%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO399^1 : 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 : n022.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:12:34 AM UTC 2026 % Result : Theorem 0.40s 0.61s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SYO399^1 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n022.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 00:06:53 EDT 2026 % 0.18/0.35 % CPUTime : % 0.27/0.52 %----Proving TH0 % 0.40/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.61 % SZS status Theorem % 0.40/0.61 % SZS output start Proof % 0.40/0.61 ( % 0.40/0.61 (declare-sort $$unsorted 0) % 0.40/0.61 (declare-sort tptp.mu 0) % 0.40/0.61 (declare-const tptp.rel_k (-> $$unsorted $$unsorted Bool)) % 0.40/0.61 (declare-const tptp.q (-> $$unsorted Bool)) % 0.40/0.61 (declare-const tptp.r (-> $$unsorted Bool)) % 0.40/0.61 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.40/0.61 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.40/0.61 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.40/0.61 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.40/0.61 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.40/0.61 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.40/0.61 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.40/0.61 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.40/0.61 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.40/0.61 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.40/0.61 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.40/0.61 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.40/0.61 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.40/0.61 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.40/0.61 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.40/0.61 (define tptp.mbox () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.40/0.61 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.40/0.61 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.40/0.61 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.40/0.61 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.40/0.61 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "T" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.40/0.61 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.40/0.61 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.40/0.61 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.40/0.61 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.40/0.61 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.40/0.61 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "T" $$unsorted))) (let ((_let_5 (@var "S" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.40/0.61 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.40/0.61 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.40/0.61 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.40/0.61 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.40/0.61 (define tptp.mbox_k () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_k _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.40/0.61 (define tptp.mdia_k () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_k (_ tptp.mnot _let_2))) _let_1))))) % 0.40/0.61 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mequiv (_ tptp.mnot (_ tptp.mdia_k (_ (_ tptp.mand tptp.q) tptp.r)))) (_ tptp.mbox_k (_ (_ tptp.mimplies tptp.q) (_ tptp.mnot tptp.r))))))) % 0.40/0.61 (define @t2 () (@var "Y" tptp.mu)) % 0.40/0.61 (define @t3 () (@var "X" tptp.mu)) % 0.40/0.61 (define @t4 () (@var "W" $$unsorted)) % 0.40/0.61 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.40/0.61 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.40/0.61 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.40/0.61 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.40/0.61 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.40/0.61 (define @t10 () (_ @t9 @t4)) % 0.40/0.61 (define @t11 () (not @t10)) % 0.40/0.61 (define @t12 () (@list @t9 @t4)) % 0.40/0.61 (define @t13 () (lambda @t12 @t11)) % 0.40/0.61 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.40/0.61 (define @t15 () (_ @t14 @t4)) % 0.40/0.61 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.40/0.62 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.40/0.62 (define @t18 () (_ tptp.mnot @t14)) % 0.40/0.62 (define @t19 () (_ tptp.mnot @t9)) % 0.40/0.62 (define @t20 () (_ tptp.mor @t19)) % 0.40/0.62 (define @t21 () (@list @t9 @t14 @t17)) % 0.40/0.62 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.40/0.62 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.40/0.62 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.40/0.62 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.40/0.62 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.40/0.62 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.40/0.62 (define @t28 () (_ @t27 @t3)) % 0.40/0.62 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.40/0.62 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.40/0.62 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.40/0.62 (define @t32 () (_ @t31 @t30)) % 0.40/0.62 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.40/0.62 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.40/0.62 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.40/0.62 (define @t36 () (@list @t4)) % 0.40/0.62 (define @t37 () (lambda @t36 true)) % 0.40/0.62 (define @t38 () (@var "V" $$unsorted)) % 0.40/0.62 (define @t39 () (_ @t9 @t38)) % 0.40/0.62 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.40/0.62 (define @t41 () (@list @t38)) % 0.40/0.62 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.40/0.62 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.40/0.62 (define @t44 () (@var "S" $$unsorted)) % 0.40/0.62 (define @t45 () (_ @t40 @t44)) % 0.40/0.62 (define @t46 () (@list @t44)) % 0.40/0.62 (define @t47 () (@list @t40)) % 0.40/0.62 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.40/0.62 (define @t49 () (@var "T" $$unsorted)) % 0.40/0.62 (define @t50 () (_ @t40 @t49)) % 0.40/0.62 (define @t51 () (_ @t45 @t49)) % 0.40/0.62 (define @t52 () (lambda @t47 (forall (@list @t44 @t49) (=> @t51 (_ @t50 @t44))))) % 0.40/0.62 (define @t53 () (@list @t49)) % 0.40/0.62 (define @t54 () (lambda @t47 (forall @t46 (exists @t53 @t51)))) % 0.40/0.62 (define @t55 () (@var "U" $$unsorted)) % 0.40/0.62 (define @t56 () (_ @t45 @t55)) % 0.40/0.62 (define @t57 () (_ @t50 @t55)) % 0.40/0.62 (define @t58 () (@list @t44 @t49 @t55)) % 0.40/0.62 (define @t59 () (lambda @t47 (forall @t58 (=> (and @t51 @t57) @t56)))) % 0.40/0.62 (define @t60 () (and @t51 @t56)) % 0.40/0.62 (define @t61 () (lambda @t47 (forall @t58 (=> @t60 @t57)))) % 0.40/0.62 (define @t62 () (= @t49 @t55)) % 0.40/0.62 (define @t63 () (lambda @t47 (forall @t58 (=> @t60 @t62)))) % 0.40/0.62 (define @t64 () (@list @t55)) % 0.40/0.62 (define @t65 () (lambda @t47 (forall @t46 (exists @t53 (and @t51 (forall @t64 (=> @t56 @t62))))))) % 0.40/0.62 (define @t66 () (_ @t40 @t55)) % 0.40/0.62 (define @t67 () (_ @t66 @t49)) % 0.40/0.62 (define @t68 () (lambda @t47 (forall @t58 (=> @t51 (exists @t64 (and @t56 @t67)))))) % 0.40/0.62 (define @t69 () (lambda @t47 (forall @t58 (=> @t60 (or @t57 @t62 @t67))))) % 0.40/0.62 (define @t70 () (lambda @t47 (forall @t58 (=> @t60 (exists @t41 (and (_ @t50 @t38) (_ @t66 @t38))))))) % 0.40/0.62 (define @t71 () (forall @t36 @t10)) % 0.40/0.62 (define @t72 () (@list @t9)) % 0.40/0.62 (define @t73 () (lambda @t72 @t71)) % 0.40/0.62 (define @t74 () (lambda @t72 (forall @t36 @t11))) % 0.40/0.62 (define @t75 () (lambda @t72 (exists @t36 @t10))) % 0.40/0.62 (define @t76 () (lambda @t72 (exists @t36 @t11))) % 0.40/0.62 (define @t77 () (_ (_ tptp.rel_k @t4) @t38)) % 0.40/0.62 (define @t78 () (not @t77)) % 0.40/0.62 (define @t79 () (or @t78 @t39)) % 0.40/0.62 (define @t80 () (forall @t41 @t79)) % 0.40/0.62 (define @t81 () (lambda @t12 @t80)) % 0.40/0.62 (define @t82 () (@list @t9 @t17)) % 0.40/0.62 (define @t83 () (lambda @t82 (_ (_ tptp.mnot (_ tptp.mbox_k @t19)) @t17))) % 0.40/0.62 (define @t84 () (tptp.r @t38)) % 0.40/0.62 (define @t85 () (not @t84)) % 0.40/0.62 (define @t86 () (tptp.q @t38)) % 0.40/0.62 (define @t87 () (not @t86)) % 0.40/0.62 (define @t88 () (tptp.rel_k @t4 @t38)) % 0.40/0.62 (define @t89 () (not @t88)) % 0.40/0.62 (define @t90 () (forall @t41 (or @t89 @t87 @t85))) % 0.40/0.62 (define @t91 () (not @t90)) % 0.40/0.62 (define @t92 () (or @t91 @t90)) % 0.40/0.62 (define @t93 () (not (tptp.rel_k @t17 @t38))) % 0.40/0.62 (define @t94 () (forall @t41 (or @t93 @t87 @t85))) % 0.40/0.62 (define @t95 () (not @t94)) % 0.40/0.62 (define @t96 () (or @t95 @t94)) % 0.40/0.62 (define @t97 () (@list @t17)) % 0.40/0.62 (define @t98 () (lambda @t97 @t96)) % 0.40/0.62 (define @t99 () (_ @t98 @t4)) % 0.40/0.62 (define @t100 () (forall @t36 @t99)) % 0.40/0.62 (define @t101 () (_ @t9 @t4)) % 0.40/0.62 (define @t102 () (lambda @t72 (forall @t36 @t101))) % 0.40/0.62 (define @t103 () (not @t96)) % 0.40/0.62 (define @t104 () (lambda @t36 @t90)) % 0.40/0.62 (define @t105 () (_ @t104 @t17)) % 0.40/0.62 (define @t106 () (not @t105)) % 0.40/0.62 (define @t107 () (or @t106 @t94)) % 0.40/0.62 (define @t108 () (not @t107)) % 0.40/0.62 (define @t109 () (or @t95 @t105)) % 0.40/0.62 (define @t110 () (not @t109)) % 0.40/0.62 (define @t111 () (or @t110 @t108)) % 0.40/0.62 (define @t112 () (not @t111)) % 0.40/0.62 (define @t113 () (lambda @t97 @t112)) % 0.40/0.62 (define @t114 () (_ @t14 @t17)) % 0.40/0.62 (define @t115 () (not @t114)) % 0.40/0.62 (define @t116 () (@list @t14 @t17)) % 0.40/0.62 (define @t117 () (_ tptp.r @t38)) % 0.40/0.62 (define @t118 () (not @t117)) % 0.40/0.62 (define @t119 () (_ tptp.q @t38)) % 0.40/0.62 (define @t120 () (not @t119)) % 0.40/0.62 (define @t121 () (or @t89 @t120 @t118)) % 0.40/0.62 (define @t122 () (or @t120 @t118)) % 0.40/0.62 (define @t123 () (not (_ tptp.r @t17))) % 0.40/0.62 (define @t124 () (not (_ tptp.q @t17))) % 0.40/0.62 (define @t125 () (or @t124 @t123)) % 0.40/0.62 (define @t126 () (lambda @t97 @t125)) % 0.40/0.62 (define @t127 () (_ @t126 @t38)) % 0.40/0.62 (define @t128 () (or @t89 @t127)) % 0.40/0.62 (define @t129 () (forall @t41 @t128)) % 0.40/0.62 (define @t130 () (lambda @t36 @t129)) % 0.40/0.62 (define @t131 () (_ @t9 @t38)) % 0.40/0.62 (define @t132 () (lambda @t12 (forall @t41 (or @t89 @t131)))) % 0.40/0.62 (define @t133 () (lambda @t36 (not (_ tptp.r @t4)))) % 0.40/0.62 (define @t134 () (_ @t133 @t17)) % 0.40/0.62 (define @t135 () (or @t124 @t134)) % 0.40/0.62 (define @t136 () (lambda @t97 @t135)) % 0.40/0.62 (define @t137 () (lambda @t116 (or @t124 @t114))) % 0.40/0.62 (define @t138 () (_ @t13 tptp.r)) % 0.40/0.62 (define @t139 () (_ @t9 @t17)) % 0.40/0.62 (define @t140 () (not @t139)) % 0.40/0.62 (define @t141 () (or @t140 @t114)) % 0.40/0.62 (define @t142 () (lambda @t21 @t141)) % 0.40/0.62 (define @t143 () (_ @t142 tptp.q)) % 0.40/0.62 (define @t144 () (or @t115 @t105)) % 0.40/0.62 (define @t145 () (not @t144)) % 0.40/0.62 (define @t146 () (or @t106 @t114)) % 0.40/0.62 (define @t147 () (not @t146)) % 0.40/0.62 (define @t148 () (or @t147 @t145)) % 0.40/0.62 (define @t149 () (not @t148)) % 0.40/0.62 (define @t150 () (lambda @t116 @t149)) % 0.40/0.62 (define @t151 () (or @t115 @t139)) % 0.40/0.62 (define @t152 () (not @t141)) % 0.40/0.62 (define @t153 () (not (or @t152 (not @t151)))) % 0.40/0.62 (define @t154 () (lambda @t21 @t153)) % 0.40/0.62 (define @t155 () (lambda @t97 @t95)) % 0.40/0.62 (define @t156 () (_ @t155 @t4)) % 0.40/0.62 (define @t157 () (not @t156)) % 0.40/0.62 (define @t158 () (lambda @t36 @t157)) % 0.40/0.62 (define @t159 () (or @t93 @t120 @t118)) % 0.40/0.62 (define @t160 () (lambda @t97 (not @t125))) % 0.40/0.62 (define @t161 () (_ @t160 @t38)) % 0.40/0.62 (define @t162 () (not @t161)) % 0.40/0.62 (define @t163 () (or @t93 @t162)) % 0.40/0.62 (define @t164 () (forall @t41 @t163)) % 0.40/0.62 (define @t165 () (not @t164)) % 0.40/0.62 (define @t166 () (lambda @t97 @t165)) % 0.40/0.62 (define @t167 () (not @t131)) % 0.40/0.62 (define @t168 () (not (forall @t41 (or @t93 @t167)))) % 0.40/0.62 (define @t169 () (lambda @t82 @t168)) % 0.40/0.62 (define @t170 () (lambda @t116 (not (or @t124 @t115)))) % 0.40/0.62 (define @t171 () (not (or @t140 @t115))) % 0.40/0.62 (define @t172 () (lambda @t21 @t171)) % 0.40/0.62 (define @t173 () (_ @t172 tptp.q)) % 0.40/0.62 (define @t174 () (or @t11 @t15)) % 0.40/0.62 (define @t175 () (lambda @t36 @t174)) % 0.40/0.62 (define @t176 () (@list @t14 @t4)) % 0.40/0.62 (define @t177 () (lambda @t176 @t174)) % 0.40/0.62 (define @t178 () (lambda @t36 @t11)) % 0.40/0.62 (define @t179 () (_ @t178 @t4)) % 0.40/0.62 (define @t180 () (or @t179 @t15)) % 0.40/0.62 (define @t181 () (lambda @t176 @t180)) % 0.40/0.62 (define @t182 () (not @t15)) % 0.40/0.62 (define @t183 () (or @t11 @t182)) % 0.40/0.62 (define @t184 () (lambda @t36 @t183)) % 0.40/0.62 (define @t185 () (_ @t184 @t4)) % 0.40/0.62 (define @t186 () (not @t185)) % 0.40/0.62 (define @t187 () (lambda @t36 @t186)) % 0.40/0.62 (define @t188 () (lambda @t36 @t182)) % 0.40/0.62 (define @t189 () (_ @t188 @t4)) % 0.40/0.62 (define @t190 () (or @t11 @t189)) % 0.40/0.62 (define @t191 () (lambda @t36 @t190)) % 0.40/0.62 (define @t192 () (forall @t41 (or @t89 @t167))) % 0.40/0.62 (define @t193 () (lambda @t36 @t192)) % 0.40/0.62 (define @t194 () (_ @t193 @t4)) % 0.40/0.62 (define @t195 () (not @t194)) % 0.40/0.62 (define @t196 () (lambda @t36 @t195)) % 0.40/0.62 (define @t197 () (not @t39)) % 0.40/0.62 (define @t198 () (or @t89 @t197)) % 0.40/0.62 (define @t199 () (_ @t178 @t38)) % 0.40/0.62 (define @t200 () (or @t89 @t199)) % 0.40/0.62 (define @t201 () (forall @t41 @t200)) % 0.40/0.62 (define @t202 () (lambda @t36 @t201)) % 0.40/0.62 (define @t203 () (lambda @t97 @t151)) % 0.40/0.62 (define @t204 () (_ @t203 @t17)) % 0.40/0.62 (define @t205 () (not @t204)) % 0.40/0.62 (define @t206 () (or @t152 @t205)) % 0.40/0.62 (define @t207 () (not @t206)) % 0.40/0.62 (define @t208 () (lambda @t97 @t207)) % 0.40/0.62 (define @t209 () (@var "BOUND_VARIABLE_7581" (-> $$unsorted Bool))) % 0.40/0.62 (define @t210 () (not (_ @t209 @t17))) % 0.40/0.62 (define @t211 () (@list @t209 @t17)) % 0.40/0.62 (define @t212 () (@var "BOUND_VARIABLE_7601" (-> $$unsorted Bool))) % 0.40/0.62 (define @t213 () (_ @t212 @t17)) % 0.40/0.62 (define @t214 () (lambda (@list @t212 @t17) (or @t115 @t213))) % 0.40/0.62 (define @t215 () (@list @t14)) % 0.40/0.62 (define @t216 () (lambda @t97 @t141)) % 0.40/0.62 (define @t217 () (_ @t216 @t17)) % 0.40/0.62 (define @t218 () (not @t217)) % 0.40/0.62 (define @t219 () (or @t218 @t210)) % 0.40/0.62 (define @t220 () (not @t219)) % 0.40/0.62 (define @t221 () (lambda @t211 @t220)) % 0.40/0.62 (define @t222 () (lambda @t116 @t141)) % 0.40/0.62 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.40/0.62 (assume @p2 @t1) % 0.40/0.62 (assume @p3 true) % 0.40/0.62 (step @p4 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.40/0.62 (step @p5 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.40/0.62 (step @p6 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.40/0.62 (step @p7 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.40/0.62 (step @p8 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.40/0.62 (step @p9 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.40/0.62 (step @p10 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.40/0.62 (step @p11 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.40/0.62 (step @p12 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.40/0.62 (step @p13 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.40/0.62 (step @p14 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.40/0.62 (step @p15 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.40/0.62 (step @p16 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.40/0.62 (step @p17 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.40/0.62 (step @p18 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.40/0.62 (step @p19 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.40/0.62 (step @p20 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.40/0.62 (step @p21 (= tptp.msymmetric @t52) :rule refl :args (@t52)) % 0.40/0.62 (step @p22 (= tptp.mserial @t54) :rule refl :args (@t54)) % 0.40/0.62 (step @p23 (= tptp.mtransitive @t59) :rule refl :args (@t59)) % 0.40/0.62 (step @p24 (= tptp.meuclidean @t61) :rule refl :args (@t61)) % 0.40/0.62 (step @p25 (= tptp.mpartially_functional @t63) :rule refl :args (@t63)) % 0.40/0.62 (step @p26 (= tptp.mfunctional @t65) :rule refl :args (@t65)) % 0.40/0.62 (step @p27 (= tptp.mweakly_dense @t68) :rule refl :args (@t68)) % 0.40/0.62 (step @p28 (= tptp.mweakly_connected @t69) :rule refl :args (@t69)) % 0.40/0.62 (step @p29 (= tptp.mweakly_directed @t70) :rule refl :args (@t70)) % 0.40/0.62 (step @p30 (= tptp.mvalid @t73) :rule refl :args (@t73)) % 0.40/0.62 (step @p31 (= tptp.minvalid @t74) :rule refl :args (@t74)) % 0.40/0.62 (step @p32 (= tptp.msatisfiable @t75) :rule refl :args (@t75)) % 0.40/0.62 (step @p33 (= tptp.mcountersatisfiable @t76) :rule refl :args (@t76)) % 0.40/0.62 (step @p34 (= tptp.mbox_k @t81) :rule refl :args (@t81)) % 0.40/0.62 (step @p35 (= tptp.mdia_k @t83) :rule refl :args (@t83)) % 0.40/0.62 (step @p36 :rule evaluate :args ((not true))) % 0.40/0.62 (step @p37 :rule quant-unused-vars :args ((= (forall @t36 true) true))) % 0.40/0.62 (step @p38 :rule bool-or-taut2 :args (false @t90 false false)) % 0.40/0.62 (step @p39 :rule cong :premises (@p38) :args ((forall @t36 @t92))) % 0.40/0.62 (step @p40 :rule trans :premises (@p39 @p37)) % 0.40/0.62 (step @p41 :rule beta-reduce :args ((= @t99 @t92))) % 0.40/0.62 (step @p42 :rule cong :premises (@p41) :args (@t100)) % 0.40/0.62 (step @p43 :rule trans :premises (@p42 @p40)) % 0.40/0.62 (step @p44 :rule beta-reduce :args ((= (_ @t102 @t98) @t100))) % 0.40/0.62 (step @p45 :rule trans :premises (@p44 @p43)) % 0.40/0.62 (step @p46 :rule bool-double-not-elim :args (@t96)) % 0.40/0.62 (step @p47 :rule aci_norm :args ((= (or @t103 @t103) @t103))) % 0.40/0.62 (step @p48 :rule refl :args (@t94)) % 0.40/0.62 (step @p49 :rule beta-reduce :args ((= @t105 @t94))) % 0.40/0.62 (step @p50 :rule cong :premises (@p49) :args (@t106)) % 0.40/0.62 (step @p51 :rule nary_cong :premises (@p50 @p48) :args (@t107)) % 0.40/0.62 (step @p52 :rule cong :premises (@p51) :args (@t108)) % 0.40/0.62 (step @p53 :rule refl :args (@t95)) % 0.40/0.62 (step @p54 :rule nary_cong :premises (@p53 @p49) :args (@t109)) % 0.40/0.62 (step @p55 :rule cong :premises (@p54) :args (@t110)) % 0.40/0.62 (step @p56 :rule nary_cong :premises (@p55 @p52) :args (@t111)) % 0.40/0.62 (step @p57 :rule trans :premises (@p56 @p47)) % 0.40/0.62 (step @p58 :rule cong :premises (@p57) :args (@t112)) % 0.40/0.62 (step @p59 :rule trans :premises (@p58 @p46)) % 0.40/0.62 (step @p60 :rule cong :premises (@p59) :args (@t113)) % 0.40/0.62 (step @p61 :rule beta-reduce :args ((= (_ (lambda @t116 (not (or (not (or @t95 @t114)) (not (or @t115 @t94))))) @t104) @t113))) % 0.40/0.62 (step @p62 :rule trans :premises (@p61 @p60)) % 0.40/0.62 (step @p63 :rule refl :args (@t84)) % 0.40/0.62 (step @p64 :rule refl :args (@t117)) % 0.40/0.62 (step @p65 :rule cong :premises (@p64 @p63) :args ((= @t117 @t84))) % 0.40/0.62 (step @p66 :rule symm :premises (@p65)) % 0.40/0.62 (step @p67 :rule eq_resolve :premises (@p64 @p66)) % 0.40/0.62 (step @p68 :rule cong :premises (@p67) :args (@t118)) % 0.40/0.62 (step @p69 :rule refl :args (@t86)) % 0.40/0.62 (step @p70 :rule refl :args (@t119)) % 0.40/0.62 (step @p71 :rule cong :premises (@p70 @p69) :args ((= @t119 @t86))) % 0.40/0.62 (step @p72 :rule symm :premises (@p71)) % 0.40/0.62 (step @p73 :rule eq_resolve :premises (@p70 @p72)) % 0.40/0.62 (step @p74 :rule cong :premises (@p73) :args (@t120)) % 0.40/0.62 (step @p75 :rule refl :args (@t89)) % 0.40/0.62 (step @p76 :rule nary_cong :premises (@p75 @p74 @p68) :args (@t121)) % 0.40/0.62 (step @p77 :rule cong :premises (@p76) :args ((forall @t41 @t121))) % 0.40/0.62 (step @p78 :rule aci_norm :args ((= (or @t89 @t122) @t121))) % 0.40/0.62 (step @p79 :rule beta-reduce :args ((= @t127 @t122))) % 0.40/0.62 (step @p80 :rule refl :args (@t89)) % 0.40/0.62 (step @p81 :rule nary_cong :premises (@p80 @p79) :args (@t128)) % 0.40/0.62 (step @p82 :rule trans :premises (@p81 @p78)) % 0.40/0.62 (step @p83 :rule cong :premises (@p82) :args (@t129)) % 0.40/0.62 (step @p84 :rule trans :premises (@p83 @p77)) % 0.40/0.62 (step @p85 :rule cong :premises (@p84) :args (@t130)) % 0.40/0.62 (step @p86 :rule beta-reduce :args ((= (_ @t132 @t126) @t130))) % 0.40/0.62 (step @p87 :rule trans :premises (@p86 @p85)) % 0.40/0.62 (step @p88 :rule beta-reduce :args ((= @t134 @t123))) % 0.40/0.62 (step @p89 :rule refl :args (@t124)) % 0.40/0.62 (step @p90 :rule nary_cong :premises (@p89 @p88) :args (@t135)) % 0.40/0.62 (step @p91 :rule cong :premises (@p90) :args (@t136)) % 0.40/0.62 (step @p92 :rule beta-reduce :args ((= (_ @t137 @t133) @t136))) % 0.40/0.62 (step @p93 :rule trans :premises (@p92 @p91)) % 0.40/0.62 (step @p94 :rule beta-reduce :args ((= @t138 @t133))) % 0.40/0.62 (step @p95 :rule beta-reduce :args ((= @t143 @t137))) % 0.40/0.62 (step @p96 :rule ho_cong :premises (@p95 @p94)) % 0.40/0.62 (step @p97 :rule trans :premises (@p96 @p93)) % 0.40/0.62 (step @p98 :rule refl :args (@t132)) % 0.40/0.62 (step @p99 :rule ho_cong :premises (@p98 @p97)) % 0.40/0.62 (step @p100 :rule trans :premises (@p99 @p87)) % 0.40/0.62 (step @p101 :rule refl :args (@t115)) % 0.40/0.62 (step @p102 :rule nary_cong :premises (@p101 @p49) :args (@t144)) % 0.40/0.62 (step @p103 :rule cong :premises (@p102) :args (@t145)) % 0.40/0.62 (step @p104 :rule refl :args (@t114)) % 0.40/0.62 (step @p105 :rule nary_cong :premises (@p50 @p104) :args (@t146)) % 0.40/0.62 (step @p106 :rule cong :premises (@p105) :args (@t147)) % 0.40/0.62 (step @p107 :rule nary_cong :premises (@p106 @p103) :args (@t148)) % 0.40/0.62 (step @p108 :rule cong :premises (@p107) :args (@t149)) % 0.40/0.62 (step @p109 :rule cong :premises (@p108) :args (@t150)) % 0.40/0.62 (step @p110 :rule beta-reduce :args ((= (_ @t154 @t104) @t150))) % 0.40/0.62 (step @p111 :rule trans :premises (@p110 @p109)) % 0.40/0.62 (step @p112 :rule bool-double-not-elim :args (@t90)) % 0.40/0.62 (step @p113 :rule beta-reduce :args ((= @t156 @t91))) % 0.40/0.62 (step @p114 :rule cong :premises (@p113) :args (@t157)) % 0.40/0.62 (step @p115 :rule trans :premises (@p114 @p112)) % 0.40/0.62 (step @p116 :rule cong :premises (@p115) :args (@t158)) % 0.40/0.62 (step @p117 :rule beta-reduce :args ((= (_ @t13 @t155) @t158))) % 0.40/0.62 (step @p118 :rule trans :premises (@p117 @p116)) % 0.40/0.62 (step @p119 :rule refl :args (@t93)) % 0.40/0.62 (step @p120 :rule nary_cong :premises (@p119 @p74 @p68) :args (@t159)) % 0.40/0.62 (step @p121 :rule cong :premises (@p120) :args ((forall @t41 @t159))) % 0.40/0.62 (step @p122 :rule aci_norm :args ((= (or @t93 @t122) @t159))) % 0.40/0.62 (step @p123 :rule bool-double-not-elim :args (@t122)) % 0.40/0.62 (step @p124 :rule beta-reduce :args ((= @t161 (not @t122)))) % 0.40/0.62 (step @p125 :rule cong :premises (@p124) :args (@t162)) % 0.40/0.62 (step @p126 :rule trans :premises (@p125 @p123)) % 0.40/0.62 (step @p127 :rule refl :args (@t93)) % 0.40/0.62 (step @p128 :rule nary_cong :premises (@p127 @p126) :args (@t163)) % 0.40/0.62 (step @p129 :rule trans :premises (@p128 @p122)) % 0.40/0.62 (step @p130 :rule cong :premises (@p129) :args (@t164)) % 0.40/0.62 (step @p131 :rule trans :premises (@p130 @p121)) % 0.40/0.62 (step @p132 :rule cong :premises (@p131) :args (@t165)) % 0.40/0.62 (step @p133 :rule cong :premises (@p132) :args (@t166)) % 0.40/0.62 (step @p134 :rule beta-reduce :args ((= (_ @t169 @t160) @t166))) % 0.40/0.62 (step @p135 :rule trans :premises (@p134 @p133)) % 0.40/0.62 (step @p136 :rule beta-reduce :args ((= (_ @t170 tptp.r) @t160))) % 0.40/0.62 (step @p137 :rule refl :args (tptp.r)) % 0.40/0.62 (step @p138 :rule beta-reduce :args ((= @t173 @t170))) % 0.40/0.62 (step @p139 :rule ho_cong :premises (@p138 @p137)) % 0.40/0.62 (step @p140 :rule trans :premises (@p139 @p136)) % 0.40/0.62 (step @p141 :rule refl :args (@t169)) % 0.40/0.62 (step @p142 :rule ho_cong :premises (@p141 @p140)) % 0.40/0.62 (step @p143 :rule trans :premises (@p142 @p135)) % 0.40/0.62 (step @p144 :rule refl :args (@t13)) % 0.40/0.62 (step @p145 :rule ho_cong :premises (@p144 @p143)) % 0.40/0.62 (step @p146 :rule trans :premises (@p145 @p118)) % 0.40/0.62 (step @p147 :rule refl :args (@t154)) % 0.40/0.62 (step @p148 :rule ho_cong :premises (@p147 @p146)) % 0.40/0.62 (step @p149 :rule trans :premises (@p148 @p111)) % 0.40/0.62 (step @p150 :rule ho_cong :premises (@p149 @p100)) % 0.40/0.62 (step @p151 :rule trans :premises (@p150 @p62)) % 0.40/0.62 (step @p152 :rule refl :args (@t102)) % 0.40/0.62 (step @p153 :rule ho_cong :premises (@p152 @p151)) % 0.40/0.62 (step @p154 :rule trans :premises (@p153 @p45)) % 0.40/0.62 (step @p155 :rule cong :premises (@p154) :args ((not (_ @t102 (_ (_ @t154 (_ @t13 (_ @t169 (_ @t173 tptp.r)))) (_ @t132 (_ @t143 @t138))))))) % 0.40/0.62 (step @p156 :rule trans :premises (@p155 @p36)) % 0.40/0.62 (step @p157 :rule ho_cong :premises (@p6 @p137)) % 0.40/0.62 (step @p158 :rule refl :args (tptp.q)) % 0.40/0.62 (step @p159 :rule beta-reduce :args ((= (_ @t175 @t17) @t141))) % 0.40/0.62 (step @p160 :rule refl :args (@t17)) % 0.40/0.62 (step @p161 :rule beta-reduce :args ((= (_ @t177 @t14) @t175))) % 0.40/0.62 (step @p162 :rule refl :args (@t14)) % 0.40/0.62 (step @p163 :rule refl :args (@t15)) % 0.40/0.62 (step @p164 :rule beta-reduce :args ((= @t179 @t11))) % 0.40/0.62 (step @p165 :rule nary_cong :premises (@p164 @p163) :args (@t180)) % 0.40/0.62 (step @p166 :rule cong :premises (@p165) :args (@t181)) % 0.40/0.62 (step @p167 :rule beta-reduce :args ((= (_ @t16 @t178) @t181))) % 0.40/0.62 (step @p168 :rule trans :premises (@p167 @p166)) % 0.40/0.62 (step @p169 :rule beta-reduce :args ((= (_ @t13 @t9) @t178))) % 0.40/0.62 (step @p170 :rule refl :args (@t16)) % 0.40/0.62 (step @p171 :rule ho_cong :premises (@p170 @p169)) % 0.40/0.62 (step @p172 :rule trans :premises (@p171 @p168)) % 0.40/0.62 (step @p173 :rule ho_cong :premises (@p172 @p162)) % 0.40/0.62 (step @p174 :rule trans :premises (@p173 @p161)) % 0.40/0.62 (step @p175 :rule ho_cong :premises (@p174 @p160)) % 0.40/0.62 (step @p176 :rule trans :premises (@p175 @p159)) % 0.40/0.62 (step @p177 :rule refl :args (@t9)) % 0.40/0.62 (step @p178 :rule ho_cong :premises (@p6 @p177)) % 0.40/0.62 (step @p179 :rule ho_cong :premises (@p7 @p178)) % 0.40/0.62 (step @p180 :rule ho_cong :premises (@p179 @p162)) % 0.40/0.62 (step @p181 :rule ho_cong :premises (@p180 @p160)) % 0.40/0.62 (step @p182 :rule trans :premises (@p181 @p176)) % 0.40/0.62 (step @p183 :rule cong :premises (@p182) :args (@t23)) % 0.40/0.62 (step @p184 :rule trans :premises (@p9 @p183)) % 0.40/0.62 (step @p185 :rule ho_cong :premises (@p184 @p158)) % 0.40/0.62 (step @p186 :rule ho_cong :premises (@p185 @p157)) % 0.40/0.62 (step @p187 :rule refl :args (@t131)) % 0.40/0.62 (step @p188 :rule refl :args (@t39)) % 0.40/0.62 (step @p189 :rule cong :premises (@p188 @p187) :args ((= @t39 @t131))) % 0.40/0.62 (step @p190 :rule symm :premises (@p189)) % 0.40/0.62 (step @p191 :rule eq_resolve :premises (@p188 @p190)) % 0.40/0.62 (step @p192 :rule refl :args (@t88)) % 0.40/0.62 (step @p193 :rule refl :args (@t77)) % 0.40/0.62 (step @p194 :rule cong :premises (@p193 @p192) :args ((= @t77 @t88))) % 0.40/0.62 (step @p195 :rule symm :premises (@p194)) % 0.40/0.62 (step @p196 :rule eq_resolve :premises (@p193 @p195)) % 0.40/0.62 (step @p197 :rule cong :premises (@p196) :args (@t78)) % 0.40/0.62 (step @p198 :rule nary_cong :premises (@p197 @p191) :args (@t79)) % 0.40/0.62 (step @p199 :rule cong :premises (@p198) :args (@t80)) % 0.40/0.62 (step @p200 :rule cong :premises (@p199) :args (@t81)) % 0.40/0.62 (step @p201 :rule trans :premises (@p34 @p200)) % 0.40/0.62 (step @p202 :rule ho_cong :premises (@p201 @p186)) % 0.40/0.62 (step @p203 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t183)) @t17) @t171))) % 0.40/0.62 (step 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(step @p219 :rule trans :premises (@p218 @p208)) % 0.40/0.62 (step @p220 :rule ho_cong :premises (@p219 @p160)) % 0.40/0.62 (step @p221 :rule trans :premises (@p220 @p203)) % 0.40/0.62 (step @p222 :rule ho_cong :premises (@p6 @p162)) % 0.40/0.62 (step @p223 :rule ho_cong :premises (@p179 @p222)) % 0.40/0.62 (step @p224 :rule ho_cong :premises (@p6 @p223)) % 0.40/0.62 (step @p225 :rule ho_cong :premises (@p224 @p160)) % 0.40/0.62 (step @p226 :rule trans :premises (@p225 @p221)) % 0.40/0.62 (step @p227 :rule cong :premises (@p226) :args (@t22)) % 0.40/0.62 (step @p228 :rule trans :premises (@p8 @p227)) % 0.40/0.62 (step @p229 :rule ho_cong :premises (@p228 @p158)) % 0.40/0.62 (step @p230 :rule ho_cong :premises (@p229 @p137)) % 0.40/0.62 (step @p231 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t192)) @t17) @t168))) % 0.40/0.62 (step @p232 :rule beta-reduce :args ((= @t194 @t192))) % 0.40/0.62 (step @p233 :rule cong :premises (@p232) :args (@t195)) % 0.40/0.62 (step @p234 :rule cong :premises (@p233) :args (@t196)) % 0.40/0.62 (step @p235 :rule beta-reduce :args ((= (_ @t13 @t193) @t196))) % 0.40/0.62 (step @p236 :rule trans :premises (@p235 @p234)) % 0.40/0.62 (step @p237 :rule cong :premises (@p191) :args (@t197)) % 0.40/0.62 (step @p238 :rule nary_cong :premises (@p75 @p237) :args (@t198)) % 0.40/0.62 (step @p239 :rule cong :premises (@p238) :args ((forall @t41 @t198))) % 0.40/0.62 (step @p240 :rule beta-reduce :args ((= @t199 @t197))) % 0.40/0.62 (step @p241 :rule nary_cong :premises (@p80 @p240) :args (@t200)) % 0.40/0.62 (step @p242 :rule cong :premises (@p241) :args (@t201)) % 0.40/0.62 (step @p243 :rule trans :premises (@p242 @p239)) % 0.40/0.62 (step @p244 :rule cong :premises (@p243) :args (@t202)) % 0.40/0.62 (step @p245 :rule beta-reduce :args ((= (_ @t132 @t178) @t202))) % 0.40/0.62 (step @p246 :rule trans :premises (@p245 @p244)) % 0.40/0.62 (step @p247 :rule ho_cong :premises (@p98 @p169)) % 0.40/0.62 (step @p248 :rule trans :premises (@p247 @p246)) % 0.40/0.62 (step @p249 :rule ho_cong :premises (@p144 @p248)) % 0.40/0.62 (step @p250 :rule trans :premises (@p249 @p236)) % 0.40/0.62 (step @p251 :rule ho_cong :premises (@p250 @p160)) % 0.40/0.62 (step @p252 :rule trans :premises (@p251 @p231)) % 0.40/0.62 (step @p253 :rule ho_cong :premises (@p201 @p178)) % 0.40/0.62 (step @p254 :rule ho_cong :premises (@p6 @p253)) % 0.40/0.62 (step @p255 :rule ho_cong :premises (@p254 @p160)) % 0.40/0.62 (step @p256 :rule trans :premises (@p255 @p252)) % 0.40/0.62 (step @p257 :rule cong :premises (@p256) :args (@t83)) % 0.40/0.62 (step @p258 :rule trans :premises (@p35 @p257)) % 0.40/0.62 (step @p259 :rule ho_cong :premises (@p258 @p230)) % 0.40/0.62 (step @p260 :rule ho_cong :premises (@p6 @p259)) % 0.40/0.62 (step @p261 :rule beta-reduce :args ((= (_ (lambda @t97 @t153) @t17) @t153))) % 0.40/0.62 (step @p262 :rule beta-reduce :args ((= @t204 @t151))) % 0.40/0.62 (step @p263 :rule cong :premises (@p262) :args (@t205)) % 0.40/0.62 (step @p264 :rule refl :args (@t152)) % 0.40/0.62 (step @p265 :rule nary_cong :premises (@p264 @p263) :args (@t206)) % 0.40/0.62 (step @p266 :rule cong :premises (@p265) :args (@t207)) % 0.40/0.62 (step @p267 :rule cong :premises (@p266) :args (@t208)) % 0.40/0.62 (step @p268 :rule beta-reduce :args ((= (_ (lambda @t211 (not (or @t152 @t210))) @t203) @t208))) % 0.40/0.62 (step @p269 :rule trans :premises (@p268 @p267)) % 0.40/0.62 (step @p270 :rule beta-reduce :args ((= (_ @t214 @t9) @t203))) % 0.40/0.62 (step @p271 :rule beta-reduce :args ((= (_ (lambda (@list @t9 @t212 @t17) (or @t140 @t213)) @t14) @t214))) % 0.40/0.62 (step @p272 :rule refl :args (@t14)) % 0.40/0.62 (step @p273 :rule alpha_equiv :args (@t142 @t215 (@list @t212))) % 0.40/0.62 (step @p274 :rule ho_cong :premises (@p273 @p272)) % 0.40/0.62 (step @p275 :rule trans :premises (@p274 @p271)) % 0.40/0.62 (step @p276 :rule ho_cong :premises (@p275 @p177)) % 0.40/0.62 (step @p277 :rule trans :premises (@p276 @p270)) % 0.40/0.62 (step @p278 :rule refl :args (@t210)) % 0.40/0.62 (step @p279 :rule beta-reduce :args ((= @t217 @t141))) % 0.40/0.62 (step @p280 :rule cong :premises (@p279) :args (@t218)) % 0.40/0.62 (step @p281 :rule nary_cong :premises (@p280 @p278) :args (@t219)) % 0.40/0.62 (step @p282 :rule cong :premises (@p281) :args (@t220)) % 0.40/0.62 (step @p283 :rule cong :premises (@p282) :args (@t221)) % 0.40/0.62 (step @p284 :rule beta-reduce :args ((= (_ (lambda (@list @t9 @t209 @t17) (not (or @t140 @t210))) @t216) @t221))) % 0.40/0.62 (step @p285 :rule trans :premises (@p284 @p283)) % 0.40/0.62 (step @p286 :rule refl :args (@t216)) % 0.40/0.62 (step @p287 :rule alpha_equiv :args (@t172 @t215 (@list @t209))) % 0.40/0.62 (step @p288 :rule ho_cong :premises (@p287 @p286)) % 0.40/0.62 (step @p289 :rule trans :premises (@p288 @p285)) % 0.40/0.62 (step @p290 :rule beta-reduce :args ((= (_ @t222 @t14) @t216))) % 0.40/0.62 (step @p291 :rule beta-reduce :args ((= (_ @t142 @t9) @t222))) % 0.40/0.62 (step @p292 :rule ho_cong :premises (@p291 @p162)) % 0.40/0.62 (step @p293 :rule trans :premises (@p292 @p290)) % 0.40/0.62 (step @p294 :rule refl :args (@t172)) % 0.40/0.62 (step @p295 :rule ho_cong :premises (@p294 @p293)) % 0.40/0.62 (step @p296 :rule trans :premises (@p295 @p289)) % 0.40/0.62 (step @p297 :rule ho_cong :premises (@p296 @p277)) % 0.40/0.62 (step @p298 :rule trans :premises (@p297 @p269)) % 0.40/0.62 (step @p299 :rule ho_cong :premises (@p298 @p160)) % 0.40/0.62 (step @p300 :rule trans :premises (@p299 @p261)) % 0.40/0.62 (step @p301 :rule ho_cong :premises (@p184 @p162)) % 0.40/0.62 (step @p302 :rule ho_cong :premises (@p301 @p177)) % 0.40/0.62 (step @p303 :rule ho_cong :premises (@p184 @p177)) % 0.40/0.62 (step @p304 :rule ho_cong :premises (@p303 @p162)) % 0.40/0.62 (step @p305 :rule ho_cong :premises (@p228 @p304)) % 0.40/0.62 (step @p306 :rule ho_cong :premises (@p305 @p302)) % 0.40/0.62 (step @p307 :rule ho_cong :premises (@p306 @p160)) % 0.40/0.62 (step @p308 :rule trans :premises (@p307 @p300)) % 0.40/0.62 (step @p309 :rule cong :premises (@p308) :args (@t25)) % 0.40/0.62 (step @p310 :rule trans :premises (@p11 @p309)) % 0.40/0.62 (step @p311 :rule ho_cong :premises (@p310 @p260)) % 0.40/0.62 (step @p312 :rule ho_cong :premises (@p311 @p202)) % 0.40/0.62 (step @p313 :rule refl :args (@t101)) % 0.40/0.62 (step @p314 :rule refl :args (@t10)) % 0.40/0.62 (step @p315 :rule cong :premises (@p314 @p313) :args ((= @t10 @t101))) % 0.40/0.62 (step @p316 :rule symm :premises (@p315)) % 0.40/0.62 (step @p317 :rule eq_resolve :premises (@p314 @p316)) % 0.40/0.62 (step @p318 :rule cong :premises (@p317) :args (@t71)) % 0.40/0.62 (step @p319 :rule cong :premises (@p318) :args (@t73)) % 0.40/0.62 (step @p320 :rule trans :premises (@p30 @p319)) % 0.40/0.62 (step @p321 :rule ho_cong :premises (@p320 @p312)) % 0.40/0.62 (step @p322 :rule cong :premises (@p321) :args (@t1)) % 0.40/0.62 (step @p323 :rule trans :premises (@p322 @p156)) % 0.40/0.62 (step @p324 false :rule eq_resolve :premises (@p2 @p323)) % 0.40/0.62 ) % 0.40/0.62 % SZS output end Proof % 0.40/0.62 % cvc5 exiting %------------------------------------------------------------------------------