p243 :rule trans :premises (@p242 @p238)) % 0.14/0.38 (step @p244 :rule ho_cong :premises (@p178 @p174)) % 0.14/0.38 (step @p245 :rule ho_cong :premises (@p244 @p144)) % 0.14/0.38 (step @p246 :rule trans :premises (@p245 @p243)) % 0.14/0.38 (step @p247 :rule cong :premises (@p246) :args (@t23)) % 0.14/0.38 (step @p248 :rule trans :premises (@p9 @p247)) % 0.14/0.38 (step @p249 :rule ho_cong :premises (@p248 @p237)) % 0.14/0.38 (step @p250 :rule ho_cong :premises (@p249 @p233)) % 0.14/0.38 (step @p251 :rule refl :args (@t115)) % 0.14/0.38 (step @p252 :rule refl :args (@t10)) % 0.14/0.38 (step @p253 :rule cong :premises (@p252 @p251) :args ((= @t10 @t115))) % 0.14/0.38 (step @p254 :rule symm :premises (@p253)) % 0.14/0.38 (step @p255 :rule eq_resolve :premises (@p252 @p254)) % 0.14/0.38 (step @p256 :rule cong :premises (@p255) :args (@t71)) % 0.14/0.38 (step @p257 :rule cong :premises (@p256) :args (@t73)) % 0.14/0.38 (step @p258 :rule trans :premises (@p30 @p257)) % 0.14/0.38 (step @p259 :rule ho_cong :premises (@p258 @p250)) % 0.14/0.38 (step @p260 :rule cong :premises (@p259) :args (@t1)) % 0.14/0.38 (step @p261 :rule trans :premises (@p260 @p141)) % 0.14/0.38 (step @p262 :rule eq_resolve :premises (@p2 @p261)) % 0.14/0.38 (step @p263 :rule skolemize :premises (@p262)) % 0.14/0.38 (step @p264 :rule bool-double-not-elim :args (@t205)) % 0.14/0.38 (step @p265 :rule refl :args (@t214)) % 0.14/0.38 (step @p266 :rule nary_cong :premises (@p265 @p264) :args ((or @t214 (not @t208)))) % 0.14/0.38 (step @p267 :rule cnf_or_neg :args (@t214 2)) % 0.14/0.38 (step @p268 :rule eq_resolve :premises (@p267 @p266)) % 0.14/0.38 (step @p269 :rule reordering :premises (@p268) :args ((or @t205 @t214))) % 0.14/0.38 (step @p270 :rule chain_m_resolution :premises (@p269 @p263) :args (@t205 @t215 @t216)) % 0.14/0.38 (step @p271 :rule bool-double-not-elim :args (@t210)) % 0.14/0.38 (step @p272 :rule nary_cong :premises (@p265 @p271) :args ((or @t214 (not @t211)))) % 0.14/0.38 (step @p273 :rule cnf_or_neg :args (@t214 1)) % 0.14/0.38 (step @p274 :rule eq_resolve :premises (@p273 @p272)) % 0.14/0.38 (step @p275 :rule reordering :premises (@p274) :args ((or @t210 @t214))) % 0.14/0.38 (step @p276 :rule chain_m_resolution :premises (@p275 @p263) :args (@t210 @t215 @t216)) % 0.14/0.38 (step @p277 :rule instantiate :premises (@p276) :args (@t217)) % 0.14/0.38 (step @p278 :rule bool-double-not-elim :args (@t212)) % 0.14/0.38 (step @p279 :rule nary_cong :premises (@p265 @p278) :args ((or @t214 (not @t213)))) % 0.14/0.38 (step @p280 :rule cnf_or_neg :args (@t214 0)) % 0.14/0.38 (step @p281 :rule eq_resolve :premises (@p280 @p279)) % 0.14/0.38 (step @p282 :rule reordering :premises (@p281) :args ((or @t212 @t214))) % 0.14/0.38 (step @p283 :rule chain_m_resolution :premises (@p282 @p263) :args (@t212 @t215 @t216)) % 0.14/0.38 (step @p284 :rule instantiate :premises (@p283) :args (@t217)) % 0.14/0.38 (step @p285 :rule bool-double-not-elim :args (@t206)) % 0.14/0.38 (step @p286 :rule nary_cong :premises (@p265 @p285) :args ((or @t214 (not @t207)))) % 0.14/0.38 (step @p287 :rule cnf_or_neg :args (@t214 3)) % 0.14/0.38 (step @p288 :rule eq_resolve :premises (@p287 @p286)) % 0.14/0.38 (step @p289 :rule reordering :premises (@p288) :args ((or @t206 @t214))) % 0.14/0.38 (step @p290 :rule chain_m_resolution :premises (@p289 @p263) :args (@t206 @t215 @t216)) % 0.14/0.38 (step @p291 :rule cnf_or_pos :args (@t220)) % 0.14/0.38 (step @p292 :rule reordering :premises (@p291) :args ((or @t208 @t207 @t219 (not @t220)))) % 0.14/0.38 (step @p293 :rule chain_m_resolution :premises (@p292 @p270 @p290 @p284) :args (@t219 (@list false false false) (@list @t205 @t206 @t220))) % 0.14/0.38 (step @p294 :rule cnf_or_pos :args (@t221)) % 0.14/0.38 (step @p295 :rule reordering :premises (@p294) :args ((or @t208 @t218 (not @t221)))) % 0.14/0.38 (step @p296 false :rule chain_m_resolution :premises (@p295 @p293 @p277 @p270) :args (false (@list true false false) (@list @t218 @t221 @t205))) % 0.14/0.38 ) % 0.14/0.38 % SZS output end Proof % 0.14/0.38 % cvc5 exiting %------------------------------------------------------------------------------