%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO407^1 : 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 : n005.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:12:35 AM UTC 2026 % Result : Theorem 0.37s 0.61s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO407^1 : 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 % 0.17/0.35 % Computer : n005.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Jun 3 00:06:48 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.37/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.61 % SZS status Theorem % 0.37/0.61 % SZS output start Proof % 0.37/0.61 ( % 0.37/0.61 (declare-sort $$unsorted 0) % 0.37/0.61 (declare-sort tptp.mu 0) % 0.37/0.61 (declare-const tptp.rel_k (-> $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.q (-> $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.p (-> $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.r (-> $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.37/0.61 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.37/0.61 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.61 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.61 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.37/0.61 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.37/0.61 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.37/0.61 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.37/0.61 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.37/0.61 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.37/0.61 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.61 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.61 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.37/0.61 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.37/0.61 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.37/0.61 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.37/0.61 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.37/0.61 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.37/0.61 (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)))))))) % 0.37/0.61 (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)))))))) % 0.37/0.61 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.37/0.61 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 0.37/0.61 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.37/0.61 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 0.37/0.61 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.37/0.61 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 0.37/0.61 (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))))))))))))) % 0.37/0.61 (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)))))) % 0.37/0.61 (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))))))) % 0.37/0.61 (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)))))) % 0.37/0.61 (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))))))) % 0.37/0.61 (define tptp.mbox_k () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_k _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.37/0.61 (define tptp.mdia_k () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_k (_ tptp.mnot _let_2))) _let_1))))) % 0.37/0.61 (define @t1 () (_ tptp.mimplies tptp.p)) % 0.37/0.61 (define @t2 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ (_ tptp.mand (_ tptp.mbox_k (_ @t1 tptp.q))) (_ tptp.mbox_k (_ (_ tptp.mimplies tptp.q) tptp.r)))) (_ tptp.mbox_k (_ @t1 tptp.r)))))) % 0.37/0.61 (define @t3 () (@var "Y" tptp.mu)) % 0.37/0.61 (define @t4 () (@var "X" tptp.mu)) % 0.37/0.61 (define @t5 () (@var "W" $$unsorted)) % 0.37/0.61 (define @t6 () (lambda (@list @t4 @t3 @t5) (= @t4 @t3))) % 0.37/0.61 (define @t7 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.61 (define @t8 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.61 (define @t9 () (lambda (@list @t8 @t7 @t5) (= (_ @t8 @t5) (_ @t7 @t5)))) % 0.37/0.61 (define @t10 () (@var "Phi" (-> $$unsorted Bool))) % 0.37/0.61 (define @t11 () (_ @t10 @t5)) % 0.37/0.61 (define @t12 () (not @t11)) % 0.37/0.61 (define @t13 () (@list @t10 @t5)) % 0.37/0.61 (define @t14 () (lambda @t13 @t12)) % 0.37/0.61 (define @t15 () (@var "Psi" (-> $$unsorted Bool))) % 0.37/0.61 (define @t16 () (_ @t15 @t5)) % 0.37/0.61 (define @t17 () (lambda (@list @t10 @t15 @t5) (or @t11 @t16))) % 0.37/0.61 (define @t18 () (@var "__flatten_var_0" $$unsorted)) % 0.37/0.61 (define @t19 () (_ tptp.mnot @t15)) % 0.37/0.61 (define @t20 () (_ tptp.mnot @t10)) % 0.37/0.61 (define @t21 () (_ tptp.mor @t20)) % 0.37/0.61 (define @t22 () (@list @t10 @t15 @t18)) % 0.37/0.61 (define @t23 () (lambda @t22 (_ (_ tptp.mnot (_ @t21 @t19)) @t18))) % 0.37/0.61 (define @t24 () (lambda @t22 (_ (_ @t21 @t15) @t18))) % 0.37/0.61 (define @t25 () (lambda @t22 (_ (_ (_ tptp.mor @t19) @t10) @t18))) % 0.37/0.61 (define @t26 () (lambda @t22 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t10) @t15)) (_ (_ tptp.mimplies @t15) @t10)) @t18))) % 0.37/0.61 (define @t27 () (lambda @t22 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t10) @t15)) @t18))) % 0.37/0.61 (define @t28 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.37/0.61 (define @t29 () (_ @t28 @t4)) % 0.37/0.61 (define @t30 () (lambda (@list @t28 @t5) (forall (@list @t4) (_ @t29 @t5)))) % 0.37/0.61 (define @t31 () (@var "P" (-> $$unsorted Bool))) % 0.37/0.61 (define @t32 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.37/0.61 (define @t33 () (_ @t32 @t31)) % 0.37/0.61 (define @t34 () (lambda (@list @t32 @t5) (forall (@list @t31) (_ @t33 @t5)))) % 0.37/0.61 (define @t35 () (lambda (@list @t28 @t18) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t4 @t18) (_ (_ tptp.mnot @t29) @t18)))) @t18))) % 0.37/0.61 (define @t36 () (lambda (@list @t32 @t18) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t31 @t18) (_ (_ tptp.mnot @t33) @t18)))) @t18))) % 0.37/0.61 (define @t37 () (@list @t5)) % 0.37/0.61 (define @t38 () (lambda @t37 true)) % 0.37/0.61 (define @t39 () (@var "V" $$unsorted)) % 0.37/0.61 (define @t40 () (_ @t10 @t39)) % 0.37/0.61 (define @t41 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.37/0.61 (define @t42 () (@list @t39)) % 0.37/0.61 (define @t43 () (lambda (@list @t41 @t10 @t5) (forall @t42 (or (not (_ (_ @t41 @t5) @t39)) @t40)))) % 0.37/0.61 (define @t44 () (lambda (@list @t41 @t10 @t18) (_ (_ tptp.mnot (_ (_ tptp.mbox @t41) @t20)) @t18))) % 0.37/0.61 (define @t45 () (@var "S" $$unsorted)) % 0.37/0.61 (define @t46 () (_ @t41 @t45)) % 0.37/0.61 (define @t47 () (@list @t45)) % 0.37/0.61 (define @t48 () (@list @t41)) % 0.37/0.61 (define @t49 () (lambda @t48 (forall @t47 (_ @t46 @t45)))) % 0.37/0.61 (define @t50 () (@var "T" $$unsorted)) % 0.37/0.61 (define @t51 () (_ @t41 @t50)) % 0.37/0.61 (define @t52 () (_ @t46 @t50)) % 0.37/0.61 (define @t53 () (lambda @t48 (forall (@list @t45 @t50) (=> @t52 (_ @t51 @t45))))) % 0.37/0.61 (define @t54 () (@list @t50)) % 0.37/0.61 (define @t55 () (lambda @t48 (forall @t47 (exists @t54 @t52)))) % 0.37/0.61 (define @t56 () (@var "U" $$unsorted)) % 0.37/0.61 (define @t57 () (_ @t46 @t56)) % 0.37/0.61 (define @t58 () (_ @t51 @t56)) % 0.37/0.61 (define @t59 () (@list @t45 @t50 @t56)) % 0.37/0.61 (define @t60 () (lambda @t48 (forall @t59 (=> (and @t52 @t58) @t57)))) % 0.37/0.61 (define @t61 () (and @t52 @t57)) % 0.37/0.61 (define @t62 () (lambda @t48 (forall @t59 (=> @t61 @t58)))) % 0.37/0.61 (define @t63 () (= @t50 @t56)) % 0.37/0.61 (define @t64 () (lambda @t48 (forall @t59 (=> @t61 @t63)))) % 0.37/0.61 (define @t65 () (@list @t56)) % 0.37/0.61 (define @t66 () (lambda @t48 (forall @t47 (exists @t54 (and @t52 (forall @t65 (=> @t57 @t63))))))) % 0.37/0.61 (define @t67 () (_ @t41 @t56)) % 0.37/0.61 (define @t68 () (_ @t67 @t50)) % 0.37/0.61 (define @t69 () (lambda @t48 (forall @t59 (=> @t52 (exists @t65 (and @t57 @t68)))))) % 0.37/0.61 (define @t70 () (lambda @t48 (forall @t59 (=> @t61 (or @t58 @t63 @t68))))) % 0.37/0.61 (define @t71 () (lambda @t48 (forall @t59 (=> @t61 (exists @t42 (and (_ @t51 @t39) (_ @t67 @t39))))))) % 0.37/0.61 (define @t72 () (forall @t37 @t11)) % 0.37/0.61 (define @t73 () (@list @t10)) % 0.37/0.61 (define @t74 () (lambda @t73 @t72)) % 0.37/0.61 (define @t75 () (lambda @t73 (forall @t37 @t12))) % 0.37/0.61 (define @t76 () (lambda @t73 (exists @t37 @t11))) % 0.37/0.61 (define @t77 () (lambda @t73 (exists @t37 @t12))) % 0.37/0.61 (define @t78 () (_ (_ tptp.rel_k @t5) @t39)) % 0.37/0.61 (define @t79 () (not @t78)) % 0.37/0.61 (define @t80 () (or @t79 @t40)) % 0.37/0.61 (define @t81 () (forall @t42 @t80)) % 0.37/0.61 (define @t82 () (lambda @t13 @t81)) % 0.37/0.61 (define @t83 () (lambda (@list @t10 @t18) (_ (_ tptp.mnot (_ tptp.mbox_k @t20)) @t18))) % 0.37/0.61 (define @t84 () (@var "BOUND_VARIABLE_8529" $$unsorted)) % 0.37/0.61 (define @t85 () (tptp.r @t84)) % 0.37/0.61 (define @t86 () (not (tptp.p @t84))) % 0.37/0.61 (define @t87 () (not (tptp.rel_k @t5 @t84))) % 0.37/0.61 (define @t88 () (tptp.r @t39)) % 0.37/0.61 (define @t89 () (tptp.q @t39)) % 0.37/0.61 (define @t90 () (not @t89)) % 0.37/0.61 (define @t91 () (tptp.rel_k @t5 @t39)) % 0.37/0.61 (define @t92 () (not @t91)) % 0.37/0.61 (define @t93 () (forall @t42 (or @t92 @t90 @t88))) % 0.37/0.61 (define @t94 () (not @t93)) % 0.37/0.61 (define @t95 () (tptp.p @t39)) % 0.37/0.62 (define @t96 () (not @t95)) % 0.37/0.62 (define @t97 () (forall @t42 (or @t92 @t96 @t89))) % 0.37/0.62 (define @t98 () (not @t97)) % 0.37/0.62 (define @t99 () (or @t98 @t94 @t87 @t86 @t85)) % 0.37/0.62 (define @t100 () (or @t87 @t86 @t85)) % 0.37/0.62 (define @t101 () (or @t100 @t98 @t94)) % 0.37/0.62 (define @t102 () (@list @t5 @t84)) % 0.37/0.62 (define @t103 () (forall @t102 @t101)) % 0.37/0.62 (define @t104 () (@list @t84)) % 0.37/0.62 (define @t105 () (forall @t104 @t101)) % 0.37/0.62 (define @t106 () (forall @t104 @t100)) % 0.37/0.62 (define @t107 () (or @t106 @t98 @t94)) % 0.37/0.62 (define @t108 () (forall @t42 (or @t92 @t96 @t88))) % 0.37/0.62 (define @t109 () (or @t108 @t98 @t94)) % 0.37/0.62 (define @t110 () (not (tptp.rel_k @t18 @t39))) % 0.37/0.62 (define @t111 () (forall @t42 (or @t110 @t90 @t88))) % 0.37/0.62 (define @t112 () (not @t111)) % 0.37/0.62 (define @t113 () (forall @t42 (or @t110 @t96 @t89))) % 0.37/0.62 (define @t114 () (not @t113)) % 0.37/0.62 (define @t115 () (forall @t42 (or @t110 @t96 @t88))) % 0.37/0.62 (define @t116 () (@list @t18)) % 0.37/0.62 (define @t117 () (lambda @t116 (or @t115 @t114 @t112))) % 0.37/0.62 (define @t118 () (_ @t117 @t5)) % 0.37/0.62 (define @t119 () (forall @t37 @t118)) % 0.37/0.62 (define @t120 () (_ @t10 @t5)) % 0.37/0.62 (define @t121 () (lambda @t73 (forall @t37 @t120))) % 0.37/0.62 (define @t122 () (lambda @t37 @t108)) % 0.37/0.62 (define @t123 () (_ @t122 @t18)) % 0.37/0.62 (define @t124 () (or @t123 @t114 @t112)) % 0.37/0.62 (define @t125 () (lambda @t116 @t124)) % 0.37/0.62 (define @t126 () (_ @t15 @t18)) % 0.37/0.62 (define @t127 () (or @t126 @t114 @t112)) % 0.37/0.62 (define @t128 () (@list @t15 @t18)) % 0.37/0.62 (define @t129 () (_ tptp.r @t39)) % 0.37/0.62 (define @t130 () (_ tptp.p @t39)) % 0.37/0.62 (define @t131 () (not @t130)) % 0.37/0.62 (define @t132 () (or @t92 @t131 @t129)) % 0.37/0.62 (define @t133 () (or @t131 @t129)) % 0.37/0.62 (define @t134 () (_ tptp.r @t18)) % 0.37/0.62 (define @t135 () (not (_ tptp.p @t18))) % 0.37/0.62 (define @t136 () (lambda @t116 (or @t135 @t134))) % 0.37/0.62 (define @t137 () (_ @t136 @t39)) % 0.37/0.62 (define @t138 () (or @t92 @t137)) % 0.37/0.62 (define @t139 () (forall @t42 @t138)) % 0.37/0.62 (define @t140 () (lambda @t37 @t139)) % 0.37/0.62 (define @t141 () (_ @t10 @t39)) % 0.37/0.62 (define @t142 () (lambda @t13 (forall @t42 (or @t92 @t141)))) % 0.37/0.62 (define @t143 () (lambda @t128 (or @t135 @t126))) % 0.37/0.62 (define @t144 () (not (_ @t10 @t18))) % 0.37/0.62 (define @t145 () (or @t144 @t126)) % 0.37/0.62 (define @t146 () (lambda @t22 @t145)) % 0.37/0.62 (define @t147 () (_ @t146 tptp.p)) % 0.37/0.62 (define @t148 () (or @t114 @t112)) % 0.37/0.62 (define @t149 () (not @t148)) % 0.37/0.62 (define @t150 () (lambda @t116 @t149)) % 0.37/0.62 (define @t151 () (_ @t150 @t18)) % 0.37/0.62 (define @t152 () (not @t151)) % 0.37/0.62 (define @t153 () (or @t152 @t126)) % 0.37/0.62 (define @t154 () (lambda @t128 @t153)) % 0.37/0.62 (define @t155 () (lambda @t37 @t93)) % 0.37/0.62 (define @t156 () (_ @t155 @t18)) % 0.37/0.62 (define @t157 () (not @t156)) % 0.37/0.62 (define @t158 () (or @t114 @t157)) % 0.37/0.62 (define @t159 () (not @t158)) % 0.37/0.62 (define @t160 () (lambda @t116 @t159)) % 0.37/0.62 (define @t161 () (not @t126)) % 0.37/0.62 (define @t162 () (_ tptp.q @t39)) % 0.37/0.62 (define @t163 () (not @t162)) % 0.37/0.62 (define @t164 () (or @t92 @t163 @t129)) % 0.37/0.62 (define @t165 () (or @t163 @t129)) % 0.37/0.62 (define @t166 () (_ tptp.q @t18)) % 0.37/0.62 (define @t167 () (not @t166)) % 0.37/0.62 (define @t168 () (lambda @t116 (or @t167 @t134))) % 0.37/0.62 (define @t169 () (_ @t168 @t39)) % 0.37/0.62 (define @t170 () (or @t92 @t169)) % 0.37/0.62 (define @t171 () (forall @t42 @t170)) % 0.37/0.62 (define @t172 () (lambda @t37 @t171)) % 0.37/0.62 (define @t173 () (lambda @t128 (or @t167 @t126))) % 0.37/0.62 (define @t174 () (_ @t146 tptp.q)) % 0.37/0.62 (define @t175 () (lambda @t37 @t97)) % 0.37/0.62 (define @t176 () (_ @t175 @t18)) % 0.37/0.62 (define @t177 () (not @t176)) % 0.37/0.62 (define @t178 () (or @t177 @t161)) % 0.37/0.62 (define @t179 () (not @t178)) % 0.37/0.62 (define @t180 () (lambda @t128 @t179)) % 0.37/0.62 (define @t181 () (not (or @t144 @t161))) % 0.37/0.62 (define @t182 () (lambda @t22 @t181)) % 0.37/0.62 (define @t183 () (or @t92 @t131 @t162)) % 0.37/0.62 (define @t184 () (or @t131 @t162)) % 0.37/0.62 (define @t185 () (lambda @t116 (or @t135 @t166))) % 0.37/0.62 (define @t186 () (_ @t185 @t39)) % 0.37/0.62 (define @t187 () (or @t92 @t186)) % 0.37/0.62 (define @t188 () (forall @t42 @t187)) % 0.37/0.62 (define @t189 () (lambda @t37 @t188)) % 0.37/0.62 (define @t190 () (or @t12 @t16)) % 0.37/0.62 (define @t191 () (lambda @t37 @t190)) % 0.37/0.62 (define @t192 () (@list @t15 @t5)) % 0.37/0.62 (define @t193 () (lambda @t192 @t190)) % 0.37/0.62 (define @t194 () (lambda @t37 @t12)) % 0.37/0.62 (define @t195 () (_ @t194 @t5)) % 0.37/0.62 (define @t196 () (or @t195 @t16)) % 0.37/0.62 (define @t197 () (lambda @t192 @t196)) % 0.37/0.62 (define @t198 () (not @t16)) % 0.37/0.62 (define @t199 () (or @t12 @t198)) % 0.37/0.62 (define @t200 () (lambda @t37 @t199)) % 0.37/0.62 (define @t201 () (_ @t200 @t5)) % 0.37/0.62 (define @t202 () (not @t201)) % 0.37/0.62 (define @t203 () (lambda @t37 @t202)) % 0.37/0.62 (define @t204 () (lambda @t37 @t198)) % 0.37/0.62 (define @t205 () (_ @t204 @t5)) % 0.37/0.62 (define @t206 () (or @t12 @t205)) % 0.37/0.62 (define @t207 () (lambda @t37 @t206)) % 0.37/0.62 (define @t208 () (forall @t102 @t99)) % 0.37/0.62 (define @t209 () (@quantifiers_skolemize @t208 1)) % 0.37/0.62 (define @t210 () (@quantifiers_skolemize @t208 0)) % 0.37/0.62 (define @t211 () (tptp.rel_k @t210 @t209)) % 0.37/0.62 (define @t212 () (tptp.r @t209)) % 0.37/0.62 (define @t213 () (tptp.p @t209)) % 0.37/0.62 (define @t214 () (not @t213)) % 0.37/0.62 (define @t215 () (not @t211)) % 0.37/0.62 (define @t216 () (not (tptp.rel_k @t210 @t39))) % 0.37/0.62 (define @t217 () (forall @t42 (or @t216 @t90 @t88))) % 0.37/0.62 (define @t218 () (not @t217)) % 0.37/0.62 (define @t219 () (forall @t42 (or @t216 @t96 @t89))) % 0.37/0.62 (define @t220 () (not @t219)) % 0.37/0.62 (define @t221 () (or @t220 @t218 @t215 @t214 @t212)) % 0.37/0.62 (define @t222 () (@list true)) % 0.37/0.62 (define @t223 () (@list @t221)) % 0.37/0.62 (define @t224 () (@list @t209)) % 0.37/0.62 (define @t225 () (tptp.q @t209)) % 0.37/0.62 (define @t226 () (or @t215 @t214 @t225)) % 0.37/0.62 (define @t227 () (not @t225)) % 0.37/0.62 (define @t228 () (or @t215 @t227 @t212)) % 0.37/0.62 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.37/0.62 (assume @p2 @t2) % 0.37/0.62 (assume @p3 true) % 0.37/0.62 (step @p4 (= tptp.meq_ind @t6) :rule refl :args (@t6)) % 0.37/0.62 (step @p5 (= tptp.meq_prop @t9) :rule refl :args (@t9)) % 0.37/0.62 (step @p6 (= tptp.mnot @t14) :rule refl :args (@t14)) % 0.37/0.62 (step @p7 (= tptp.mor @t17) :rule refl :args (@t17)) % 0.37/0.62 (step @p8 (= tptp.mand @t23) :rule refl :args (@t23)) % 0.37/0.62 (step @p9 (= tptp.mimplies @t24) :rule refl :args (@t24)) % 0.37/0.62 (step @p10 (= tptp.mimplied @t25) :rule refl :args (@t25)) % 0.37/0.62 (step @p11 (= tptp.mequiv @t26) :rule refl :args (@t26)) % 0.37/0.62 (step @p12 (= tptp.mxor @t27) :rule refl :args (@t27)) % 0.37/0.62 (step @p13 (= tptp.mforall_ind @t30) :rule refl :args (@t30)) % 0.37/0.62 (step @p14 (= tptp.mforall_prop @t34) :rule refl :args (@t34)) % 0.37/0.62 (step @p15 (= tptp.mexists_ind @t35) :rule refl :args (@t35)) % 0.37/0.62 (step @p16 (= tptp.mexists_prop @t36) :rule refl :args (@t36)) % 0.37/0.62 (step @p17 (= tptp.mtrue @t38) :rule refl :args (@t38)) % 0.37/0.62 (step @p18 (= tptp.mbox @t43) :rule refl :args (@t43)) % 0.37/0.62 (step @p19 (= tptp.mdia @t44) :rule refl :args (@t44)) % 0.37/0.62 (step @p20 (= tptp.mreflexive @t49) :rule refl :args (@t49)) % 0.37/0.62 (step @p21 (= tptp.msymmetric @t53) :rule refl :args (@t53)) % 0.37/0.62 (step @p22 (= tptp.mserial @t55) :rule refl :args (@t55)) % 0.37/0.62 (step @p23 (= tptp.mtransitive @t60) :rule refl :args (@t60)) % 0.37/0.62 (step @p24 (= tptp.meuclidean @t62) :rule refl :args (@t62)) % 0.37/0.62 (step @p25 (= tptp.mpartially_functional @t64) :rule refl :args (@t64)) % 0.37/0.62 (step @p26 (= tptp.mfunctional @t66) :rule refl :args (@t66)) % 0.37/0.62 (step @p27 (= tptp.mweakly_dense @t69) :rule refl :args (@t69)) % 0.37/0.62 (step @p28 (= tptp.mweakly_connected @t70) :rule refl :args (@t70)) % 0.37/0.62 (step @p29 (= tptp.mweakly_directed @t71) :rule refl :args (@t71)) % 0.37/0.62 (step @p30 (= tptp.mvalid @t74) :rule refl :args (@t74)) % 0.37/0.62 (step @p31 (= tptp.minvalid @t75) :rule refl :args (@t75)) % 0.37/0.62 (step @p32 (= tptp.msatisfiable @t76) :rule refl :args (@t76)) % 0.37/0.62 (step @p33 (= tptp.mcountersatisfiable @t77) :rule refl :args (@t77)) % 0.37/0.62 (step @p34 (= tptp.mbox_k @t82) :rule refl :args (@t82)) % 0.37/0.62 (step @p35 (= tptp.mdia_k @t83) :rule refl :args (@t83)) % 0.37/0.62 (step @p36 :rule aci_norm :args ((= @t101 @t99))) % 0.37/0.62 (step @p37 :rule cong :premises (@p36) :args (@t103)) % 0.37/0.62 (step @p38 :rule quant-merge-prenex :args ((= (forall @t37 @t105) @t103))) % 0.37/0.62 (step @p39 :rule refl :args (@t94)) % 0.37/0.62 (step @p40 :rule refl :args (@t98)) % 0.37/0.62 (step @p41 :rule alpha_equiv :args (@t106 (@list @t84) (@list @t39))) % 0.37/0.62 (step @p42 :rule nary_cong :premises (@p41 @p40 @p39) :args (@t107)) % 0.37/0.62 (step @p43 :rule quant-miniscope-or :args ((= @t105 @t107))) % 0.37/0.62 (step @p44 :rule trans :premises (@p43 @p42)) % 0.37/0.62 (step @p45 :rule symm :premises (@p44)) % 0.37/0.62 (step @p46 :rule cong :premises (@p45) :args ((forall @t37 @t109))) % 0.37/0.62 (step @p47 :rule trans :premises (@p46 @p38)) % 0.37/0.62 (step @p48 :rule trans :premises (@p47 @p37)) % 0.37/0.62 (step @p49 :rule beta-reduce :args ((= @t118 @t109))) % 0.37/0.62 (step @p50 :rule cong :premises (@p49) :args (@t119)) % 0.37/0.62 (step @p51 :rule trans :premises (@p50 @p48)) % 0.37/0.62 (step @p52 :rule beta-reduce :args ((= (_ @t121 @t117) @t119))) % 0.37/0.62 (step @p53 :rule trans :premises (@p52 @p51)) % 0.37/0.62 (step @p54 :rule refl :args (@t112)) % 0.37/0.62 (step @p55 :rule refl :args (@t114)) % 0.37/0.62 (step @p56 :rule beta-reduce :args ((= @t123 @t115))) % 0.37/0.62 (step @p57 :rule nary_cong :premises (@p56 @p55 @p54) :args (@t124)) % 0.37/0.62 (step @p58 :rule cong :premises (@p57) :args (@t125)) % 0.37/0.62 (step @p59 :rule beta-reduce :args ((= (_ (lambda @t128 @t127) @t122) @t125))) % 0.37/0.62 (step @p60 :rule trans :premises (@p59 @p58)) % 0.37/0.62 (step @p61 :rule refl :args (@t88)) % 0.37/0.62 (step @p62 :rule refl :args (@t129)) % 0.37/0.62 (step @p63 :rule cong :premises (@p62 @p61) :args ((= @t129 @t88))) % 0.37/0.62 (step @p64 :rule symm :premises (@p63)) % 0.37/0.62 (step @p65 :rule eq_resolve :premises (@p62 @p64)) % 0.37/0.62 (step @p66 :rule refl :args (@t95)) % 0.37/0.62 (step @p67 :rule refl :args (@t130)) % 0.37/0.62 (step @p68 :rule cong :premises (@p67 @p66) :args ((= @t130 @t95))) % 0.37/0.62 (step @p69 :rule symm :premises (@p68)) % 0.37/0.62 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 0.37/0.62 (step @p71 :rule cong :premises (@p70) :args (@t131)) % 0.37/0.62 (step @p72 :rule refl :args (@t92)) % 0.37/0.62 (step @p73 :rule nary_cong :premises (@p72 @p71 @p65) :args (@t132)) % 0.37/0.62 (step @p74 :rule cong :premises (@p73) :args ((forall @t42 @t132))) % 0.37/0.62 (step @p75 :rule aci_norm :args ((= (or @t92 @t133) @t132))) % 0.37/0.62 (step @p76 :rule beta-reduce :args ((= @t137 @t133))) % 0.37/0.62 (step @p77 :rule refl :args (@t92)) % 0.37/0.62 (step @p78 :rule nary_cong :premises (@p77 @p76) :args (@t138)) % 0.37/0.62 (step @p79 :rule trans :premises (@p78 @p75)) % 0.37/0.62 (step @p80 :rule cong :premises (@p79) :args (@t139)) % 0.37/0.62 (step @p81 :rule trans :premises (@p80 @p74)) % 0.37/0.62 (step @p82 :rule cong :premises (@p81) :args (@t140)) % 0.37/0.62 (step @p83 :rule beta-reduce :args ((= (_ @t142 @t136) @t140))) % 0.37/0.62 (step @p84 :rule trans :premises (@p83 @p82)) % 0.37/0.62 (step @p85 :rule beta-reduce :args ((= (_ @t143 tptp.r) @t136))) % 0.37/0.62 (step @p86 :rule refl :args (tptp.r)) % 0.37/0.62 (step @p87 :rule beta-reduce :args ((= @t147 @t143))) % 0.37/0.62 (step @p88 :rule ho_cong :premises (@p87 @p86)) % 0.37/0.62 (step @p89 :rule trans :premises (@p88 @p85)) % 0.37/0.62 (step @p90 :rule refl :args (@t142)) % 0.37/0.62 (step @p91 :rule ho_cong :premises (@p90 @p89)) % 0.37/0.62 (step @p92 :rule trans :premises (@p91 @p84)) % 0.37/0.62 (step @p93 :rule aci_norm :args ((= (or @t148 @t126) @t127))) % 0.37/0.62 (step @p94 :rule refl :args (@t126)) % 0.37/0.62 (step @p95 :rule bool-double-not-elim :args (@t148)) % 0.37/0.62 (step @p96 :rule beta-reduce :args ((= @t151 @t149))) % 0.37/0.62 (step @p97 :rule cong :premises (@p96) :args (@t152)) % 0.37/0.62 (step @p98 :rule trans :premises (@p97 @p95)) % 0.37/0.62 (step @p99 :rule nary_cong :premises (@p98 @p94) :args (@t153)) % 0.37/0.62 (step @p100 :rule trans :premises (@p99 @p93)) % 0.37/0.62 (step @p101 :rule cong :premises (@p100) :args (@t154)) % 0.37/0.62 (step @p102 :rule beta-reduce :args ((= (_ @t146 @t150) @t154))) % 0.37/0.62 (step @p103 :rule trans :premises (@p102 @p101)) % 0.37/0.62 (step @p104 :rule beta-reduce :args ((= @t156 @t111))) % 0.37/0.62 (step @p105 :rule cong :premises (@p104) :args (@t157)) % 0.37/0.62 (step @p106 :rule nary_cong :premises (@p55 @p105) :args (@t158)) % 0.37/0.62 (step @p107 :rule cong :premises (@p106) :args (@t159)) % 0.37/0.62 (step @p108 :rule cong :premises (@p107) :args (@t160)) % 0.37/0.62 (step @p109 :rule beta-reduce :args ((= (_ (lambda @t128 (not (or @t114 @t161))) @t155) @t160))) % 0.37/0.62 (step @p110 :rule trans :premises (@p109 @p108)) % 0.37/0.62 (step @p111 :rule refl :args (@t89)) % 0.37/0.62 (step @p112 :rule refl :args (@t162)) % 0.37/0.62 (step @p113 :rule cong :premises (@p112 @p111) :args ((= @t162 @t89))) % 0.37/0.62 (step @p114 :rule symm :premises (@p113)) % 0.37/0.62 (step @p115 :rule eq_resolve :premises (@p112 @p114)) % 0.37/0.62 (step @p116 :rule cong :premises (@p115) :args (@t163)) % 0.37/0.62 (step @p117 :rule nary_cong :premises (@p72 @p116 @p65) :args (@t164)) % 0.37/0.62 (step @p118 :rule cong :premises (@p117) :args ((forall @t42 @t164))) % 0.37/0.62 (step @p119 :rule aci_norm :args ((= (or @t92 @t165) @t164))) % 0.37/0.62 (step @p120 :rule beta-reduce :args ((= @t169 @t165))) % 0.37/0.62 (step @p121 :rule nary_cong :premises (@p77 @p120) :args (@t170)) % 0.37/0.62 (step @p122 :rule trans :premises (@p121 @p119)) % 0.37/0.62 (step @p123 :rule cong :premises (@p122) :args (@t171)) % 0.37/0.62 (step @p124 :rule trans :premises (@p123 @p118)) % 0.37/0.62 (step @p125 :rule cong :premises (@p124) :args (@t172)) % 0.37/0.62 (step @p126 :rule beta-reduce :args ((= (_ @t142 @t168) @t172))) % 0.37/0.62 (step @p127 :rule trans :premises (@p126 @p125)) % 0.37/0.62 (step @p128 :rule beta-reduce :args ((= (_ @t173 tptp.r) @t168))) % 0.37/0.62 (step @p129 :rule beta-reduce :args ((= @t174 @t173))) % 0.37/0.62 (step @p130 :rule ho_cong :premises (@p129 @p86)) % 0.37/0.62 (step @p131 :rule trans :premises (@p130 @p128)) % 0.37/0.62 (step @p132 :rule ho_cong :premises (@p90 @p131)) % 0.37/0.62 (step @p133 :rule trans :premises (@p132 @p127)) % 0.37/0.62 (step @p134 :rule refl :args (@t161)) % 0.37/0.62 (step @p135 :rule beta-reduce :args ((= @t176 @t113))) % 0.37/0.62 (step @p136 :rule cong :premises (@p135) :args (@t177)) % 0.37/0.62 (step @p137 :rule nary_cong :premises (@p136 @p134) :args (@t178)) % 0.37/0.62 (step @p138 :rule cong :premises (@p137) :args (@t179)) % 0.37/0.62 (step @p139 :rule cong :premises (@p138) :args (@t180)) % 0.37/0.62 (step @p140 :rule beta-reduce :args ((= (_ @t182 @t175) @t180))) % 0.37/0.62 (step @p141 :rule trans :premises (@p140 @p139)) % 0.37/0.62 (step @p142 :rule nary_cong :premises (@p72 @p71 @p115) :args (@t183)) % 0.37/0.62 (step @p143 :rule cong :premises (@p142) :args ((forall @t42 @t183))) % 0.37/0.62 (step @p144 :rule aci_norm :args ((= (or @t92 @t184) @t183))) % 0.37/0.62 (step @p145 :rule beta-reduce :args ((= @t186 @t184))) % 0.37/0.62 (step @p146 :rule nary_cong :premises (@p77 @p145) :args (@t187)) % 0.37/0.62 (step @p147 :rule trans :premises (@p146 @p144)) % 0.37/0.62 (step @p148 :rule cong :premises (@p147) :args (@t188)) % 0.37/0.62 (step @p149 :rule trans :premises (@p148 @p143)) % 0.37/0.62 (step @p150 :rule cong :premises (@p149) :args (@t189)) % 0.37/0.62 (step @p151 :rule beta-reduce :args ((= (_ @t142 @t185) @t189))) % 0.37/0.62 (step @p152 :rule trans :premises (@p151 @p150)) % 0.37/0.62 (step @p153 :rule beta-reduce :args ((= (_ @t143 tptp.q) @t185))) % 0.37/0.62 (step @p154 :rule refl :args (tptp.q)) % 0.37/0.62 (step @p155 :rule ho_cong :premises (@p87 @p154)) % 0.37/0.62 (step @p156 :rule trans :premises (@p155 @p153)) % 0.37/0.62 (step @p157 :rule ho_cong :premises (@p90 @p156)) % 0.37/0.62 (step @p158 :rule trans :premises (@p157 @p152)) % 0.37/0.62 (step @p159 :rule refl :args (@t182)) % 0.37/0.62 (step @p160 :rule ho_cong :premises (@p159 @p158)) % 0.37/0.62 (step @p161 :rule trans :premises (@p160 @p141)) % 0.37/0.62 (step @p162 :rule ho_cong :premises (@p161 @p133)) % 0.37/0.62 (step @p163 :rule trans :premises (@p162 @p110)) % 0.37/0.62 (step @p164 :rule refl :args (@t146)) % 0.37/0.62 (step @p165 :rule ho_cong :premises (@p164 @p163)) % 0.37/0.62 (step @p166 :rule trans :premises (@p165 @p103)) % 0.37/0.62 (step @p167 :rule ho_cong :premises (@p166 @p92)) % 0.37/0.62 (step @p168 :rule trans :premises (@p167 @p60)) % 0.37/0.62 (step @p169 :rule refl :args (@t121)) % 0.37/0.62 (step @p170 :rule ho_cong :premises (@p169 @p168)) % 0.37/0.62 (step @p171 :rule trans :premises (@p170 @p53)) % 0.37/0.62 (step @p172 :rule cong :premises (@p171) :args ((not (_ @t121 (_ (_ @t146 (_ (_ @t182 (_ @t142 (_ @t147 tptp.q))) (_ @t142 (_ @t174 tptp.r)))) (_ @t142 (_ @t147 tptp.r))))))) % 0.37/0.62 (step @p173 :rule refl :args (tptp.p)) % 0.37/0.62 (step @p174 :rule beta-reduce :args ((= (_ @t191 @t18) @t145))) % 0.37/0.62 (step @p175 :rule refl :args (@t18)) % 0.37/0.62 (step @p176 :rule beta-reduce :args ((= (_ @t193 @t15) @t191))) % 0.37/0.62 (step @p177 :rule refl :args (@t15)) % 0.37/0.62 (step @p178 :rule refl :args (@t16)) % 0.37/0.62 (step @p179 :rule beta-reduce :args ((= @t195 @t12))) % 0.37/0.62 (step @p180 :rule nary_cong :premises (@p179 @p178) :args (@t196)) % 0.37/0.62 (step @p181 :rule cong :premises (@p180) :args (@t197)) % 0.37/0.62 (step @p182 :rule beta-reduce :args ((= (_ @t17 @t194) @t197))) % 0.37/0.62 (step @p183 :rule trans :premises (@p182 @p181)) % 0.37/0.62 (step @p184 :rule beta-reduce :args ((= (_ @t14 @t10) @t194))) % 0.37/0.62 (step @p185 :rule refl :args (@t17)) % 0.37/0.62 (step @p186 :rule ho_cong :premises (@p185 @p184)) % 0.37/0.62 (step @p187 :rule trans :premises (@p186 @p183)) % 0.37/0.62 (step @p188 :rule ho_cong :premises (@p187 @p177)) % 0.37/0.62 (step @p189 :rule trans :premises (@p188 @p176)) % 0.37/0.62 (step @p190 :rule ho_cong :premises (@p189 @p175)) % 0.37/0.62 (step @p191 :rule trans :premises (@p190 @p174)) % 0.37/0.62 (step @p192 :rule refl :args (@t10)) % 0.37/0.62 (step @p193 :rule ho_cong :premises (@p6 @p192)) % 0.37/0.62 (step @p194 :rule ho_cong :premises (@p7 @p193)) % 0.37/0.62 (step @p195 :rule ho_cong :premises (@p194 @p177)) % 0.37/0.62 (step @p196 :rule ho_cong :premises (@p195 @p175)) % 0.37/0.62 (step @p197 :rule trans :premises (@p196 @p191)) % 0.37/0.62 (step @p198 :rule cong :premises (@p197) :args (@t24)) % 0.37/0.62 (step @p199 :rule trans :premises (@p9 @p198)) % 0.37/0.62 (step @p200 :rule ho_cong :premises (@p199 @p173)) % 0.37/0.62 (step @p201 :rule ho_cong :premises (@p200 @p86)) % 0.37/0.62 (step @p202 :rule refl :args (@t141)) % 0.37/0.62 (step @p203 :rule refl :args (@t40)) % 0.37/0.62 (step @p204 :rule cong :premises (@p203 @p202) :args ((= @t40 @t141))) % 0.37/0.62 (step @p205 :rule symm :premises (@p204)) % 0.37/0.62 (step @p206 :rule eq_resolve :premises (@p203 @p205)) % 0.37/0.62 (step @p207 :rule refl :args (@t91)) % 0.37/0.62 (step @p208 :rule refl :args (@t78)) % 0.37/0.62 (step @p209 :rule cong :premises (@p208 @p207) :args ((= @t78 @t91))) % 0.37/0.62 (step @p210 :rule symm :premises (@p209)) % 0.37/0.62 (step @p211 :rule eq_resolve :premises (@p208 @p210)) % 0.37/0.62 (step @p212 :rule cong :premises (@p211) :args (@t79)) % 0.37/0.62 (step @p213 :rule nary_cong :premises (@p212 @p206) :args (@t80)) % 0.37/0.62 (step @p214 :rule cong :premises (@p213) :args (@t81)) % 0.37/0.62 (step @p215 :rule cong :premises (@p214) :args (@t82)) % 0.37/0.62 (step @p216 :rule trans :premises (@p34 @p215)) % 0.37/0.62 (step @p217 :rule ho_cong :premises (@p216 @p201)) % 0.37/0.62 (step @p218 :rule ho_cong :premises (@p199 @p154)) % 0.37/0.62 (step @p219 :rule ho_cong :premises (@p218 @p86)) % 0.37/0.62 (step @p220 :rule ho_cong :premises (@p216 @p219)) % 0.37/0.62 (step @p221 :rule ho_cong :premises (@p200 @p154)) % 0.37/0.62 (step @p222 :rule ho_cong :premises (@p216 @p221)) % 0.37/0.62 (step @p223 :rule beta-reduce :args ((= (_ (lambda @t37 (not @t199)) @t18) @t181))) % 0.37/0.62 (step @p224 :rule beta-reduce :args ((= @t201 @t199))) % 0.37/0.62 (step @p225 :rule cong :premises (@p224) :args (@t202)) % 0.37/0.62 (step @p226 :rule cong :premises (@p225) :args (@t203)) % 0.37/0.62 (step @p227 :rule beta-reduce :args ((= (_ @t14 @t200) @t203))) % 0.37/0.62 (step @p228 :rule trans :premises (@p227 @p226)) % 0.37/0.62 (step @p229 :rule beta-reduce :args ((= @t205 @t198))) % 0.37/0.62 (step @p230 :rule refl :args (@t12)) % 0.37/0.62 (step @p231 :rule nary_cong :premises (@p230 @p229) :args (@t206)) % 0.37/0.62 (step @p232 :rule cong :premises (@p231) :args (@t207)) % 0.37/0.62 (step @p233 :rule beta-reduce :args ((= (_ @t193 @t204) @t207))) % 0.37/0.62 (step @p234 :rule trans :premises (@p233 @p232)) % 0.37/0.62 (step @p235 :rule beta-reduce :args ((= (_ @t14 @t15) @t204))) % 0.37/0.62 (step @p236 :rule ho_cong :premises (@p187 @p235)) % 0.37/0.62 (step @p237 :rule trans :premises (@p236 @p234)) % 0.37/0.62 (step @p238 :rule refl :args (@t14)) % 0.37/0.62 (step @p239 :rule ho_cong :premises (@p238 @p237)) % 0.37/0.62 (step @p240 :rule trans :premises (@p239 @p228)) % 0.37/0.62 (step @p241 :rule ho_cong :premises (@p240 @p175)) % 0.37/0.62 (step @p242 :rule trans :premises (@p241 @p223)) % 0.37/0.62 (step @p243 :rule ho_cong :premises (@p6 @p177)) % 0.37/0.62 (step @p244 :rule ho_cong :premises (@p194 @p243)) % 0.37/0.62 (step @p245 :rule ho_cong :premises (@p6 @p244)) % 0.37/0.62 (step @p246 :rule ho_cong :premises (@p245 @p175)) % 0.37/0.62 (step @p247 :rule trans :premises (@p246 @p242)) % 0.37/0.62 (step @p248 :rule cong :premises (@p247) :args (@t23)) % 0.37/0.62 (step @p249 :rule trans :premises (@p8 @p248)) % 0.37/0.62 (step @p250 :rule ho_cong :premises (@p249 @p222)) % 0.37/0.62 (step @p251 :rule ho_cong :premises (@p250 @p220)) % 0.37/0.62 (step @p252 :rule ho_cong :premises (@p199 @p251)) % 0.37/0.62 (step @p253 :rule ho_cong :premises (@p252 @p217)) % 0.37/0.62 (step @p254 :rule refl :args (@t120)) % 0.37/0.62 (step @p255 :rule refl :args (@t11)) % 0.37/0.62 (step @p256 :rule cong :premises (@p255 @p254) :args ((= @t11 @t120))) % 0.37/0.62 (step @p257 :rule symm :premises (@p256)) % 0.37/0.62 (step @p258 :rule eq_resolve :premises (@p255 @p257)) % 0.37/0.62 (step @p259 :rule cong :premises (@p258) :args (@t72)) % 0.37/0.62 (step @p260 :rule cong :premises (@p259) :args (@t74)) % 0.37/0.62 (step @p261 :rule trans :premises (@p30 @p260)) % 0.37/0.62 (step @p262 :rule ho_cong :premises (@p261 @p253)) % 0.37/0.62 (step @p263 :rule cong :premises (@p262) :args (@t2)) % 0.37/0.62 (step @p264 :rule trans :premises (@p263 @p172)) % 0.37/0.62 (step @p265 :rule eq_resolve :premises (@p2 @p264)) % 0.37/0.62 (step @p266 :rule skolemize :premises (@p265)) % 0.37/0.62 (step @p267 :rule bool-double-not-elim :args (@t211)) % 0.37/0.62 (step @p268 :rule refl :args (@t221)) % 0.37/0.62 (step @p269 :rule nary_cong :premises (@p268 @p267) :args ((or @t221 (not @t215)))) % 0.37/0.62 (step @p270 :rule cnf_or_neg :args (@t221 2)) % 0.37/0.62 (step @p271 :rule eq_resolve :premises (@p270 @p269)) % 0.37/0.62 (step @p272 :rule reordering :premises (@p271) :args ((or @t211 @t221))) % 0.37/0.62 (step @p273 :rule chain_m_resolution :premises (@p272 @p266) :args (@t211 @t222 @t223)) % 0.37/0.62 (step @p274 :rule cnf_or_neg :args (@t221 4)) % 0.37/0.62 (step @p275 :rule chain_m_resolution :premises (@p274 @p266) :args ((not @t212) @t222 @t223)) % 0.37/0.62 (step @p276 :rule bool-double-not-elim :args (@t217)) % 0.37/0.62 (step @p277 :rule nary_cong :premises (@p268 @p276) :args ((or @t221 (not @t218)))) % 0.37/0.62 (step @p278 :rule cnf_or_neg :args (@t221 1)) % 0.37/0.62 (step @p279 :rule eq_resolve :premises (@p278 @p277)) % 0.37/0.62 (step @p280 :rule reordering :premises (@p279) :args ((or @t217 @t221))) % 0.37/0.62 (step @p281 :rule chain_m_resolution :premises (@p280 @p266) :args (@t217 @t222 @t223)) % 0.37/0.62 (step @p282 :rule instantiate :premises (@p281) :args (@t224)) % 0.37/0.62 (step @p283 :rule bool-double-not-elim :args (@t219)) % 0.37/0.62 (step @p284 :rule nary_cong :premises (@p268 @p283) :args ((or @t221 (not @t220)))) % 0.37/0.62 (step @p285 :rule cnf_or_neg :args (@t221 0)) % 0.37/0.62 (step @p286 :rule eq_resolve :premises (@p285 @p284)) % 0.37/0.62 (step @p287 :rule reordering :premises (@p286) :args ((or @t219 @t221))) % 0.37/0.62 (step @p288 :rule chain_m_resolution :premises (@p287 @p266) :args (@t219 @t222 @t223)) % 0.37/0.62 (step @p289 :rule instantiate :premises (@p288) :args (@t224)) % 0.37/0.62 (step @p290 :rule bool-double-not-elim :args (@t213)) % 0.37/0.62 (step @p291 :rule nary_cong :premises (@p268 @p290) :args ((or @t221 (not @t214)))) % 0.37/0.62 (step @p292 :rule cnf_or_neg :args (@t221 3)) % 0.37/0.62 (step @p293 :rule eq_resolve :premises (@p292 @p291)) % 0.37/0.62 (step @p294 :rule reordering :premises (@p293) :args ((or @t213 @t221))) % 0.37/0.62 (step @p295 :rule chain_m_resolution :premises (@p294 @p266) :args (@t213 @t222 @t223)) % 0.37/0.62 (step @p296 :rule cnf_or_pos :args (@t226)) % 0.37/0.62 (step @p297 :rule reordering :premises (@p296) :args ((or @t215 @t214 @t225 (not @t226)))) % 0.37/0.62 (step @p298 :rule chain_m_resolution :premises (@p297 @p273 @p295 @p289) :args (@t225 (@list false false false) (@list @t211 @t213 @t226))) % 0.37/0.62 (step @p299 :rule cnf_or_pos :args (@t228)) % 0.37/0.62 (step @p300 :rule reordering :premises (@p299) :args ((or @t215 @t212 @t227 (not @t228)))) % 0.37/0.62 (step @p301 false :rule chain_m_resolution :premises (@p300 @p298 @p282 @p275 @p273) :args (false (@list false false true false) (@list @t225 @t228 @t212 @t211))) % 0.37/0.62 ) % 0.37/0.62 % SZS output end Proof % 0.37/0.62 % cvc5 exiting %------------------------------------------------------------------------------