%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO429^1 : 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 : n015.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 09:12:38 AM UTC 2026 % Result : Theorem 0.39s 0.61s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO429^1 : 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 % 0.18/0.35 % Computer : n015.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Wed Jun 3 00:07:49 EDT 2026 % 0.18/0.35 % CPUTime : % 0.29/0.51 %----Proving TH0 % 0.39/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.61 % SZS status Theorem % 0.39/0.61 % SZS output start Proof % 0.39/0.61 ( % 0.39/0.61 (declare-sort $$unsorted 0) % 0.39/0.61 (declare-sort tptp.mu 0) % 0.39/0.61 (declare-const tptp.rel_b (-> $$unsorted $$unsorted Bool)) % 0.39/0.61 (declare-const tptp.p (-> $$unsorted Bool)) % 0.39/0.61 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.39/0.61 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.39/0.61 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.39/0.61 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.39/0.61 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.39/0.61 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.39/0.61 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.61 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.39/0.61 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.61 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.39/0.61 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.39/0.61 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.39/0.61 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.39/0.61 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.39/0.61 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.39/0.61 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.39/0.61 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.39/0.61 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.39/0.61 (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)))))))) % 0.39/0.61 (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)))))))) % 0.39/0.61 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.39/0.61 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 0.39/0.61 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.39/0.61 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 0.39/0.61 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.39/0.61 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 0.39/0.61 (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))))))))))))) % 0.39/0.61 (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)))))) % 0.39/0.61 (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))))))) % 0.39/0.61 (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)))))) % 0.39/0.61 (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))))))) % 0.39/0.61 (define tptp.mbox_b () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_b _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.39/0.61 (define tptp.mdia_b () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_b (_ tptp.mnot _let_2))) _let_1))))) % 0.39/0.61 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mdia_b (_ tptp.mbox_b tptp.p))) (_ tptp.mbox_b (_ tptp.mdia_b tptp.p)))))) % 0.39/0.61 (define @t2 () (@var "Y" tptp.mu)) % 0.39/0.61 (define @t3 () (@var "X" tptp.mu)) % 0.39/0.61 (define @t4 () (@var "W" $$unsorted)) % 0.39/0.61 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.39/0.61 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.39/0.61 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.39/0.61 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.39/0.61 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.39/0.61 (define @t10 () (_ @t9 @t4)) % 0.39/0.61 (define @t11 () (not @t10)) % 0.39/0.61 (define @t12 () (@list @t9 @t4)) % 0.39/0.61 (define @t13 () (lambda @t12 @t11)) % 0.39/0.61 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.39/0.61 (define @t15 () (_ @t14 @t4)) % 0.39/0.61 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.39/0.61 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.39/0.61 (define @t18 () (_ tptp.mnot @t14)) % 0.39/0.61 (define @t19 () (_ tptp.mnot @t9)) % 0.39/0.61 (define @t20 () (_ tptp.mor @t19)) % 0.39/0.61 (define @t21 () (@list @t9 @t14 @t17)) % 0.39/0.61 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.39/0.61 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.39/0.61 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.39/0.61 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.39/0.61 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.39/0.61 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.39/0.61 (define @t28 () (_ @t27 @t3)) % 0.39/0.61 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.39/0.61 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.39/0.61 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.39/0.61 (define @t32 () (_ @t31 @t30)) % 0.39/0.61 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.39/0.61 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.39/0.61 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.39/0.61 (define @t36 () (@list @t4)) % 0.39/0.61 (define @t37 () (lambda @t36 true)) % 0.39/0.61 (define @t38 () (@var "V" $$unsorted)) % 0.39/0.61 (define @t39 () (_ @t9 @t38)) % 0.39/0.61 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.39/0.61 (define @t41 () (@list @t38)) % 0.39/0.61 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.39/0.61 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.39/0.61 (define @t44 () (@var "S" $$unsorted)) % 0.39/0.61 (define @t45 () (_ @t40 @t44)) % 0.39/0.61 (define @t46 () (@list @t44)) % 0.39/0.61 (define @t47 () (@list @t40)) % 0.39/0.61 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.39/0.61 (define @t49 () (@var "T" $$unsorted)) % 0.39/0.61 (define @t50 () (_ @t40 @t49)) % 0.39/0.61 (define @t51 () (_ @t50 @t44)) % 0.39/0.61 (define @t52 () (_ @t45 @t49)) % 0.39/0.61 (define @t53 () (@list @t44 @t49)) % 0.39/0.61 (define @t54 () (forall @t53 (=> @t52 @t51))) % 0.39/0.61 (define @t55 () (lambda @t47 @t54)) % 0.39/0.61 (define @t56 () (@list @t49)) % 0.39/0.61 (define @t57 () (lambda @t47 (forall @t46 (exists @t56 @t52)))) % 0.39/0.61 (define @t58 () (@var "U" $$unsorted)) % 0.39/0.61 (define @t59 () (_ @t45 @t58)) % 0.39/0.61 (define @t60 () (_ @t50 @t58)) % 0.39/0.61 (define @t61 () (@list @t44 @t49 @t58)) % 0.39/0.61 (define @t62 () (lambda @t47 (forall @t61 (=> (and @t52 @t60) @t59)))) % 0.39/0.61 (define @t63 () (and @t52 @t59)) % 0.39/0.61 (define @t64 () (lambda @t47 (forall @t61 (=> @t63 @t60)))) % 0.39/0.61 (define @t65 () (= @t49 @t58)) % 0.39/0.61 (define @t66 () (lambda @t47 (forall @t61 (=> @t63 @t65)))) % 0.39/0.61 (define @t67 () (@list @t58)) % 0.39/0.61 (define @t68 () (lambda @t47 (forall @t46 (exists @t56 (and @t52 (forall @t67 (=> @t59 @t65))))))) % 0.39/0.61 (define @t69 () (_ @t40 @t58)) % 0.39/0.61 (define @t70 () (_ @t69 @t49)) % 0.39/0.61 (define @t71 () (lambda @t47 (forall @t61 (=> @t52 (exists @t67 (and @t59 @t70)))))) % 0.39/0.61 (define @t72 () (lambda @t47 (forall @t61 (=> @t63 (or @t60 @t65 @t70))))) % 0.39/0.61 (define @t73 () (lambda @t47 (forall @t61 (=> @t63 (exists @t41 (and (_ @t50 @t38) (_ @t69 @t38))))))) % 0.39/0.61 (define @t74 () (forall @t36 @t10)) % 0.39/0.61 (define @t75 () (@list @t9)) % 0.39/0.61 (define @t76 () (lambda @t75 @t74)) % 0.39/0.61 (define @t77 () (lambda @t75 (forall @t36 @t11))) % 0.39/0.61 (define @t78 () (lambda @t75 (exists @t36 @t10))) % 0.39/0.61 (define @t79 () (lambda @t75 (exists @t36 @t11))) % 0.39/0.61 (define @t80 () (_ (_ tptp.rel_b @t4) @t38)) % 0.39/0.61 (define @t81 () (not @t80)) % 0.39/0.61 (define @t82 () (or @t81 @t39)) % 0.39/0.61 (define @t83 () (forall @t41 @t82)) % 0.39/0.61 (define @t84 () (lambda @t12 @t83)) % 0.39/0.61 (define @t85 () (@list @t9 @t17)) % 0.39/0.61 (define @t86 () (lambda @t85 (_ (_ tptp.mnot (_ tptp.mbox_b @t19)) @t17))) % 0.39/0.61 (define @t87 () (_ @t40 @t49 @t44)) % 0.39/0.61 (define @t88 () (_ @t40 @t44 @t49)) % 0.39/0.61 (define @t89 () (not @t52)) % 0.39/0.61 (define @t90 () (or @t89 @t51)) % 0.39/0.61 (define @t91 () (@var "BOUND_VARIABLE_8461" $$unsorted)) % 0.39/0.61 (define @t92 () (not (tptp.p @t91))) % 0.39/0.61 (define @t93 () (@var "BOUND_VARIABLE_8507" $$unsorted)) % 0.39/0.61 (define @t94 () (@list @t91)) % 0.39/0.61 (define @t95 () (not (forall @t94 (or (not (tptp.rel_b @t93 @t91)) @t92)))) % 0.39/0.61 (define @t96 () (not (tptp.rel_b @t4 @t93))) % 0.39/0.61 (define @t97 () (@var "BOUND_VARIABLE_8424" $$unsorted)) % 0.39/0.61 (define @t98 () (tptp.p @t97)) % 0.39/0.62 (define @t99 () (@var "BOUND_VARIABLE_8497" $$unsorted)) % 0.39/0.62 (define @t100 () (@list @t97)) % 0.39/0.62 (define @t101 () (not (forall @t100 (or (not (tptp.rel_b @t99 @t97)) @t98)))) % 0.39/0.62 (define @t102 () (not (tptp.rel_b @t4 @t99))) % 0.39/0.62 (define @t103 () (or @t102 @t101 @t96 @t95)) % 0.39/0.62 (define @t104 () (@list @t4 @t99 @t93)) % 0.39/0.62 (define @t105 () (forall @t104 @t103)) % 0.39/0.62 (define @t106 () (@quantifiers_skolemize @t105 2)) % 0.39/0.62 (define @t107 () (@quantifiers_skolemize @t105 0)) % 0.39/0.62 (define @t108 () (or @t96 @t95)) % 0.39/0.62 (define @t109 () (or @t102 @t101)) % 0.39/0.62 (define @t110 () (or @t109 @t108)) % 0.39/0.62 (define @t111 () (forall @t104 @t110)) % 0.39/0.62 (define @t112 () (forall (@list @t99 @t93) @t110)) % 0.39/0.62 (define @t113 () (forall (@list @t93) @t108)) % 0.39/0.62 (define @t114 () (@list @t38)) % 0.39/0.62 (define @t115 () (forall (@list @t99) @t109)) % 0.39/0.62 (define @t116 () (or @t115 @t113)) % 0.39/0.62 (define @t117 () (not (forall @t94 (or (not (tptp.rel_b @t38 @t91)) @t92)))) % 0.39/0.62 (define @t118 () (tptp.rel_b @t4 @t38)) % 0.39/0.62 (define @t119 () (not @t118)) % 0.39/0.62 (define @t120 () (forall @t41 (or @t119 @t117))) % 0.39/0.62 (define @t121 () (forall @t100 (or (not (tptp.rel_b @t38 @t97)) @t98))) % 0.39/0.62 (define @t122 () (not @t121)) % 0.39/0.62 (define @t123 () (or (forall @t41 (or @t119 @t122)) @t120)) % 0.39/0.62 (define @t124 () (not (tptp.rel_b @t17 @t38))) % 0.39/0.62 (define @t125 () (forall @t41 (or @t124 @t117))) % 0.39/0.62 (define @t126 () (forall @t41 (or @t124 @t122))) % 0.39/0.62 (define @t127 () (@list @t17)) % 0.39/0.62 (define @t128 () (lambda @t127 (or @t126 @t125))) % 0.39/0.62 (define @t129 () (_ @t128 @t4)) % 0.39/0.62 (define @t130 () (forall @t36 @t129)) % 0.39/0.62 (define @t131 () (_ @t9 @t4)) % 0.39/0.62 (define @t132 () (lambda @t75 (forall @t36 @t131))) % 0.39/0.62 (define @t133 () (lambda @t36 @t120)) % 0.39/0.62 (define @t134 () (_ @t133 @t17)) % 0.39/0.62 (define @t135 () (or @t126 @t134)) % 0.39/0.62 (define @t136 () (lambda @t127 @t135)) % 0.39/0.62 (define @t137 () (_ @t14 @t17)) % 0.39/0.62 (define @t138 () (@list @t14 @t17)) % 0.39/0.62 (define @t139 () (tptp.p @t38)) % 0.39/0.62 (define @t140 () (forall @t41 (or @t124 (not @t139)))) % 0.39/0.62 (define @t141 () (not @t140)) % 0.39/0.62 (define @t142 () (lambda @t127 @t141)) % 0.39/0.62 (define @t143 () (or @t119 (_ @t142 @t38))) % 0.39/0.62 (define @t144 () (forall @t41 @t143)) % 0.39/0.62 (define @t145 () (lambda @t36 @t144)) % 0.39/0.62 (define @t146 () (_ @t9 @t38)) % 0.39/0.62 (define @t147 () (lambda @t12 (forall @t41 (or @t119 @t146)))) % 0.39/0.62 (define @t148 () (not @t146)) % 0.39/0.62 (define @t149 () (not (forall @t41 (or @t124 @t148)))) % 0.39/0.62 (define @t150 () (lambda @t85 @t149)) % 0.39/0.62 (define @t151 () (_ @t150 tptp.p)) % 0.39/0.62 (define @t152 () (not @t126)) % 0.39/0.62 (define @t153 () (lambda @t127 @t152)) % 0.39/0.62 (define @t154 () (_ @t153 @t17)) % 0.39/0.62 (define @t155 () (not @t154)) % 0.39/0.62 (define @t156 () (or @t155 @t137)) % 0.39/0.62 (define @t157 () (lambda @t138 @t156)) % 0.39/0.62 (define @t158 () (or (not (_ @t9 @t17)) @t137)) % 0.39/0.62 (define @t159 () (lambda @t21 @t158)) % 0.39/0.62 (define @t160 () (forall @t41 (or @t119 @t139))) % 0.39/0.62 (define @t161 () (lambda @t36 @t160)) % 0.39/0.62 (define @t162 () (not (_ @t161 @t38))) % 0.39/0.62 (define @t163 () (or @t124 @t162)) % 0.39/0.62 (define @t164 () (forall @t41 @t163)) % 0.39/0.62 (define @t165 () (not @t164)) % 0.39/0.62 (define @t166 () (lambda @t127 @t165)) % 0.39/0.62 (define @t167 () (_ @t147 tptp.p)) % 0.39/0.62 (define @t168 () (forall @t41 (or @t119 @t148))) % 0.39/0.62 (define @t169 () (lambda @t36 @t168)) % 0.39/0.62 (define @t170 () (_ @t169 @t4)) % 0.39/0.62 (define @t171 () (not @t170)) % 0.39/0.62 (define @t172 () (lambda @t36 @t171)) % 0.39/0.62 (define @t173 () (not @t39)) % 0.39/0.62 (define @t174 () (or @t119 @t173)) % 0.39/0.62 (define @t175 () (lambda @t36 @t11)) % 0.39/0.62 (define @t176 () (_ @t175 @t38)) % 0.39/0.62 (define @t177 () (or @t119 @t176)) % 0.39/0.62 (define @t178 () (forall @t41 @t177)) % 0.39/0.62 (define @t179 () (lambda @t36 @t178)) % 0.39/0.62 (define @t180 () (or @t11 @t15)) % 0.39/0.62 (define @t181 () (lambda @t36 @t180)) % 0.39/0.62 (define @t182 () (@list @t14 @t4)) % 0.39/0.62 (define @t183 () (_ @t175 @t4)) % 0.39/0.62 (define @t184 () (or @t183 @t15)) % 0.39/0.62 (define @t185 () (lambda @t182 @t184)) % 0.39/0.62 (define @t186 () (tptp.rel_b @t107 @t106)) % 0.39/0.62 (define @t187 () (forall @t94 (or (not (tptp.rel_b @t106 @t91)) @t92))) % 0.39/0.62 (define @t188 () (not @t187)) % 0.39/0.62 (define @t189 () (not @t186)) % 0.39/0.62 (define @t190 () (@quantifiers_skolemize @t105 1)) % 0.39/0.62 (define @t191 () (forall @t100 (or (not (tptp.rel_b @t190 @t97)) @t98))) % 0.39/0.62 (define @t192 () (not @t191)) % 0.39/0.62 (define @t193 () (tptp.rel_b @t107 @t190)) % 0.39/0.62 (define @t194 () (not @t193)) % 0.39/0.62 (define @t195 () (or @t194 @t192 @t189 @t188)) % 0.39/0.62 (define @t196 () (@list true)) % 0.39/0.62 (define @t197 () (@list @t195)) % 0.39/0.62 (define @t198 () (tptp.rel_b @t106 @t107)) % 0.39/0.62 (define @t199 () (or @t189 @t198)) % 0.39/0.62 (define @t200 () (@list false false)) % 0.39/0.62 (define @t201 () (@list @t107)) % 0.39/0.62 (define @t202 () (tptp.rel_b @t190 @t107)) % 0.39/0.62 (define @t203 () (or @t194 @t202)) % 0.39/0.62 (define @t204 () (tptp.p @t107)) % 0.39/0.62 (define @t205 () (not @t202)) % 0.39/0.62 (define @t206 () (or @t205 @t204)) % 0.39/0.62 (define @t207 () (not @t204)) % 0.39/0.62 (define @t208 () (not @t198)) % 0.39/0.62 (define @t209 () (or @t208 @t207)) % 0.39/0.62 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.39/0.62 (assume @p2 (_ tptp.mreflexive tptp.rel_b)) % 0.39/0.62 (assume @p3 (_ tptp.msymmetric tptp.rel_b)) % 0.39/0.62 (assume @p4 @t1) % 0.39/0.62 (assume @p5 true) % 0.39/0.62 (step @p6 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.39/0.62 (step @p7 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.39/0.62 (step @p8 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.39/0.62 (step @p9 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.39/0.62 (step @p10 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.39/0.62 (step @p11 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.39/0.62 (step @p12 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.39/0.62 (step @p13 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.39/0.62 (step @p14 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.39/0.62 (step @p15 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.39/0.62 (step @p16 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.39/0.62 (step @p17 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.39/0.62 (step @p18 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.39/0.62 (step @p19 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.39/0.62 (step @p20 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.39/0.62 (step @p21 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.39/0.62 (step @p22 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.39/0.62 (step @p23 (= tptp.msymmetric @t55) :rule refl :args (@t55)) % 0.39/0.62 (step @p24 (= tptp.mserial @t57) :rule refl :args (@t57)) % 0.39/0.62 (step @p25 (= tptp.mtransitive @t62) :rule refl :args (@t62)) % 0.39/0.62 (step @p26 (= tptp.meuclidean @t64) :rule refl :args (@t64)) % 0.39/0.62 (step @p27 (= tptp.mpartially_functional @t66) :rule refl :args (@t66)) % 0.39/0.62 (step @p28 (= tptp.mfunctional @t68) :rule refl :args (@t68)) % 0.39/0.62 (step @p29 (= tptp.mweakly_dense @t71) :rule refl :args (@t71)) % 0.39/0.62 (step @p30 (= tptp.mweakly_connected @t72) :rule refl :args (@t72)) % 0.39/0.62 (step @p31 (= tptp.mweakly_directed @t73) :rule refl :args (@t73)) % 0.39/0.62 (step @p32 (= tptp.mvalid @t76) :rule refl :args (@t76)) % 0.39/0.62 (step @p33 (= tptp.minvalid @t77) :rule refl :args (@t77)) % 0.39/0.62 (step @p34 (= tptp.msatisfiable @t78) :rule refl :args (@t78)) % 0.39/0.62 (step @p35 (= tptp.mcountersatisfiable @t79) :rule refl :args (@t79)) % 0.39/0.62 (step @p36 (= tptp.mbox_b @t84) :rule refl :args (@t84)) % 0.39/0.62 (step @p37 (= tptp.mdia_b @t86) :rule refl :args (@t86)) % 0.39/0.62 (step @p38 :rule beta-reduce :args ((= (_ (lambda @t47 (forall @t53 (or (not @t88) @t87))) tptp.rel_b) (forall @t53 (or (not (tptp.rel_b @t44 @t49)) (tptp.rel_b @t49 @t44)))))) % 0.39/0.62 (step @p39 :rule refl :args (tptp.rel_b)) % 0.39/0.62 (step @p40 :rule refl :args (@t87)) % 0.39/0.62 (step @p41 :rule refl :args (@t51)) % 0.39/0.62 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t51 @t87))) % 0.39/0.62 (step @p43 :rule symm :premises (@p42)) % 0.39/0.62 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 0.39/0.62 (step @p45 :rule refl :args (@t88)) % 0.39/0.62 (step @p46 :rule refl :args (@t52)) % 0.39/0.62 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t52 @t88))) % 0.39/0.62 (step @p48 :rule symm :premises (@p47)) % 0.39/0.62 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.39/0.62 (step @p50 :rule cong :premises (@p49) :args (@t89)) % 0.39/0.62 (step @p51 :rule nary_cong :premises (@p50 @p44) :args (@t90)) % 0.39/0.62 (step @p52 :rule cong :premises (@p51) :args ((forall @t53 @t90))) % 0.39/0.62 (step @p53 :rule bool-impl-elim :args (@t52 @t51)) % 0.39/0.62 (step @p54 :rule cong :premises (@p53) :args (@t54)) % 0.39/0.62 (step @p55 :rule trans :premises (@p54 @p52)) % 0.39/0.62 (step @p56 :rule cong :premises (@p55) :args (@t55)) % 0.39/0.62 (step @p57 :rule trans :premises (@p23 @p56)) % 0.39/0.62 (step @p58 :rule ho_cong :premises (@p57 @p39)) % 0.39/0.62 (step @p59 :rule trans :premises (@p58 @p38)) % 0.39/0.62 (step @p60 :rule eq_resolve :premises (@p3 @p59)) % 0.39/0.62 (step @p61 :rule instantiate :premises (@p60) :args ((@list @t107 @t106))) % 0.39/0.62 (step @p62 :rule aci_norm :args ((= @t110 @t103))) % 0.39/0.62 (step @p63 :rule cong :premises (@p62) :args (@t111)) % 0.39/0.62 (step @p64 :rule quant-merge-prenex :args ((= (forall @t36 @t112) @t111))) % 0.39/0.62 (step @p65 :rule alpha_equiv :args (@t113 (@list @t93) @t114)) % 0.39/0.62 (step @p66 :rule alpha_equiv :args (@t115 (@list @t99) @t114)) % 0.39/0.62 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t116)) % 0.39/0.62 (step @p68 :rule quant-miniscope-or :args ((= @t112 @t116))) % 0.39/0.62 (step @p69 :rule trans :premises (@p68 @p67)) % 0.39/0.62 (step @p70 :rule symm :premises (@p69)) % 0.39/0.62 (step @p71 :rule cong :premises (@p70) :args ((forall @t36 @t123))) % 0.39/0.62 (step @p72 :rule trans :premises (@p71 @p64)) % 0.39/0.62 (step @p73 :rule trans :premises (@p72 @p63)) % 0.39/0.62 (step @p74 :rule beta-reduce :args ((= @t129 @t123))) % 0.39/0.62 (step @p75 :rule cong :premises (@p74) :args (@t130)) % 0.39/0.62 (step @p76 :rule trans :premises (@p75 @p73)) % 0.39/0.62 (step @p77 :rule beta-reduce :args ((= (_ @t132 @t128) @t130))) % 0.39/0.62 (step @p78 :rule trans :premises (@p77 @p76)) % 0.39/0.62 (step @p79 :rule beta-reduce :args ((= @t134 @t125))) % 0.39/0.62 (step @p80 :rule refl :args (@t126)) % 0.39/0.62 (step @p81 :rule nary_cong :premises (@p80 @p79) :args (@t135)) % 0.39/0.62 (step @p82 :rule cong :premises (@p81) :args (@t136)) % 0.39/0.62 (step @p83 :rule beta-reduce :args ((= (_ (lambda @t138 (or @t126 @t137)) @t133) @t136))) % 0.39/0.62 (step @p84 :rule trans :premises (@p83 @p82)) % 0.39/0.62 (step @p85 :rule beta-reduce :args ((= (_ (lambda @t127 (not (forall @t94 (or (not (tptp.rel_b @t17 @t91)) @t92)))) @t38) @t117))) % 0.39/0.62 (step @p86 :rule refl :args (@t38)) % 0.39/0.62 (step @p87 :rule alpha_equiv :args (@t140 @t114 (@list @t91))) % 0.39/0.62 (step @p88 :rule cong :premises (@p87) :args (@t141)) % 0.39/0.62 (step @p89 :rule cong :premises (@p88) :args (@t142)) % 0.39/0.62 (step @p90 :rule ho_cong :premises (@p89 @p86)) % 0.39/0.62 (step @p91 :rule trans :premises (@p90 @p85)) % 0.39/0.62 (step @p92 :rule refl :args (@t119)) % 0.39/0.62 (step @p93 :rule nary_cong :premises (@p92 @p91) :args (@t143)) % 0.39/0.62 (step @p94 :rule cong :premises (@p93) :args (@t144)) % 0.39/0.62 (step @p95 :rule cong :premises (@p94) :args (@t145)) % 0.39/0.62 (step @p96 :rule beta-reduce :args ((= (_ @t147 @t142) @t145))) % 0.39/0.62 (step @p97 :rule trans :premises (@p96 @p95)) % 0.39/0.62 (step @p98 :rule beta-reduce :args ((= @t151 @t142))) % 0.39/0.62 (step @p99 :rule refl :args (@t147)) % 0.39/0.62 (step @p100 :rule ho_cong :premises (@p99 @p98)) % 0.39/0.62 (step @p101 :rule trans :premises (@p100 @p97)) % 0.39/0.62 (step @p102 :rule refl :args (@t137)) % 0.39/0.62 (step @p103 :rule bool-double-not-elim :args (@t126)) % 0.39/0.62 (step @p104 :rule beta-reduce :args ((= @t154 @t152))) % 0.39/0.62 (step @p105 :rule cong :premises (@p104) :args (@t155)) % 0.39/0.62 (step @p106 :rule trans :premises (@p105 @p103)) % 0.39/0.62 (step @p107 :rule nary_cong :premises (@p106 @p102) :args (@t156)) % 0.39/0.62 (step @p108 :rule cong :premises (@p107) :args (@t157)) % 0.39/0.62 (step @p109 :rule beta-reduce :args ((= (_ @t159 @t153) @t157))) % 0.39/0.62 (step @p110 :rule trans :premises (@p109 @p108)) % 0.39/0.62 (step @p111 :rule beta-reduce :args ((= (_ (lambda @t36 (forall @t100 (or (not (tptp.rel_b @t4 @t97)) @t98))) @t38) @t121))) % 0.39/0.62 (step @p112 :rule alpha_equiv :args (@t160 @t114 (@list @t97))) % 0.39/0.62 (step @p113 :rule cong :premises (@p112) :args (@t161)) % 0.39/0.62 (step @p114 :rule ho_cong :premises (@p113 @p86)) % 0.39/0.62 (step @p115 :rule trans :premises (@p114 @p111)) % 0.39/0.62 (step @p116 :rule cong :premises (@p115) :args (@t162)) % 0.39/0.62 (step @p117 :rule refl :args (@t124)) % 0.39/0.62 (step @p118 :rule nary_cong :premises (@p117 @p116) :args (@t163)) % 0.39/0.62 (step @p119 :rule cong :premises (@p118) :args (@t164)) % 0.39/0.62 (step @p120 :rule cong :premises (@p119) :args (@t165)) % 0.39/0.62 (step @p121 :rule cong :premises (@p120) :args (@t166)) % 0.39/0.62 (step @p122 :rule beta-reduce :args ((= (_ @t150 @t161) @t166))) % 0.39/0.62 (step @p123 :rule trans :premises (@p122 @p121)) % 0.39/0.62 (step @p124 :rule beta-reduce :args ((= @t167 @t161))) % 0.39/0.62 (step @p125 :rule refl :args (@t150)) % 0.39/0.62 (step @p126 :rule ho_cong :premises (@p125 @p124)) % 0.39/0.62 (step @p127 :rule trans :premises (@p126 @p123)) % 0.39/0.62 (step @p128 :rule refl :args (@t159)) % 0.39/0.62 (step @p129 :rule ho_cong :premises (@p128 @p127)) % 0.39/0.62 (step @p130 :rule trans :premises (@p129 @p110)) % 0.39/0.62 (step @p131 :rule ho_cong :premises (@p130 @p101)) % 0.39/0.62 (step @p132 :rule trans :premises (@p131 @p84)) % 0.39/0.62 (step @p133 :rule refl :args (@t132)) % 0.39/0.62 (step @p134 :rule ho_cong :premises (@p133 @p132)) % 0.39/0.62 (step @p135 :rule trans :premises (@p134 @p78)) % 0.39/0.62 (step @p136 :rule cong :premises (@p135) :args ((not (_ @t132 (_ (_ @t159 (_ @t150 @t167)) (_ @t147 @t151)))))) % 0.39/0.62 (step @p137 :rule refl :args (tptp.p)) % 0.39/0.62 (step @p138 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t168)) @t17) @t149))) % 0.39/0.62 (step @p139 :rule refl :args (@t17)) % 0.39/0.62 (step @p140 :rule beta-reduce :args ((= @t170 @t168))) % 0.39/0.62 (step @p141 :rule cong :premises (@p140) :args (@t171)) % 0.39/0.62 (step @p142 :rule cong :premises (@p141) :args (@t172)) % 0.39/0.62 (step @p143 :rule beta-reduce :args ((= (_ @t13 @t169) @t172))) % 0.39/0.62 (step @p144 :rule trans :premises (@p143 @p142)) % 0.39/0.62 (step @p145 :rule refl :args (@t146)) % 0.39/0.62 (step @p146 :rule refl :args (@t39)) % 0.39/0.62 (step @p147 :rule cong :premises (@p146 @p145) :args ((= @t39 @t146))) % 0.39/0.62 (step @p148 :rule symm :premises (@p147)) % 0.39/0.62 (step @p149 :rule eq_resolve :premises (@p146 @p148)) % 0.39/0.62 (step @p150 :rule cong :premises (@p149) :args (@t173)) % 0.39/0.62 (step @p151 :rule refl :args (@t119)) % 0.39/0.62 (step @p152 :rule nary_cong :premises (@p151 @p150) :args (@t174)) % 0.39/0.62 (step @p153 :rule cong :premises (@p152) :args ((forall @t41 @t174))) % 0.39/0.62 (step @p154 :rule beta-reduce :args ((= @t176 @t173))) % 0.39/0.62 (step @p155 :rule nary_cong :premises (@p92 @p154) :args (@t177)) % 0.39/0.62 (step @p156 :rule cong :premises (@p155) :args (@t178)) % 0.39/0.62 (step @p157 :rule trans :premises (@p156 @p153)) % 0.39/0.62 (step @p158 :rule cong :premises (@p157) :args (@t179)) % 0.39/0.62 (step @p159 :rule beta-reduce :args ((= (_ @t147 @t175) @t179))) % 0.39/0.62 (step @p160 :rule trans :premises (@p159 @p158)) % 0.39/0.62 (step @p161 :rule beta-reduce :args ((= (_ @t13 @t9) @t175))) % 0.39/0.62 (step @p162 :rule ho_cong :premises (@p99 @p161)) % 0.39/0.62 (step @p163 :rule trans :premises (@p162 @p160)) % 0.39/0.62 (step @p164 :rule refl :args (@t13)) % 0.39/0.62 (step @p165 :rule ho_cong :premises (@p164 @p163)) % 0.39/0.62 (step @p166 :rule trans :premises (@p165 @p144)) % 0.39/0.62 (step @p167 :rule ho_cong :premises (@p166 @p139)) % 0.39/0.62 (step @p168 :rule trans :premises (@p167 @p138)) % 0.39/0.62 (step @p169 :rule refl :args (@t9)) % 0.39/0.62 (step @p170 :rule ho_cong :premises (@p8 @p169)) % 0.39/0.62 (step @p171 :rule refl :args (@t118)) % 0.39/0.62 (step @p172 :rule refl :args (@t80)) % 0.39/0.62 (step @p173 :rule cong :premises (@p172 @p171) :args ((= @t80 @t118))) % 0.39/0.62 (step @p174 :rule symm :premises (@p173)) % 0.39/0.62 (step @p175 :rule eq_resolve :premises (@p172 @p174)) % 0.39/0.62 (step @p176 :rule cong :premises (@p175) :args (@t81)) % 0.39/0.62 (step @p177 :rule nary_cong :premises (@p176 @p149) :args (@t82)) % 0.39/0.62 (step @p178 :rule cong :premises (@p177) :args (@t83)) % 0.39/0.62 (step @p179 :rule cong :premises (@p178) :args (@t84)) % 0.39/0.62 (step @p180 :rule trans :premises (@p36 @p179)) % 0.39/0.62 (step @p181 :rule ho_cong :premises (@p180 @p170)) % 0.39/0.62 (step @p182 :rule ho_cong :premises (@p8 @p181)) % 0.39/0.62 (step @p183 :rule ho_cong :premises (@p182 @p139)) % 0.39/0.62 (step @p184 :rule trans :premises (@p183 @p168)) % 0.39/0.62 (step @p185 :rule cong :premises (@p184) :args (@t86)) % 0.39/0.62 (step @p186 :rule trans :premises (@p37 @p185)) % 0.39/0.62 (step @p187 :rule ho_cong :premises (@p186 @p137)) % 0.39/0.62 (step @p188 :rule ho_cong :premises (@p180 @p187)) % 0.39/0.62 (step @p189 :rule ho_cong :premises (@p180 @p137)) % 0.39/0.62 (step @p190 :rule ho_cong :premises (@p186 @p189)) % 0.39/0.62 (step @p191 :rule beta-reduce :args ((= (_ @t181 @t17) @t158))) % 0.39/0.62 (step @p192 :rule beta-reduce :args ((= (_ (lambda @t182 @t180) @t14) @t181))) % 0.39/0.62 (step @p193 :rule refl :args (@t14)) % 0.39/0.62 (step @p194 :rule refl :args (@t15)) % 0.39/0.62 (step @p195 :rule beta-reduce :args ((= @t183 @t11))) % 0.39/0.62 (step @p196 :rule nary_cong :premises (@p195 @p194) :args (@t184)) % 0.39/0.62 (step @p197 :rule cong :premises (@p196) :args (@t185)) % 0.39/0.62 (step @p198 :rule beta-reduce :args ((= (_ @t16 @t175) @t185))) % 0.39/0.62 (step @p199 :rule trans :premises (@p198 @p197)) % 0.39/0.62 (step @p200 :rule refl :args (@t16)) % 0.39/0.62 (step @p201 :rule ho_cong :premises (@p200 @p161)) % 0.39/0.62 (step @p202 :rule trans :premises (@p201 @p199)) % 0.39/0.62 (step @p203 :rule ho_cong :premises (@p202 @p193)) % 0.39/0.62 (step @p204 :rule trans :premises (@p203 @p192)) % 0.39/0.62 (step @p205 :rule ho_cong :premises (@p204 @p139)) % 0.39/0.62 (step @p206 :rule trans :premises (@p205 @p191)) % 0.39/0.62 (step @p207 :rule ho_cong :premises (@p9 @p170)) % 0.39/0.62 (step @p208 :rule ho_cong :premises (@p207 @p193)) % 0.39/0.62 (step @p209 :rule ho_cong :premises (@p208 @p139)) % 0.39/0.62 (step @p210 :rule trans :premises (@p209 @p206)) % 0.39/0.62 (step @p211 :rule cong :premises (@p210) :args (@t23)) % 0.39/0.62 (step @p212 :rule trans :premises (@p11 @p211)) % 0.39/0.62 (step @p213 :rule ho_cong :premises (@p212 @p190)) % 0.39/0.62 (step @p214 :rule ho_cong :premises (@p213 @p188)) % 0.39/0.62 (step @p215 :rule refl :args (@t131)) % 0.39/0.62 (step @p216 :rule refl :args (@t10)) % 0.39/0.62 (step @p217 :rule cong :premises (@p216 @p215) :args ((= @t10 @t131))) % 0.39/0.62 (step @p218 :rule symm :premises (@p217)) % 0.39/0.62 (step @p219 :rule eq_resolve :premises (@p216 @p218)) % 0.39/0.62 (step @p220 :rule cong :premises (@p219) :args (@t74)) % 0.39/0.62 (step @p221 :rule cong :premises (@p220) :args (@t76)) % 0.39/0.62 (step @p222 :rule trans :premises (@p32 @p221)) % 0.39/0.62 (step @p223 :rule ho_cong :premises (@p222 @p214)) % 0.39/0.62 (step @p224 :rule cong :premises (@p223) :args (@t1)) % 0.39/0.62 (step @p225 :rule trans :premises (@p224 @p136)) % 0.39/0.62 (step @p226 :rule eq_resolve :premises (@p4 @p225)) % 0.39/0.62 (step @p227 :rule skolemize :premises (@p226)) % 0.39/0.62 (step @p228 :rule bool-double-not-elim :args (@t186)) % 0.39/0.62 (step @p229 :rule refl :args (@t195)) % 0.39/0.62 (step @p230 :rule nary_cong :premises (@p229 @p228) :args ((or @t195 (not @t189)))) % 0.39/0.62 (step @p231 :rule cnf_or_neg :args (@t195 2)) % 0.39/0.62 (step @p232 :rule eq_resolve :premises (@p231 @p230)) % 0.39/0.62 (step @p233 :rule reordering :premises (@p232) :args ((or @t186 @t195))) % 0.39/0.62 (step @p234 :rule chain_m_resolution :premises (@p233 @p227) :args (@t186 @t196 @t197)) % 0.39/0.62 (step @p235 :rule cnf_or_pos :args (@t199)) % 0.39/0.62 (step @p236 :rule reordering :premises (@p235) :args ((or @t189 @t198 (not @t199)))) % 0.39/0.62 (step @p237 :rule chain_m_resolution :premises (@p236 @p234 @p61) :args (@t198 @t200 (@list @t186 @t199))) % 0.39/0.62 (step @p238 :rule bool-double-not-elim :args (@t187)) % 0.39/0.62 (step @p239 :rule nary_cong :premises (@p229 @p238) :args ((or @t195 (not @t188)))) % 0.39/0.62 (step @p240 :rule cnf_or_neg :args (@t195 3)) % 0.39/0.62 (step @p241 :rule eq_resolve :premises (@p240 @p239)) % 0.39/0.62 (step @p242 :rule reordering :premises (@p241) :args ((or @t187 @t195))) % 0.39/0.62 (step @p243 :rule chain_m_resolution :premises (@p242 @p227) :args (@t187 @t196 @t197)) % 0.39/0.62 (step @p244 :rule instantiate :premises (@p243) :args (@t201)) % 0.39/0.62 (step @p245 :rule bool-double-not-elim :args (@t191)) % 0.39/0.62 (step @p246 :rule nary_cong :premises (@p229 @p245) :args ((or @t195 (not @t192)))) % 0.39/0.62 (step @p247 :rule cnf_or_neg :args (@t195 1)) % 0.39/0.62 (step @p248 :rule eq_resolve :premises (@p247 @p246)) % 0.39/0.62 (step @p249 :rule reordering :premises (@p248) :args ((or @t191 @t195))) % 0.39/0.62 (step @p250 :rule chain_m_resolution :premises (@p249 @p227) :args (@t191 @t196 @t197)) % 0.39/0.62 (step @p251 :rule instantiate :premises (@p250) :args (@t201)) % 0.39/0.62 (step @p252 :rule instantiate :premises (@p60) :args ((@list @t107 @t190))) % 0.39/0.62 (step @p253 :rule bool-double-not-elim :args (@t193)) % 0.39/0.62 (step @p254 :rule nary_cong :premises (@p229 @p253) :args ((or @t195 (not @t194)))) % 0.39/0.62 (step @p255 :rule cnf_or_neg :args (@t195 0)) % 0.39/0.62 (step @p256 :rule eq_resolve :premises (@p255 @p254)) % 0.39/0.62 (step @p257 :rule reordering :premises (@p256) :args ((or @t193 @t195))) % 0.39/0.62 (step @p258 :rule chain_m_resolution :premises (@p257 @p227) :args (@t193 @t196 @t197)) % 0.39/0.62 (step @p259 :rule cnf_or_pos :args (@t203)) % 0.39/0.62 (step @p260 :rule reordering :premises (@p259) :args ((or @t194 @t202 (not @t203)))) % 0.39/0.62 (step @p261 :rule chain_m_resolution :premises (@p260 @p258 @p252) :args (@t202 @t200 (@list @t193 @t203))) % 0.39/0.62 (step @p262 :rule cnf_or_pos :args (@t206)) % 0.39/0.62 (step @p263 :rule reordering :premises (@p262) :args ((or @t205 @t204 (not @t206)))) % 0.39/0.62 (step @p264 :rule chain_m_resolution :premises (@p263 @p261 @p251) :args (@t204 @t200 (@list @t202 @t206))) % 0.39/0.62 (step @p265 :rule cnf_or_pos :args (@t209)) % 0.39/0.62 (step @p266 :rule reordering :premises (@p265) :args ((or @t208 @t207 (not @t209)))) % 0.39/0.62 (step @p267 false :rule chain_m_resolution :premises (@p266 @p264 @p244 @p237) :args (false (@list false false false) (@list @t204 @t209 @t198))) % 0.39/0.62 ) % 0.39/0.62 % SZS output end Proof % 0.39/0.62 % cvc5 exiting %------------------------------------------------------------------------------