%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO488^6 : 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 09:12:58 AM UTC 2026 % Result : Theorem 0.38s 0.60s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO488^6 : 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 % 0.17/0.33 % Computer : n005.cluster.edu % 0.17/0.33 % Model : x86_64 x86_64 % 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.33 % Memory : 8042.1875MB % 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.33 % CPULimit : 300 % 0.17/0.33 % WCLimit : 300 % 0.17/0.33 % DateTime : Wed Jun 3 00:16:48 EDT 2026 % 0.17/0.33 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.38/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.60 % SZS status Theorem % 0.38/0.60 % SZS output start Proof % 0.38/0.60 ( % 0.38/0.60 (declare-sort $$unsorted 0) % 0.38/0.60 (declare-sort tptp.mu 0) % 0.38/0.60 (declare-const tptp.rel_s5 (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.f (-> tptp.mu $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.38/0.60 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.38/0.60 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.38/0.60 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.38/0.60 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.38/0.60 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.38/0.60 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.38/0.60 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.38/0.60 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.60 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.60 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.38/0.60 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.38/0.60 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.38/0.60 (define tptp.mbox () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.38/0.60 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.38/0.60 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.38/0.60 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.60 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.60 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "T" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.38/0.60 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.38/0.60 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.38/0.60 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.38/0.60 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.38/0.60 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.38/0.60 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "T" $$unsorted))) (let ((_let_5 (@var "S" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.38/0.60 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.60 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.60 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.mbox_s5 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s5 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.38/0.60 (define tptp.mdia_s5 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s5 (_ tptp.mnot _let_2))) _let_1))))) % 0.38/0.60 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.38/0.60 (define @t2 () (@var "X" tptp.mu)) % 0.38/0.60 (define @t3 () (_ tptp.f @t2)) % 0.38/0.60 (define @t4 () (@list @t2 @t1)) % 0.38/0.60 (define @t5 () (lambda @t4 (_ (_ tptp.mbox_s5 (_ tptp.mnot @t3)) @t1))) % 0.38/0.60 (define @t6 () (lambda @t4 (_ @t3 @t1))) % 0.38/0.60 (define @t7 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mdia_s5 (_ tptp.mforall_ind @t6))) (_ tptp.mnot (_ tptp.mexists_ind @t5)))))) % 0.38/0.60 (define @t8 () (@var "Y" tptp.mu)) % 0.38/0.60 (define @t9 () (@var "W" $$unsorted)) % 0.38/0.60 (define @t10 () (lambda (@list @t2 @t8 @t9) (= @t2 @t8))) % 0.38/0.60 (define @t11 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.60 (define @t12 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.60 (define @t13 () (lambda (@list @t12 @t11 @t9) (= (_ @t12 @t9) (_ @t11 @t9)))) % 0.38/0.60 (define @t14 () (@var "Phi" (-> $$unsorted Bool))) % 0.38/0.60 (define @t15 () (_ @t14 @t9)) % 0.38/0.60 (define @t16 () (not @t15)) % 0.38/0.60 (define @t17 () (@list @t14 @t9)) % 0.38/0.60 (define @t18 () (lambda @t17 @t16)) % 0.38/0.60 (define @t19 () (@var "Psi" (-> $$unsorted Bool))) % 0.38/0.60 (define @t20 () (_ @t19 @t9)) % 0.38/0.60 (define @t21 () (lambda (@list @t14 @t19 @t9) (or @t15 @t20))) % 0.38/0.60 (define @t22 () (_ tptp.mnot @t19)) % 0.38/0.60 (define @t23 () (_ tptp.mnot @t14)) % 0.38/0.60 (define @t24 () (_ tptp.mor @t23)) % 0.38/0.60 (define @t25 () (@list @t14 @t19 @t1)) % 0.38/0.60 (define @t26 () (lambda @t25 (_ (_ tptp.mnot (_ @t24 @t22)) @t1))) % 0.38/0.60 (define @t27 () (lambda @t25 (_ (_ @t24 @t19) @t1))) % 0.38/0.60 (define @t28 () (lambda @t25 (_ (_ (_ tptp.mor @t22) @t14) @t1))) % 0.38/0.60 (define @t29 () (lambda @t25 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t14) @t19)) (_ (_ tptp.mimplies @t19) @t14)) @t1))) % 0.38/0.60 (define @t30 () (lambda @t25 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t14) @t19)) @t1))) % 0.38/0.60 (define @t31 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.38/0.60 (define @t32 () (_ @t31 @t2)) % 0.38/0.60 (define @t33 () (_ @t32 @t9)) % 0.38/0.60 (define @t34 () (@list @t2)) % 0.38/0.60 (define @t35 () (forall @t34 @t33)) % 0.38/0.60 (define @t36 () (@list @t31 @t9)) % 0.38/0.60 (define @t37 () (lambda @t36 @t35)) % 0.38/0.60 (define @t38 () (@var "P" (-> $$unsorted Bool))) % 0.38/0.60 (define @t39 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.38/0.60 (define @t40 () (_ @t39 @t38)) % 0.38/0.60 (define @t41 () (lambda (@list @t39 @t9) (forall (@list @t38) (_ @t40 @t9)))) % 0.38/0.60 (define @t42 () (lambda @t4 (_ (_ tptp.mnot @t32) @t1))) % 0.38/0.60 (define @t43 () (@list @t31 @t1)) % 0.38/0.60 (define @t44 () (lambda @t43 (_ (_ tptp.mnot (_ tptp.mforall_ind @t42)) @t1))) % 0.38/0.60 (define @t45 () (lambda (@list @t39 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t38 @t1) (_ (_ tptp.mnot @t40) @t1)))) @t1))) % 0.38/0.60 (define @t46 () (@list @t9)) % 0.38/0.60 (define @t47 () (lambda @t46 true)) % 0.38/0.60 (define @t48 () (@var "V" $$unsorted)) % 0.38/0.60 (define @t49 () (_ @t14 @t48)) % 0.38/0.60 (define @t50 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.38/0.60 (define @t51 () (@list @t48)) % 0.38/0.60 (define @t52 () (lambda (@list @t50 @t14 @t9) (forall @t51 (or (not (_ (_ @t50 @t9) @t48)) @t49)))) % 0.38/0.60 (define @t53 () (lambda (@list @t50 @t14 @t1) (_ (_ tptp.mnot (_ (_ tptp.mbox @t50) @t23)) @t1))) % 0.38/0.60 (define @t54 () (@var "S" $$unsorted)) % 0.38/0.60 (define @t55 () (_ @t50 @t54)) % 0.38/0.60 (define @t56 () (@list @t54)) % 0.38/0.60 (define @t57 () (@list @t50)) % 0.38/0.60 (define @t58 () (lambda @t57 (forall @t56 (_ @t55 @t54)))) % 0.38/0.60 (define @t59 () (@var "T" $$unsorted)) % 0.38/0.60 (define @t60 () (_ @t50 @t59)) % 0.38/0.60 (define @t61 () (_ @t55 @t59)) % 0.38/0.60 (define @t62 () (lambda @t57 (forall (@list @t54 @t59) (=> @t61 (_ @t60 @t54))))) % 0.38/0.60 (define @t63 () (@list @t59)) % 0.38/0.60 (define @t64 () (lambda @t57 (forall @t56 (exists @t63 @t61)))) % 0.38/0.60 (define @t65 () (@var "U" $$unsorted)) % 0.38/0.60 (define @t66 () (_ @t55 @t65)) % 0.38/0.60 (define @t67 () (_ @t60 @t65)) % 0.38/0.60 (define @t68 () (@list @t54 @t59 @t65)) % 0.38/0.60 (define @t69 () (lambda @t57 (forall @t68 (=> (and @t61 @t67) @t66)))) % 0.38/0.60 (define @t70 () (and @t61 @t66)) % 0.38/0.60 (define @t71 () (lambda @t57 (forall @t68 (=> @t70 @t67)))) % 0.38/0.60 (define @t72 () (= @t59 @t65)) % 0.38/0.60 (define @t73 () (lambda @t57 (forall @t68 (=> @t70 @t72)))) % 0.38/0.60 (define @t74 () (@list @t65)) % 0.38/0.60 (define @t75 () (lambda @t57 (forall @t56 (exists @t63 (and @t61 (forall @t74 (=> @t66 @t72))))))) % 0.38/0.60 (define @t76 () (_ @t50 @t65)) % 0.38/0.60 (define @t77 () (_ @t76 @t59)) % 0.38/0.60 (define @t78 () (lambda @t57 (forall @t68 (=> @t61 (exists @t74 (and @t66 @t77)))))) % 0.38/0.60 (define @t79 () (lambda @t57 (forall @t68 (=> @t70 (or @t67 @t72 @t77))))) % 0.38/0.60 (define @t80 () (lambda @t57 (forall @t68 (=> @t70 (exists @t51 (and (_ @t60 @t48) (_ @t76 @t48))))))) % 0.38/0.60 (define @t81 () (forall @t46 @t15)) % 0.38/0.60 (define @t82 () (@list @t14)) % 0.38/0.60 (define @t83 () (lambda @t82 @t81)) % 0.38/0.60 (define @t84 () (lambda @t82 (forall @t46 @t16))) % 0.38/0.60 (define @t85 () (lambda @t82 (exists @t46 @t15))) % 0.38/0.60 (define @t86 () (lambda @t82 (exists @t46 @t16))) % 0.38/0.60 (define @t87 () (_ (_ tptp.rel_s5 @t9) @t48)) % 0.38/0.60 (define @t88 () (not @t87)) % 0.38/0.60 (define @t89 () (or @t88 @t49)) % 0.38/0.60 (define @t90 () (forall @t51 @t89)) % 0.38/0.60 (define @t91 () (lambda @t17 @t90)) % 0.38/0.60 (define @t92 () (@list @t14 @t1)) % 0.38/0.60 (define @t93 () (lambda @t92 (_ (_ tptp.mnot (_ tptp.mbox_s5 @t23)) @t1))) % 0.38/0.60 (define @t94 () (@var "BOUND_VARIABLE_8517" $$unsorted)) % 0.38/0.60 (define @t95 () (not (forall @t34 (tptp.f @t2 @t94)))) % 0.38/0.60 (define @t96 () (not (tptp.rel_s5 @t9 @t94))) % 0.38/0.60 (define @t97 () (@var "BOUND_VARIABLE_8525" tptp.mu)) % 0.38/0.60 (define @t98 () (tptp.rel_s5 @t9 @t48)) % 0.38/0.60 (define @t99 () (not @t98)) % 0.38/0.60 (define @t100 () (not (forall @t51 (or @t99 (not (tptp.f @t97 @t48)))))) % 0.38/0.60 (define @t101 () (or @t100 @t96 @t95)) % 0.38/0.60 (define @t102 () (or @t96 @t95)) % 0.38/0.60 (define @t103 () (or @t102 @t100)) % 0.38/0.60 (define @t104 () (@list @t9 @t94 @t97)) % 0.38/0.60 (define @t105 () (forall @t104 @t103)) % 0.38/0.60 (define @t106 () (forall (@list @t94 @t97) @t103)) % 0.38/0.60 (define @t107 () (forall (@list @t97) @t100)) % 0.38/0.60 (define @t108 () (forall (@list @t94) @t102)) % 0.38/0.60 (define @t109 () (or @t108 @t107)) % 0.38/0.60 (define @t110 () (tptp.f @t2 @t48)) % 0.38/0.60 (define @t111 () (not @t110)) % 0.38/0.60 (define @t112 () (forall @t51 (or @t99 @t111))) % 0.38/0.60 (define @t113 () (forall @t34 (not @t112))) % 0.38/0.60 (define @t114 () (forall @t34 @t110)) % 0.38/0.60 (define @t115 () (not @t114)) % 0.38/0.60 (define @t116 () (or (forall @t51 (or @t99 @t115)) @t113)) % 0.38/0.60 (define @t117 () (not (tptp.rel_s5 @t1 @t48))) % 0.38/0.60 (define @t118 () (forall @t51 (or @t117 @t111))) % 0.38/0.60 (define @t119 () (forall @t34 (not @t118))) % 0.38/0.60 (define @t120 () (forall @t51 (or @t117 @t115))) % 0.38/0.60 (define @t121 () (@list @t1)) % 0.38/0.60 (define @t122 () (lambda @t121 (or @t120 @t119))) % 0.38/0.60 (define @t123 () (_ @t122 @t9)) % 0.38/0.60 (define @t124 () (forall @t46 @t123)) % 0.38/0.60 (define @t125 () (_ @t14 @t9)) % 0.38/0.60 (define @t126 () (lambda @t82 (forall @t46 @t125))) % 0.38/0.60 (define @t127 () (lambda @t46 @t113)) % 0.38/0.60 (define @t128 () (_ @t127 @t1)) % 0.38/0.60 (define @t129 () (or @t120 @t128)) % 0.38/0.60 (define @t130 () (lambda @t121 @t129)) % 0.38/0.60 (define @t131 () (_ @t19 @t1)) % 0.38/0.60 (define @t132 () (@list @t19 @t1)) % 0.38/0.60 (define @t133 () (lambda @t121 (not @t119))) % 0.38/0.60 (define @t134 () (_ @t133 @t9)) % 0.38/0.60 (define @t135 () (not @t134)) % 0.38/0.60 (define @t136 () (lambda @t46 @t135)) % 0.38/0.60 (define @t137 () (lambda @t4 @t118)) % 0.38/0.60 (define @t138 () (_ @t137 @t2 @t1)) % 0.38/0.60 (define @t139 () (not @t138)) % 0.38/0.60 (define @t140 () (forall @t34 @t139)) % 0.38/0.60 (define @t141 () (not @t140)) % 0.38/0.60 (define @t142 () (lambda @t121 @t141)) % 0.38/0.60 (define @t143 () (not (forall @t34 (not (_ @t31 @t2 @t1))))) % 0.38/0.60 (define @t144 () (lambda @t43 @t143)) % 0.38/0.60 (define @t145 () (_ @t3 @t48)) % 0.38/0.60 (define @t146 () (not @t145)) % 0.38/0.60 (define @t147 () (or @t99 @t146)) % 0.38/0.60 (define @t148 () (_ @t3 @t9)) % 0.38/0.60 (define @t149 () (lambda @t46 (not @t148))) % 0.38/0.60 (define @t150 () (_ @t149 @t48)) % 0.38/0.60 (define @t151 () (or @t99 @t150)) % 0.38/0.60 (define @t152 () (forall @t51 @t151)) % 0.38/0.60 (define @t153 () (lambda @t46 @t152)) % 0.38/0.60 (define @t154 () (_ @t14 @t48)) % 0.38/0.60 (define @t155 () (lambda @t17 (forall @t51 (or @t99 @t154)))) % 0.38/0.60 (define @t156 () (_ @t18 @t3)) % 0.38/0.60 (define @t157 () (lambda @t4 (_ (_ @t155 @t156) @t1))) % 0.38/0.60 (define @t158 () (not @t120)) % 0.38/0.60 (define @t159 () (lambda @t121 @t158)) % 0.38/0.60 (define @t160 () (_ @t159 @t1)) % 0.38/0.60 (define @t161 () (not @t160)) % 0.38/0.60 (define @t162 () (or @t161 @t131)) % 0.38/0.60 (define @t163 () (lambda @t132 @t162)) % 0.38/0.60 (define @t164 () (or (not (_ @t14 @t1)) @t131)) % 0.38/0.60 (define @t165 () (lambda @t25 @t164)) % 0.38/0.60 (define @t166 () (tptp.f @t2 @t9)) % 0.38/0.60 (define @t167 () (lambda @t46 (forall @t34 @t166))) % 0.38/0.60 (define @t168 () (_ @t167 @t48)) % 0.38/0.60 (define @t169 () (not @t168)) % 0.38/0.60 (define @t170 () (or @t117 @t169)) % 0.38/0.60 (define @t171 () (forall @t51 @t170)) % 0.38/0.60 (define @t172 () (not @t171)) % 0.38/0.60 (define @t173 () (lambda @t121 @t172)) % 0.38/0.60 (define @t174 () (not @t154)) % 0.38/0.60 (define @t175 () (not (forall @t51 (or @t117 @t174)))) % 0.38/0.60 (define @t176 () (lambda @t92 @t175)) % 0.38/0.60 (define @t177 () (_ @t6 @t2 @t9)) % 0.38/0.60 (define @t178 () (forall @t34 @t177)) % 0.38/0.60 (define @t179 () (lambda @t46 @t178)) % 0.38/0.60 (define @t180 () (_ @t31 @t2 @t9)) % 0.38/0.60 (define @t181 () (lambda @t36 (forall @t34 @t180))) % 0.38/0.60 (define @t182 () (_ @t181 @t6)) % 0.38/0.60 (define @t183 () (forall @t34 (not @t180))) % 0.38/0.60 (define @t184 () (lambda @t46 @t183)) % 0.38/0.60 (define @t185 () (_ @t184 @t9)) % 0.38/0.60 (define @t186 () (not @t185)) % 0.38/0.60 (define @t187 () (lambda @t46 @t186)) % 0.38/0.60 (define @t188 () (not @t33)) % 0.38/0.60 (define @t189 () (not (_ @t32 @t1))) % 0.38/0.60 (define @t190 () (lambda @t4 @t189)) % 0.38/0.60 (define @t191 () (_ @t190 @t2 @t9)) % 0.38/0.60 (define @t192 () (forall @t34 @t191)) % 0.38/0.60 (define @t193 () (lambda @t46 @t192)) % 0.38/0.60 (define @t194 () (lambda @t46 @t188)) % 0.38/0.60 (define @t195 () (_ @t18 @t32)) % 0.38/0.60 (define @t196 () (forall @t51 (or @t99 @t174))) % 0.38/0.60 (define @t197 () (lambda @t46 @t196)) % 0.38/0.60 (define @t198 () (_ @t197 @t9)) % 0.38/0.60 (define @t199 () (not @t198)) % 0.38/0.60 (define @t200 () (lambda @t46 @t199)) % 0.38/0.60 (define @t201 () (not @t49)) % 0.38/0.60 (define @t202 () (or @t99 @t201)) % 0.38/0.60 (define @t203 () (lambda @t46 @t16)) % 0.38/0.60 (define @t204 () (_ @t203 @t48)) % 0.38/0.60 (define @t205 () (or @t99 @t204)) % 0.38/0.60 (define @t206 () (forall @t51 @t205)) % 0.38/0.60 (define @t207 () (lambda @t46 @t206)) % 0.38/0.60 (define @t208 () (or @t16 @t20)) % 0.38/0.60 (define @t209 () (lambda @t46 @t208)) % 0.38/0.60 (define @t210 () (@list @t19 @t9)) % 0.38/0.60 (define @t211 () (_ @t203 @t9)) % 0.38/0.60 (define @t212 () (or @t211 @t20)) % 0.38/0.60 (define @t213 () (lambda @t210 @t212)) % 0.38/0.60 (define @t214 () (forall @t104 @t101)) % 0.38/0.60 (define @t215 () (@quantifiers_skolemize @t214 1)) % 0.38/0.60 (define @t216 () (forall @t34 (tptp.f @t2 @t215))) % 0.38/0.60 (define @t217 () (not @t216)) % 0.38/0.60 (define @t218 () (@quantifiers_skolemize @t214 0)) % 0.38/0.60 (define @t219 () (tptp.rel_s5 @t218 @t215)) % 0.38/0.60 (define @t220 () (not @t219)) % 0.38/0.60 (define @t221 () (@quantifiers_skolemize @t214 2)) % 0.38/0.60 (define @t222 () (forall @t51 (or (not (tptp.rel_s5 @t218 @t48)) (not (tptp.f @t221 @t48))))) % 0.38/0.60 (define @t223 () (not @t222)) % 0.38/0.60 (define @t224 () (or @t223 @t220 @t217)) % 0.38/0.60 (define @t225 () (@list true)) % 0.38/0.60 (define @t226 () (@list @t224)) % 0.38/0.60 (define @t227 () (tptp.f @t221 @t215)) % 0.38/0.60 (define @t228 () (not @t227)) % 0.38/0.60 (define @t229 () (or @t220 @t228)) % 0.38/0.60 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.38/0.60 (assume @p2 (_ tptp.mreflexive tptp.rel_s5)) % 0.38/0.60 (assume @p3 (_ tptp.mtransitive tptp.rel_s5)) % 0.38/0.60 (assume @p4 (_ tptp.msymmetric tptp.rel_s5)) % 0.38/0.60 (assume @p5 @t7) % 0.38/0.60 (assume @p6 true) % 0.38/0.60 (step @p7 (= tptp.meq_ind @t10) :rule refl :args (@t10)) % 0.38/0.60 (step @p8 (= tptp.meq_prop @t13) :rule refl :args (@t13)) % 0.38/0.60 (step @p9 (= tptp.mnot @t18) :rule refl :args (@t18)) % 0.38/0.60 (step @p10 (= tptp.mor @t21) :rule refl :args (@t21)) % 0.38/0.60 (step @p11 (= tptp.mand @t26) :rule refl :args (@t26)) % 0.38/0.60 (step @p12 (= tptp.mimplies @t27) :rule refl :args (@t27)) % 0.38/0.60 (step @p13 (= tptp.mimplied @t28) :rule refl :args (@t28)) % 0.38/0.60 (step @p14 (= tptp.mequiv @t29) :rule refl :args (@t29)) % 0.38/0.60 (step @p15 (= tptp.mxor @t30) :rule refl :args (@t30)) % 0.38/0.60 (step @p16 (= tptp.mforall_ind @t37) :rule refl :args (@t37)) % 0.38/0.60 (step @p17 (= tptp.mforall_prop @t41) :rule refl :args (@t41)) % 0.38/0.60 (step @p18 (= tptp.mexists_ind @t44) :rule refl :args (@t44)) % 0.38/0.60 (step @p19 (= tptp.mexists_prop @t45) :rule refl :args (@t45)) % 0.38/0.60 (step @p20 (= tptp.mtrue @t47) :rule refl :args (@t47)) % 0.38/0.60 (step @p21 (= tptp.mbox @t52) :rule refl :args (@t52)) % 0.38/0.60 (step @p22 (= tptp.mdia @t53) :rule refl :args (@t53)) % 0.38/0.60 (step @p23 (= tptp.mreflexive @t58) :rule refl :args (@t58)) % 0.38/0.60 (step @p24 (= tptp.msymmetric @t62) :rule refl :args (@t62)) % 0.38/0.60 (step @p25 (= tptp.mserial @t64) :rule refl :args (@t64)) % 0.38/0.60 (step @p26 (= tptp.mtransitive @t69) :rule refl :args (@t69)) % 0.38/0.60 (step @p27 (= tptp.meuclidean @t71) :rule refl :args (@t71)) % 0.38/0.60 (step @p28 (= tptp.mpartially_functional @t73) :rule refl :args (@t73)) % 0.38/0.60 (step @p29 (= tptp.mfunctional @t75) :rule refl :args (@t75)) % 0.38/0.60 (step @p30 (= tptp.mweakly_dense @t78) :rule refl :args (@t78)) % 0.38/0.60 (step @p31 (= tptp.mweakly_connected @t79) :rule refl :args (@t79)) % 0.38/0.60 (step @p32 (= tptp.mweakly_directed @t80) :rule refl :args (@t80)) % 0.38/0.60 (step @p33 (= tptp.mvalid @t83) :rule refl :args (@t83)) % 0.38/0.60 (step @p34 (= tptp.minvalid @t84) :rule refl :args (@t84)) % 0.38/0.60 (step @p35 (= tptp.msatisfiable @t85) :rule refl :args (@t85)) % 0.38/0.60 (step @p36 (= tptp.mcountersatisfiable @t86) :rule refl :args (@t86)) % 0.38/0.60 (step @p37 (= tptp.mbox_s5 @t91) :rule refl :args (@t91)) % 0.38/0.60 (step @p38 (= tptp.mdia_s5 @t93) :rule refl :args (@t93)) % 0.38/0.60 (step @p39 :rule aci_norm :args ((= @t103 @t101))) % 0.38/0.60 (step @p40 :rule cong :premises (@p39) :args (@t105)) % 0.38/0.60 (step @p41 :rule quant-merge-prenex :args ((= (forall @t46 @t106) @t105))) % 0.38/0.60 (step @p42 :rule alpha_equiv :args (@t107 (@list @t97) (@list @t2))) % 0.38/0.60 (step @p43 :rule alpha_equiv :args (@t108 (@list @t94) (@list @t48))) % 0.38/0.60 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t109)) % 0.38/0.60 (step @p45 :rule quant-miniscope-or :args ((= @t106 @t109))) % 0.38/0.60 (step @p46 :rule trans :premises (@p45 @p44)) % 0.38/0.60 (step @p47 :rule symm :premises (@p46)) % 0.38/0.60 (step @p48 :rule cong :premises (@p47) :args ((forall @t46 @t116))) % 0.38/0.60 (step @p49 :rule trans :premises (@p48 @p41)) % 0.38/0.60 (step @p50 :rule trans :premises (@p49 @p40)) % 0.38/0.60 (step @p51 :rule beta-reduce :args ((= @t123 @t116))) % 0.38/0.60 (step @p52 :rule cong :premises (@p51) :args (@t124)) % 0.38/0.60 (step @p53 :rule trans :premises (@p52 @p50)) % 0.38/0.60 (step @p54 :rule beta-reduce :args ((= (_ @t126 @t122) @t124))) % 0.38/0.60 (step @p55 :rule trans :premises (@p54 @p53)) % 0.38/0.60 (step @p56 :rule beta-reduce :args ((= @t128 @t119))) % 0.38/0.60 (step @p57 :rule refl :args (@t120)) % 0.38/0.60 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t129)) % 0.38/0.60 (step @p59 :rule cong :premises (@p58) :args (@t130)) % 0.38/0.60 (step @p60 :rule beta-reduce :args ((= (_ (lambda @t132 (or @t120 @t131)) @t127) @t130))) % 0.38/0.60 (step @p61 :rule trans :premises (@p60 @p59)) % 0.38/0.60 (step @p62 :rule bool-double-not-elim :args (@t113)) % 0.38/0.60 (step @p63 :rule beta-reduce :args ((= @t134 (not @t113)))) % 0.38/0.60 (step @p64 :rule cong :premises (@p63) :args (@t135)) % 0.38/0.60 (step @p65 :rule trans :premises (@p64 @p62)) % 0.38/0.60 (step @p66 :rule cong :premises (@p65) :args (@t136)) % 0.38/0.60 (step @p67 :rule beta-reduce :args ((= (_ @t18 @t133) @t136))) % 0.38/0.60 (step @p68 :rule trans :premises (@p67 @p66)) % 0.38/0.60 (step @p69 :rule beta-reduce :args ((= @t138 @t118))) % 0.38/0.60 (step @p70 :rule cong :premises (@p69) :args (@t139)) % 0.38/0.60 (step @p71 :rule cong :premises (@p70) :args (@t140)) % 0.38/0.60 (step @p72 :rule cong :premises (@p71) :args (@t141)) % 0.38/0.60 (step @p73 :rule cong :premises (@p72) :args (@t142)) % 0.38/0.60 (step @p74 :rule beta-reduce :args ((= (_ @t144 @t137) @t142))) % 0.38/0.60 (step @p75 :rule trans :premises (@p74 @p73)) % 0.38/0.60 (step @p76 :rule beta-reduce :args ((= (_ (lambda @t46 @t112) @t1) @t118))) % 0.38/0.60 (step @p77 :rule refl :args (@t1)) % 0.38/0.60 (step @p78 :rule refl :args (@t110)) % 0.38/0.60 (step @p79 :rule refl :args (@t145)) % 0.38/0.60 (step @p80 :rule cong :premises (@p79 @p78) :args ((= @t145 @t110))) % 0.38/0.60 (step @p81 :rule symm :premises (@p80)) % 0.38/0.60 (step @p82 :rule eq_resolve :premises (@p79 @p81)) % 0.38/0.60 (step @p83 :rule cong :premises (@p82) :args (@t146)) % 0.38/0.60 (step @p84 :rule refl :args (@t99)) % 0.38/0.60 (step @p85 :rule nary_cong :premises (@p84 @p83) :args (@t147)) % 0.38/0.60 (step @p86 :rule cong :premises (@p85) :args ((forall @t51 @t147))) % 0.38/0.60 (step @p87 :rule beta-reduce :args ((= @t150 @t146))) % 0.38/0.60 (step @p88 :rule refl :args (@t99)) % 0.38/0.60 (step @p89 :rule nary_cong :premises (@p88 @p87) :args (@t151)) % 0.38/0.60 (step @p90 :rule cong :premises (@p89) :args (@t152)) % 0.38/0.60 (step @p91 :rule trans :premises (@p90 @p86)) % 0.38/0.60 (step @p92 :rule cong :premises (@p91) :args (@t153)) % 0.38/0.60 (step @p93 :rule beta-reduce :args ((= (_ @t155 @t149) @t153))) % 0.38/0.60 (step @p94 :rule trans :premises (@p93 @p92)) % 0.38/0.60 (step @p95 :rule beta-reduce :args ((= @t156 @t149))) % 0.38/0.60 (step @p96 :rule refl :args (@t155)) % 0.38/0.60 (step @p97 :rule ho_cong :premises (@p96 @p95)) % 0.38/0.60 (step @p98 :rule trans :premises (@p97 @p94)) % 0.38/0.60 (step @p99 :rule ho_cong :premises (@p98 @p77)) % 0.38/0.60 (step @p100 :rule trans :premises (@p99 @p76)) % 0.38/0.60 (step @p101 :rule cong :premises (@p100) :args (@t157)) % 0.38/0.60 (step @p102 :rule refl :args (@t144)) % 0.38/0.60 (step @p103 :rule ho_cong :premises (@p102 @p101)) % 0.38/0.60 (step @p104 :rule trans :premises (@p103 @p75)) % 0.38/0.60 (step @p105 :rule refl :args (@t18)) % 0.38/0.60 (step @p106 :rule ho_cong :premises (@p105 @p104)) % 0.38/0.60 (step @p107 :rule trans :premises (@p106 @p68)) % 0.38/0.60 (step @p108 :rule refl :args (@t131)) % 0.38/0.60 (step @p109 :rule bool-double-not-elim :args (@t120)) % 0.38/0.60 (step @p110 :rule beta-reduce :args ((= @t160 @t158))) % 0.38/0.60 (step @p111 :rule cong :premises (@p110) :args (@t161)) % 0.38/0.60 (step @p112 :rule trans :premises (@p111 @p109)) % 0.38/0.60 (step @p113 :rule nary_cong :premises (@p112 @p108) :args (@t162)) % 0.38/0.60 (step @p114 :rule cong :premises (@p113) :args (@t163)) % 0.38/0.60 (step @p115 :rule beta-reduce :args ((= (_ @t165 @t159) @t163))) % 0.38/0.60 (step @p116 :rule trans :premises (@p115 @p114)) % 0.38/0.60 (step @p117 :rule beta-reduce :args ((= @t168 @t114))) % 0.38/0.60 (step @p118 :rule cong :premises (@p117) :args (@t169)) % 0.38/0.60 (step @p119 :rule refl :args (@t117)) % 0.38/0.60 (step @p120 :rule nary_cong :premises (@p119 @p118) :args (@t170)) % 0.38/0.60 (step @p121 :rule cong :premises (@p120) :args (@t171)) % 0.38/0.60 (step @p122 :rule cong :premises (@p121) :args (@t172)) % 0.38/0.60 (step @p123 :rule cong :premises (@p122) :args (@t173)) % 0.38/0.60 (step @p124 :rule beta-reduce :args ((= (_ @t176 @t167) @t173))) % 0.38/0.60 (step @p125 :rule trans :premises (@p124 @p123)) % 0.38/0.60 (step @p126 :rule refl :args (@t166)) % 0.38/0.60 (step @p127 :rule refl :args (@t148)) % 0.38/0.60 (step @p128 :rule cong :premises (@p127 @p126) :args ((= @t148 @t166))) % 0.38/0.60 (step @p129 :rule symm :premises (@p128)) % 0.38/0.60 (step @p130 :rule eq_resolve :premises (@p127 @p129)) % 0.38/0.60 (step @p131 :rule cong :premises (@p130) :args ((forall @t34 @t148))) % 0.38/0.60 (step @p132 :rule beta-reduce :args ((= @t177 @t148))) % 0.38/0.60 (step @p133 :rule cong :premises (@p132) :args (@t178)) % 0.38/0.60 (step @p134 :rule trans :premises (@p133 @p131)) % 0.38/0.60 (step @p135 :rule cong :premises (@p134) :args (@t179)) % 0.38/0.60 (step @p136 :rule beta-reduce :args ((= @t182 @t179))) % 0.38/0.60 (step @p137 :rule trans :premises (@p136 @p135)) % 0.38/0.60 (step @p138 :rule refl :args (@t176)) % 0.38/0.60 (step @p139 :rule ho_cong :premises (@p138 @p137)) % 0.38/0.60 (step @p140 :rule trans :premises (@p139 @p125)) % 0.38/0.60 (step @p141 :rule refl :args (@t165)) % 0.38/0.60 (step @p142 :rule ho_cong :premises (@p141 @p140)) % 0.38/0.60 (step @p143 :rule trans :premises (@p142 @p116)) % 0.38/0.60 (step @p144 :rule ho_cong :premises (@p143 @p107)) % 0.38/0.60 (step @p145 :rule trans :premises (@p144 @p61)) % 0.38/0.60 (step @p146 :rule refl :args (@t126)) % 0.38/0.60 (step @p147 :rule ho_cong :premises (@p146 @p145)) % 0.38/0.60 (step @p148 :rule trans :premises (@p147 @p55)) % 0.38/0.60 (step @p149 :rule cong :premises (@p148) :args ((not (_ @t126 (_ (_ @t165 (_ @t176 @t182)) (_ @t18 (_ @t144 @t157))))))) % 0.38/0.60 (step @p150 :rule refl :args (@t3)) % 0.38/0.60 (step @p151 :rule ho_cong :premises (@p9 @p150)) % 0.38/0.60 (step @p152 :rule refl :args (@t154)) % 0.38/0.60 (step @p153 :rule refl :args (@t49)) % 0.38/0.60 (step @p154 :rule cong :premises (@p153 @p152) :args ((= @t49 @t154))) % 0.38/0.60 (step @p155 :rule symm :premises (@p154)) % 0.38/0.60 (step @p156 :rule eq_resolve :premises (@p153 @p155)) % 0.38/0.60 (step @p157 :rule refl :args (@t98)) % 0.38/0.60 (step @p158 :rule refl :args (@t87)) % 0.38/0.60 (step @p159 :rule cong :premises (@p158 @p157) :args ((= @t87 @t98))) % 0.38/0.60 (step @p160 :rule symm :premises (@p159)) % 0.38/0.60 (step @p161 :rule eq_resolve :premises (@p158 @p160)) % 0.38/0.60 (step @p162 :rule cong :premises (@p161) :args (@t88)) % 0.38/0.60 (step @p163 :rule nary_cong :premises (@p162 @p156) :args (@t89)) % 0.38/0.60 (step @p164 :rule cong :premises (@p163) :args (@t90)) % 0.38/0.60 (step @p165 :rule cong :premises (@p164) :args (@t91)) % 0.38/0.60 (step @p166 :rule trans :premises (@p37 @p165)) % 0.38/0.60 (step @p167 :rule ho_cong :premises (@p166 @p151)) % 0.38/0.60 (step @p168 :rule ho_cong :premises (@p167 @p77)) % 0.38/0.60 (step @p169 :rule cong :premises (@p168) :args (@t5)) % 0.38/0.60 (step @p170 :rule beta-reduce :args ((= (_ (lambda @t46 (not @t183)) @t1) @t143))) % 0.38/0.60 (step @p171 :rule beta-reduce :args ((= @t185 @t183))) % 0.38/0.60 (step @p172 :rule cong :premises (@p171) :args (@t186)) % 0.38/0.60 (step @p173 :rule cong :premises (@p172) :args (@t187)) % 0.38/0.60 (step @p174 :rule beta-reduce :args ((= (_ @t18 @t184) @t187))) % 0.38/0.60 (step @p175 :rule trans :premises (@p174 @p173)) % 0.38/0.60 (step @p176 :rule refl :args (@t180)) % 0.38/0.60 (step @p177 :rule refl :args (@t33)) % 0.38/0.60 (step @p178 :rule cong :premises (@p177 @p176) :args ((= @t33 @t180))) % 0.38/0.60 (step @p179 :rule symm :premises (@p178)) % 0.38/0.60 (step @p180 :rule eq_resolve :premises (@p177 @p179)) % 0.38/0.60 (step @p181 :rule cong :premises (@p180) :args (@t188)) % 0.38/0.60 (step @p182 :rule cong :premises (@p181) :args ((forall @t34 @t188))) % 0.38/0.60 (step @p183 :rule beta-reduce :args ((= @t191 @t188))) % 0.38/0.60 (step @p184 :rule cong :premises (@p183) :args (@t192)) % 0.38/0.60 (step @p185 :rule trans :premises (@p184 @p182)) % 0.38/0.60 (step @p186 :rule cong :premises (@p185) :args (@t193)) % 0.38/0.60 (step @p187 :rule beta-reduce :args ((= (_ @t181 @t190) @t193))) % 0.38/0.60 (step @p188 :rule trans :premises (@p187 @p186)) % 0.38/0.60 (step @p189 :rule beta-reduce :args ((= (_ @t194 @t1) @t189))) % 0.38/0.60 (step @p190 :rule beta-reduce :args ((= @t195 @t194))) % 0.38/0.60 (step @p191 :rule ho_cong :premises (@p190 @p77)) % 0.38/0.60 (step @p192 :rule trans :premises (@p191 @p189)) % 0.38/0.60 (step @p193 :rule cong :premises (@p192) :args ((lambda @t4 (_ @t195 @t1)))) % 0.38/0.60 (step @p194 :rule refl :args (@t181)) % 0.38/0.60 (step @p195 :rule ho_cong :premises (@p194 @p193)) % 0.38/0.60 (step @p196 :rule trans :premises (@p195 @p188)) % 0.38/0.60 (step @p197 :rule ho_cong :premises (@p105 @p196)) % 0.38/0.60 (step @p198 :rule trans :premises (@p197 @p175)) % 0.38/0.60 (step @p199 :rule ho_cong :premises (@p198 @p77)) % 0.38/0.60 (step @p200 :rule trans :premises (@p199 @p170)) % 0.38/0.60 (step @p201 :rule refl :args (@t32)) % 0.38/0.60 (step @p202 :rule ho_cong :premises (@p9 @p201)) % 0.38/0.60 (step @p203 :rule ho_cong :premises (@p202 @p77)) % 0.38/0.60 (step @p204 :rule cong :premises (@p203) :args (@t42)) % 0.38/0.60 (step @p205 :rule cong :premises (@p180) :args (@t35)) % 0.38/0.60 (step @p206 :rule cong :premises (@p205) :args (@t37)) % 0.38/0.60 (step @p207 :rule trans :premises (@p16 @p206)) % 0.38/0.60 (step @p208 :rule ho_cong :premises (@p207 @p204)) % 0.38/0.60 (step @p209 :rule ho_cong :premises (@p9 @p208)) % 0.38/0.60 (step @p210 :rule ho_cong :premises (@p209 @p77)) % 0.38/0.60 (step @p211 :rule trans :premises (@p210 @p200)) % 0.38/0.60 (step @p212 :rule cong :premises (@p211) :args (@t44)) % 0.38/0.60 (step @p213 :rule trans :premises (@p18 @p212)) % 0.38/0.60 (step @p214 :rule ho_cong :premises (@p213 @p169)) % 0.38/0.60 (step @p215 :rule ho_cong :premises (@p9 @p214)) % 0.38/0.60 (step @p216 :rule refl :args (@t6)) % 0.38/0.60 (step @p217 :rule ho_cong :premises (@p207 @p216)) % 0.38/0.60 (step @p218 :rule beta-reduce :args ((= (_ (lambda @t46 (not @t196)) @t1) @t175))) % 0.38/0.60 (step @p219 :rule beta-reduce :args ((= @t198 @t196))) % 0.38/0.60 (step @p220 :rule cong :premises (@p219) :args (@t199)) % 0.38/0.60 (step @p221 :rule cong :premises (@p220) :args (@t200)) % 0.38/0.60 (step @p222 :rule beta-reduce :args ((= (_ @t18 @t197) @t200))) % 0.38/0.60 (step @p223 :rule trans :premises (@p222 @p221)) % 0.38/0.60 (step @p224 :rule cong :premises (@p156) :args (@t201)) % 0.38/0.60 (step @p225 :rule nary_cong :premises (@p84 @p224) :args (@t202)) % 0.38/0.60 (step @p226 :rule cong :premises (@p225) :args ((forall @t51 @t202))) % 0.38/0.60 (step @p227 :rule beta-reduce :args ((= @t204 @t201))) % 0.38/0.60 (step @p228 :rule nary_cong :premises (@p88 @p227) :args (@t205)) % 0.38/0.60 (step @p229 :rule cong :premises (@p228) :args (@t206)) % 0.38/0.60 (step @p230 :rule trans :premises (@p229 @p226)) % 0.38/0.60 (step @p231 :rule cong :premises (@p230) :args (@t207)) % 0.38/0.60 (step @p232 :rule beta-reduce :args ((= (_ @t155 @t203) @t207))) % 0.38/0.60 (step @p233 :rule trans :premises (@p232 @p231)) % 0.38/0.60 (step @p234 :rule beta-reduce :args ((= (_ @t18 @t14) @t203))) % 0.38/0.60 (step @p235 :rule ho_cong :premises (@p96 @p234)) % 0.38/0.60 (step @p236 :rule trans :premises (@p235 @p233)) % 0.38/0.60 (step @p237 :rule ho_cong :premises (@p105 @p236)) % 0.38/0.60 (step @p238 :rule trans :premises (@p237 @p223)) % 0.38/0.60 (step @p239 :rule ho_cong :premises (@p238 @p77)) % 0.38/0.60 (step @p240 :rule trans :premises (@p239 @p218)) % 0.38/0.60 (step @p241 :rule refl :args (@t14)) % 0.38/0.60 (step @p242 :rule ho_cong :premises (@p9 @p241)) % 0.38/0.60 (step @p243 :rule ho_cong :premises (@p166 @p242)) % 0.38/0.60 (step @p244 :rule ho_cong :premises (@p9 @p243)) % 0.38/0.60 (step @p245 :rule ho_cong :premises (@p244 @p77)) % 0.38/0.60 (step @p246 :rule trans :premises (@p245 @p240)) % 0.38/0.60 (step @p247 :rule cong :premises (@p246) :args (@t93)) % 0.38/0.60 (step @p248 :rule trans :premises (@p38 @p247)) % 0.38/0.60 (step @p249 :rule ho_cong :premises (@p248 @p217)) % 0.38/0.60 (step @p250 :rule beta-reduce :args ((= (_ @t209 @t1) @t164))) % 0.38/0.60 (step @p251 :rule beta-reduce :args ((= (_ (lambda @t210 @t208) @t19) @t209))) % 0.38/0.60 (step @p252 :rule refl :args (@t19)) % 0.38/0.60 (step @p253 :rule refl :args (@t20)) % 0.38/0.60 (step @p254 :rule beta-reduce :args ((= @t211 @t16))) % 0.38/0.60 (step @p255 :rule nary_cong :premises (@p254 @p253) :args (@t212)) % 0.38/0.60 (step @p256 :rule cong :premises (@p255) :args (@t213)) % 0.38/0.60 (step @p257 :rule beta-reduce :args ((= (_ @t21 @t203) @t213))) % 0.38/0.60 (step @p258 :rule trans :premises (@p257 @p256)) % 0.38/0.60 (step @p259 :rule refl :args (@t21)) % 0.38/0.60 (step @p260 :rule ho_cong :premises (@p259 @p234)) % 0.38/0.60 (step @p261 :rule trans :premises (@p260 @p258)) % 0.38/0.60 (step @p262 :rule ho_cong :premises (@p261 @p252)) % 0.38/0.60 (step @p263 :rule trans :premises (@p262 @p251)) % 0.38/0.60 (step @p264 :rule ho_cong :premises (@p263 @p77)) % 0.38/0.60 (step @p265 :rule trans :premises (@p264 @p250)) % 0.38/0.60 (step @p266 :rule ho_cong :premises (@p10 @p242)) % 0.38/0.60 (step @p267 :rule ho_cong :premises (@p266 @p252)) % 0.38/0.60 (step @p268 :rule ho_cong :premises (@p267 @p77)) % 0.38/0.60 (step @p269 :rule trans :premises (@p268 @p265)) % 0.38/0.60 (step @p270 :rule cong :premises (@p269) :args (@t27)) % 0.38/0.60 (step @p271 :rule trans :premises (@p12 @p270)) % 0.38/0.60 (step @p272 :rule ho_cong :premises (@p271 @p249)) % 0.38/0.60 (step @p273 :rule ho_cong :premises (@p272 @p215)) % 0.38/0.60 (step @p274 :rule refl :args (@t125)) % 0.38/0.60 (step @p275 :rule refl :args (@t15)) % 0.38/0.60 (step @p276 :rule cong :premises (@p275 @p274) :args ((= @t15 @t125))) % 0.38/0.60 (step @p277 :rule symm :premises (@p276)) % 0.38/0.60 (step @p278 :rule eq_resolve :premises (@p275 @p277)) % 0.38/0.60 (step @p279 :rule cong :premises (@p278) :args (@t81)) % 0.38/0.60 (step @p280 :rule cong :premises (@p279) :args (@t83)) % 0.38/0.60 (step @p281 :rule trans :premises (@p33 @p280)) % 0.38/0.60 (step @p282 :rule ho_cong :premises (@p281 @p273)) % 0.38/0.60 (step @p283 :rule cong :premises (@p282) :args (@t7)) % 0.38/0.60 (step @p284 :rule trans :premises (@p283 @p149)) % 0.38/0.60 (step @p285 :rule eq_resolve :premises (@p5 @p284)) % 0.38/0.60 (step @p286 :rule skolemize :premises (@p285)) % 0.38/0.60 (step @p287 :rule bool-double-not-elim :args (@t216)) % 0.38/0.60 (step @p288 :rule refl :args (@t224)) % 0.38/0.60 (step @p289 :rule nary_cong :premises (@p288 @p287) :args ((or @t224 (not @t217)))) % 0.38/0.60 (step @p290 :rule cnf_or_neg :args (@t224 2)) % 0.38/0.60 (step @p291 :rule eq_resolve :premises (@p290 @p289)) % 0.38/0.60 (step @p292 :rule reordering :premises (@p291) :args ((or @t216 @t224))) % 0.38/0.60 (step @p293 :rule chain_m_resolution :premises (@p292 @p286) :args (@t216 @t225 @t226)) % 0.38/0.60 (step @p294 :rule bool-double-not-elim :args (@t222)) % 0.38/0.60 (step @p295 :rule nary_cong :premises (@p288 @p294) :args ((or @t224 (not @t223)))) % 0.38/0.60 (step @p296 :rule cnf_or_neg :args (@t224 0)) % 0.38/0.60 (step @p297 :rule eq_resolve :premises (@p296 @p295)) % 0.38/0.60 (step @p298 :rule reordering :premises (@p297) :args ((or @t222 @t224))) % 0.38/0.60 (step @p299 :rule chain_m_resolution :premises (@p298 @p286) :args (@t222 @t225 @t226)) % 0.38/0.60 (step @p300 :rule instantiate :premises (@p299) :args ((@list @t215))) % 0.38/0.60 (step @p301 :rule bool-double-not-elim :args (@t219)) % 0.38/0.60 (step @p302 :rule nary_cong :premises (@p288 @p301) :args ((or @t224 (not @t220)))) % 0.38/0.60 (step @p303 :rule cnf_or_neg :args (@t224 1)) % 0.38/0.60 (step @p304 :rule eq_resolve :premises (@p303 @p302)) % 0.38/0.60 (step @p305 :rule reordering :premises (@p304) :args ((or @t219 @t224))) % 0.38/0.60 (step @p306 :rule chain_m_resolution :premises (@p305 @p286) :args (@t219 @t225 @t226)) % 0.38/0.60 (step @p307 :rule cnf_or_pos :args (@t229)) % 0.38/0.60 (step @p308 :rule reordering :premises (@p307) :args ((or @t220 @t228 (not @t229)))) % 0.38/0.60 (step @p309 :rule chain_m_resolution :premises (@p308 @p306 @p300) :args (@t228 (@list false false) (@list @t219 @t229))) % 0.38/0.60 (assume-push @p316 @t216) % 0.38/0.60 (step @p311 :rule instantiate :premises (@p293) :args ((@list @t221))) % 0.38/0.60 (step-pop @p317 :rule scope :premises (@p311)) % 0.38/0.60 (step @p312 :rule process_scope :premises (@p317) :args (@t227)) % 0.38/0.60 (step @p314 :rule implies_elim :premises (@p312)) % 0.38/0.60 (step @p315 false :rule chain_m_resolution :premises (@p314 @p309 @p293) :args (false (@list true false) (@list @t227 @t216))) % 0.38/0.60 ) % 0.38/0.60 % SZS output end Proof % 0.38/0.60 % cvc5 exiting %------------------------------------------------------------------------------