%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO480^6 : 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 : n028.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 09:12:57 AM UTC 2026 % Result : Theorem 0.36s 0.60s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO480^6 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n028.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Wed Jun 3 00:16:50 EDT 2026 % 0.16/0.34 % CPUTime : % 0.27/0.50 %----Proving TH0 % 0.36/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.60 % SZS status Theorem % 0.36/0.60 % SZS output start Proof % 0.36/0.60 ( % 0.36/0.60 (declare-sort $$unsorted 0) % 0.36/0.60 (declare-sort tptp.mu 0) % 0.36/0.60 (declare-const tptp.rel_s5 (-> $$unsorted $$unsorted Bool)) % 0.36/0.60 (declare-const tptp.f (-> tptp.mu $$unsorted Bool)) % 0.36/0.60 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.36/0.60 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.36/0.60 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.36/0.60 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.36/0.60 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.36/0.60 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.36/0.60 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.36/0.60 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.36/0.60 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.36/0.60 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.36/0.60 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.36/0.60 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.36/0.60 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.36/0.60 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.36/0.60 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.36/0.60 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.36/0.60 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.36/0.60 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.36/0.60 (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)))))))) % 0.36/0.60 (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)))))))) % 0.36/0.60 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.36/0.60 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 0.36/0.60 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.36/0.60 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 0.36/0.60 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.36/0.60 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 0.36/0.60 (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))))))))))))) % 0.36/0.60 (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)))))) % 0.36/0.60 (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))))))) % 0.36/0.60 (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)))))) % 0.36/0.60 (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))))))) % 0.36/0.60 (define tptp.mbox_s5 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s5 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.36/0.60 (define tptp.mdia_s5 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s5 (_ tptp.mnot _let_2))) _let_1))))) % 0.36/0.60 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.36/0.60 (define @t2 () (@var "X" tptp.mu)) % 0.36/0.60 (define @t3 () (_ tptp.f @t2)) % 0.36/0.60 (define @t4 () (@list @t2 @t1)) % 0.36/0.60 (define @t5 () (lambda @t4 (_ (_ tptp.mdia_s5 @t3) @t1))) % 0.36/0.60 (define @t6 () (lambda @t4 (_ @t3 @t1))) % 0.36/0.60 (define @t7 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mdia_s5 (_ tptp.mforall_ind @t6))) (_ tptp.mforall_ind @t5))))) % 0.36/0.60 (define @t8 () (@var "Y" tptp.mu)) % 0.36/0.60 (define @t9 () (@var "W" $$unsorted)) % 0.36/0.60 (define @t10 () (lambda (@list @t2 @t8 @t9) (= @t2 @t8))) % 0.36/0.60 (define @t11 () (@var "Y" (-> $$unsorted Bool))) % 0.36/0.60 (define @t12 () (@var "X" (-> $$unsorted Bool))) % 0.36/0.60 (define @t13 () (lambda (@list @t12 @t11 @t9) (= (_ @t12 @t9) (_ @t11 @t9)))) % 0.36/0.60 (define @t14 () (@var "Phi" (-> $$unsorted Bool))) % 0.36/0.60 (define @t15 () (_ @t14 @t9)) % 0.36/0.60 (define @t16 () (not @t15)) % 0.36/0.60 (define @t17 () (@list @t14 @t9)) % 0.36/0.60 (define @t18 () (lambda @t17 @t16)) % 0.36/0.60 (define @t19 () (@var "Psi" (-> $$unsorted Bool))) % 0.36/0.60 (define @t20 () (_ @t19 @t9)) % 0.36/0.60 (define @t21 () (lambda (@list @t14 @t19 @t9) (or @t15 @t20))) % 0.36/0.60 (define @t22 () (_ tptp.mnot @t19)) % 0.36/0.60 (define @t23 () (_ tptp.mnot @t14)) % 0.36/0.60 (define @t24 () (_ tptp.mor @t23)) % 0.36/0.60 (define @t25 () (@list @t14 @t19 @t1)) % 0.36/0.60 (define @t26 () (lambda @t25 (_ (_ tptp.mnot (_ @t24 @t22)) @t1))) % 0.36/0.60 (define @t27 () (lambda @t25 (_ (_ @t24 @t19) @t1))) % 0.36/0.60 (define @t28 () (lambda @t25 (_ (_ (_ tptp.mor @t22) @t14) @t1))) % 0.36/0.60 (define @t29 () (lambda @t25 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t14) @t19)) (_ (_ tptp.mimplies @t19) @t14)) @t1))) % 0.36/0.60 (define @t30 () (lambda @t25 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t14) @t19)) @t1))) % 0.36/0.60 (define @t31 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.36/0.60 (define @t32 () (_ @t31 @t2)) % 0.36/0.60 (define @t33 () (_ @t32 @t9)) % 0.36/0.60 (define @t34 () (@list @t2)) % 0.36/0.60 (define @t35 () (forall @t34 @t33)) % 0.36/0.60 (define @t36 () (@list @t31 @t9)) % 0.36/0.60 (define @t37 () (lambda @t36 @t35)) % 0.36/0.60 (define @t38 () (@var "P" (-> $$unsorted Bool))) % 0.36/0.60 (define @t39 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.36/0.60 (define @t40 () (_ @t39 @t38)) % 0.36/0.60 (define @t41 () (lambda (@list @t39 @t9) (forall (@list @t38) (_ @t40 @t9)))) % 0.36/0.60 (define @t42 () (lambda (@list @t31 @t1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda @t4 (_ (_ tptp.mnot @t32) @t1)))) @t1))) % 0.36/0.60 (define @t43 () (lambda (@list @t39 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t38 @t1) (_ (_ tptp.mnot @t40) @t1)))) @t1))) % 0.36/0.60 (define @t44 () (@list @t9)) % 0.36/0.60 (define @t45 () (lambda @t44 true)) % 0.36/0.60 (define @t46 () (@var "V" $$unsorted)) % 0.36/0.60 (define @t47 () (_ @t14 @t46)) % 0.36/0.60 (define @t48 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.36/0.60 (define @t49 () (@list @t46)) % 0.36/0.60 (define @t50 () (lambda (@list @t48 @t14 @t9) (forall @t49 (or (not (_ (_ @t48 @t9) @t46)) @t47)))) % 0.36/0.60 (define @t51 () (lambda (@list @t48 @t14 @t1) (_ (_ tptp.mnot (_ (_ tptp.mbox @t48) @t23)) @t1))) % 0.36/0.60 (define @t52 () (@var "S" $$unsorted)) % 0.36/0.60 (define @t53 () (_ @t48 @t52)) % 0.36/0.60 (define @t54 () (@list @t52)) % 0.36/0.60 (define @t55 () (@list @t48)) % 0.36/0.60 (define @t56 () (lambda @t55 (forall @t54 (_ @t53 @t52)))) % 0.36/0.60 (define @t57 () (@var "T" $$unsorted)) % 0.36/0.60 (define @t58 () (_ @t48 @t57)) % 0.36/0.60 (define @t59 () (_ @t53 @t57)) % 0.36/0.60 (define @t60 () (lambda @t55 (forall (@list @t52 @t57) (=> @t59 (_ @t58 @t52))))) % 0.36/0.60 (define @t61 () (@list @t57)) % 0.36/0.60 (define @t62 () (lambda @t55 (forall @t54 (exists @t61 @t59)))) % 0.36/0.60 (define @t63 () (@var "U" $$unsorted)) % 0.36/0.60 (define @t64 () (_ @t53 @t63)) % 0.36/0.60 (define @t65 () (_ @t58 @t63)) % 0.36/0.60 (define @t66 () (@list @t52 @t57 @t63)) % 0.36/0.60 (define @t67 () (lambda @t55 (forall @t66 (=> (and @t59 @t65) @t64)))) % 0.36/0.60 (define @t68 () (and @t59 @t64)) % 0.36/0.60 (define @t69 () (lambda @t55 (forall @t66 (=> @t68 @t65)))) % 0.36/0.60 (define @t70 () (= @t57 @t63)) % 0.36/0.60 (define @t71 () (lambda @t55 (forall @t66 (=> @t68 @t70)))) % 0.36/0.60 (define @t72 () (@list @t63)) % 0.36/0.60 (define @t73 () (lambda @t55 (forall @t54 (exists @t61 (and @t59 (forall @t72 (=> @t64 @t70))))))) % 0.36/0.60 (define @t74 () (_ @t48 @t63)) % 0.36/0.60 (define @t75 () (_ @t74 @t57)) % 0.36/0.60 (define @t76 () (lambda @t55 (forall @t66 (=> @t59 (exists @t72 (and @t64 @t75)))))) % 0.36/0.60 (define @t77 () (lambda @t55 (forall @t66 (=> @t68 (or @t65 @t70 @t75))))) % 0.36/0.60 (define @t78 () (lambda @t55 (forall @t66 (=> @t68 (exists @t49 (and (_ @t58 @t46) (_ @t74 @t46))))))) % 0.36/0.60 (define @t79 () (forall @t44 @t15)) % 0.36/0.60 (define @t80 () (@list @t14)) % 0.36/0.60 (define @t81 () (lambda @t80 @t79)) % 0.36/0.60 (define @t82 () (lambda @t80 (forall @t44 @t16))) % 0.36/0.60 (define @t83 () (lambda @t80 (exists @t44 @t15))) % 0.36/0.60 (define @t84 () (lambda @t80 (exists @t44 @t16))) % 0.36/0.60 (define @t85 () (_ (_ tptp.rel_s5 @t9) @t46)) % 0.36/0.60 (define @t86 () (not @t85)) % 0.36/0.60 (define @t87 () (or @t86 @t47)) % 0.36/0.60 (define @t88 () (forall @t49 @t87)) % 0.36/0.60 (define @t89 () (lambda @t17 @t88)) % 0.36/0.60 (define @t90 () (@list @t14 @t1)) % 0.36/0.60 (define @t91 () (lambda @t90 (_ (_ tptp.mnot (_ tptp.mbox_s5 @t23)) @t1))) % 0.36/0.60 (define @t92 () (@var "BOUND_VARIABLE_8500" $$unsorted)) % 0.36/0.60 (define @t93 () (not (forall @t34 (tptp.f @t2 @t92)))) % 0.36/0.60 (define @t94 () (not (tptp.rel_s5 @t9 @t92))) % 0.36/0.60 (define @t95 () (@var "BOUND_VARIABLE_8508" tptp.mu)) % 0.36/0.60 (define @t96 () (tptp.rel_s5 @t9 @t46)) % 0.36/0.60 (define @t97 () (not @t96)) % 0.36/0.60 (define @t98 () (not (forall @t49 (or @t97 (not (tptp.f @t95 @t46)))))) % 0.36/0.60 (define @t99 () (or @t98 @t94 @t93)) % 0.36/0.60 (define @t100 () (or @t94 @t93)) % 0.36/0.60 (define @t101 () (or @t100 @t98)) % 0.36/0.60 (define @t102 () (@list @t9 @t92 @t95)) % 0.36/0.60 (define @t103 () (forall @t102 @t101)) % 0.36/0.60 (define @t104 () (forall (@list @t92 @t95) @t101)) % 0.36/0.60 (define @t105 () (forall (@list @t95) @t98)) % 0.36/0.60 (define @t106 () (forall (@list @t92) @t100)) % 0.36/0.60 (define @t107 () (or @t106 @t105)) % 0.36/0.60 (define @t108 () (tptp.f @t2 @t46)) % 0.36/0.60 (define @t109 () (not @t108)) % 0.36/0.60 (define @t110 () (not (forall @t49 (or @t97 @t109)))) % 0.36/0.60 (define @t111 () (forall @t34 @t110)) % 0.36/0.60 (define @t112 () (forall @t34 @t108)) % 0.36/0.60 (define @t113 () (not @t112)) % 0.36/0.60 (define @t114 () (or (forall @t49 (or @t97 @t113)) @t111)) % 0.36/0.60 (define @t115 () (not (tptp.rel_s5 @t1 @t46))) % 0.36/0.60 (define @t116 () (not (forall @t49 (or @t115 @t109)))) % 0.36/0.60 (define @t117 () (forall @t34 @t116)) % 0.36/0.60 (define @t118 () (forall @t49 (or @t115 @t113))) % 0.36/0.60 (define @t119 () (@list @t1)) % 0.36/0.60 (define @t120 () (lambda @t119 (or @t118 @t117))) % 0.36/0.60 (define @t121 () (_ @t120 @t9)) % 0.36/0.60 (define @t122 () (forall @t44 @t121)) % 0.36/0.60 (define @t123 () (_ @t14 @t9)) % 0.36/0.60 (define @t124 () (lambda @t80 (forall @t44 @t123))) % 0.36/0.60 (define @t125 () (lambda @t44 @t111)) % 0.36/0.60 (define @t126 () (_ @t125 @t1)) % 0.36/0.60 (define @t127 () (or @t118 @t126)) % 0.36/0.60 (define @t128 () (lambda @t119 @t127)) % 0.36/0.60 (define @t129 () (_ @t19 @t1)) % 0.36/0.60 (define @t130 () (@list @t19 @t1)) % 0.36/0.60 (define @t131 () (lambda @t4 @t116)) % 0.36/0.60 (define @t132 () (_ @t131 @t2 @t9)) % 0.36/0.60 (define @t133 () (forall @t34 @t132)) % 0.36/0.60 (define @t134 () (lambda @t44 @t133)) % 0.36/0.60 (define @t135 () (_ @t31 @t2 @t9)) % 0.36/0.60 (define @t136 () (lambda @t36 (forall @t34 @t135))) % 0.36/0.60 (define @t137 () (_ @t3 @t46)) % 0.36/0.60 (define @t138 () (not @t137)) % 0.36/0.60 (define @t139 () (or @t115 @t138)) % 0.36/0.60 (define @t140 () (_ @t3 @t46)) % 0.36/0.60 (define @t141 () (not @t140)) % 0.36/0.60 (define @t142 () (or @t115 @t141)) % 0.36/0.60 (define @t143 () (forall @t49 @t142)) % 0.36/0.60 (define @t144 () (not @t143)) % 0.36/0.60 (define @t145 () (lambda @t119 @t144)) % 0.36/0.60 (define @t146 () (_ @t14 @t46)) % 0.36/0.60 (define @t147 () (not @t146)) % 0.36/0.60 (define @t148 () (not (forall @t49 (or @t115 @t147)))) % 0.36/0.60 (define @t149 () (lambda @t90 @t148)) % 0.36/0.60 (define @t150 () (_ @t149 @t3)) % 0.36/0.60 (define @t151 () (lambda @t4 (_ @t150 @t1))) % 0.36/0.60 (define @t152 () (not @t118)) % 0.36/0.60 (define @t153 () (lambda @t119 @t152)) % 0.36/0.60 (define @t154 () (_ @t153 @t1)) % 0.36/0.60 (define @t155 () (not @t154)) % 0.36/0.60 (define @t156 () (or @t155 @t129)) % 0.36/0.60 (define @t157 () (lambda @t130 @t156)) % 0.36/0.60 (define @t158 () (or (not (_ @t14 @t1)) @t129)) % 0.36/0.60 (define @t159 () (lambda @t25 @t158)) % 0.36/0.60 (define @t160 () (tptp.f @t2 @t9)) % 0.36/0.60 (define @t161 () (lambda @t44 (forall @t34 @t160))) % 0.36/0.60 (define @t162 () (_ @t161 @t46)) % 0.36/0.60 (define @t163 () (not @t162)) % 0.36/0.60 (define @t164 () (or @t115 @t163)) % 0.36/0.60 (define @t165 () (forall @t49 @t164)) % 0.36/0.60 (define @t166 () (not @t165)) % 0.36/0.60 (define @t167 () (lambda @t119 @t166)) % 0.36/0.60 (define @t168 () (_ @t3 @t9)) % 0.36/0.60 (define @t169 () (_ @t6 @t2 @t9)) % 0.36/0.60 (define @t170 () (forall @t34 @t169)) % 0.36/0.60 (define @t171 () (lambda @t44 @t170)) % 0.36/0.60 (define @t172 () (_ @t136 @t6)) % 0.36/0.60 (define @t173 () (forall @t49 (or @t97 @t147))) % 0.36/0.60 (define @t174 () (lambda @t44 @t173)) % 0.36/0.60 (define @t175 () (_ @t174 @t9)) % 0.36/0.60 (define @t176 () (not @t175)) % 0.36/0.60 (define @t177 () (lambda @t44 @t176)) % 0.36/0.60 (define @t178 () (not @t47)) % 0.36/0.60 (define @t179 () (or @t97 @t178)) % 0.36/0.60 (define @t180 () (lambda @t44 @t16)) % 0.36/0.60 (define @t181 () (_ @t180 @t46)) % 0.36/0.60 (define @t182 () (or @t97 @t181)) % 0.36/0.60 (define @t183 () (forall @t49 @t182)) % 0.36/0.60 (define @t184 () (lambda @t44 @t183)) % 0.36/0.60 (define @t185 () (lambda @t17 (forall @t49 (or @t97 @t146)))) % 0.36/0.60 (define @t186 () (or @t16 @t20)) % 0.36/0.60 (define @t187 () (lambda @t44 @t186)) % 0.36/0.60 (define @t188 () (@list @t19 @t9)) % 0.36/0.60 (define @t189 () (_ @t180 @t9)) % 0.36/0.60 (define @t190 () (or @t189 @t20)) % 0.36/0.60 (define @t191 () (lambda @t188 @t190)) % 0.36/0.60 (define @t192 () (forall @t102 @t99)) % 0.36/0.60 (define @t193 () (@quantifiers_skolemize @t192 1)) % 0.36/0.60 (define @t194 () (forall @t34 (tptp.f @t2 @t193))) % 0.36/0.60 (define @t195 () (not @t194)) % 0.36/0.60 (define @t196 () (@quantifiers_skolemize @t192 0)) % 0.36/0.60 (define @t197 () (tptp.rel_s5 @t196 @t193)) % 0.36/0.60 (define @t198 () (not @t197)) % 0.36/0.60 (define @t199 () (@quantifiers_skolemize @t192 2)) % 0.36/0.60 (define @t200 () (forall @t49 (or (not (tptp.rel_s5 @t196 @t46)) (not (tptp.f @t199 @t46))))) % 0.36/0.60 (define @t201 () (not @t200)) % 0.36/0.60 (define @t202 () (or @t201 @t198 @t195)) % 0.36/0.60 (define @t203 () (@list true)) % 0.36/0.60 (define @t204 () (@list @t202)) % 0.36/0.60 (define @t205 () (tptp.f @t199 @t193)) % 0.36/0.60 (define @t206 () (not @t205)) % 0.36/0.60 (define @t207 () (or @t198 @t206)) % 0.36/0.60 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.36/0.60 (assume @p2 (_ tptp.mreflexive tptp.rel_s5)) % 0.36/0.60 (assume @p3 (_ tptp.mtransitive tptp.rel_s5)) % 0.36/0.60 (assume @p4 (_ tptp.msymmetric tptp.rel_s5)) % 0.36/0.60 (assume @p5 @t7) % 0.36/0.60 (assume @p6 true) % 0.36/0.60 (step @p7 (= tptp.meq_ind @t10) :rule refl :args (@t10)) % 0.36/0.60 (step @p8 (= tptp.meq_prop @t13) :rule refl :args (@t13)) % 0.36/0.60 (step @p9 (= tptp.mnot @t18) :rule refl :args (@t18)) % 0.36/0.60 (step @p10 (= tptp.mor @t21) :rule refl :args (@t21)) % 0.36/0.60 (step @p11 (= tptp.mand @t26) :rule refl :args (@t26)) % 0.36/0.60 (step @p12 (= tptp.mimplies @t27) :rule refl :args (@t27)) % 0.36/0.60 (step @p13 (= tptp.mimplied @t28) :rule refl :args (@t28)) % 0.36/0.60 (step @p14 (= tptp.mequiv @t29) :rule refl :args (@t29)) % 0.36/0.60 (step @p15 (= tptp.mxor @t30) :rule refl :args (@t30)) % 0.36/0.60 (step @p16 (= tptp.mforall_ind @t37) :rule refl :args (@t37)) % 0.36/0.60 (step @p17 (= tptp.mforall_prop @t41) :rule refl :args (@t41)) % 0.36/0.60 (step @p18 (= tptp.mexists_ind @t42) :rule refl :args (@t42)) % 0.36/0.60 (step @p19 (= tptp.mexists_prop @t43) :rule refl :args (@t43)) % 0.36/0.60 (step @p20 (= tptp.mtrue @t45) :rule refl :args (@t45)) % 0.36/0.60 (step @p21 (= tptp.mbox @t50) :rule refl :args (@t50)) % 0.36/0.60 (step @p22 (= tptp.mdia @t51) :rule refl :args (@t51)) % 0.36/0.60 (step @p23 (= tptp.mreflexive @t56) :rule refl :args (@t56)) % 0.36/0.60 (step @p24 (= tptp.msymmetric @t60) :rule refl :args (@t60)) % 0.36/0.60 (step @p25 (= tptp.mserial @t62) :rule refl :args (@t62)) % 0.36/0.60 (step @p26 (= tptp.mtransitive @t67) :rule refl :args (@t67)) % 0.36/0.60 (step @p27 (= tptp.meuclidean @t69) :rule refl :args (@t69)) % 0.36/0.60 (step @p28 (= tptp.mpartially_functional @t71) :rule refl :args (@t71)) % 0.36/0.60 (step @p29 (= tptp.mfunctional @t73) :rule refl :args (@t73)) % 0.36/0.60 (step @p30 (= tptp.mweakly_dense @t76) :rule refl :args (@t76)) % 0.36/0.60 (step @p31 (= tptp.mweakly_connected @t77) :rule refl :args (@t77)) % 0.36/0.60 (step @p32 (= tptp.mweakly_directed @t78) :rule refl :args (@t78)) % 0.36/0.60 (step @p33 (= tptp.mvalid @t81) :rule refl :args (@t81)) % 0.36/0.60 (step @p34 (= tptp.minvalid @t82) :rule refl :args (@t82)) % 0.36/0.60 (step @p35 (= tptp.msatisfiable @t83) :rule refl :args (@t83)) % 0.36/0.60 (step @p36 (= tptp.mcountersatisfiable @t84) :rule refl :args (@t84)) % 0.36/0.60 (step @p37 (= tptp.mbox_s5 @t89) :rule refl :args (@t89)) % 0.36/0.60 (step @p38 (= tptp.mdia_s5 @t91) :rule refl :args (@t91)) % 0.36/0.60 (step @p39 :rule aci_norm :args ((= @t101 @t99))) % 0.36/0.60 (step @p40 :rule cong :premises (@p39) :args (@t103)) % 0.36/0.60 (step @p41 :rule quant-merge-prenex :args ((= (forall @t44 @t104) @t103))) % 0.36/0.60 (step @p42 :rule alpha_equiv :args (@t105 (@list @t95) (@list @t2))) % 0.36/0.60 (step @p43 :rule alpha_equiv :args (@t106 (@list @t92) (@list @t46))) % 0.36/0.60 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t107)) % 0.36/0.60 (step @p45 :rule quant-miniscope-or :args ((= @t104 @t107))) % 0.36/0.60 (step @p46 :rule trans :premises (@p45 @p44)) % 0.36/0.60 (step @p47 :rule symm :premises (@p46)) % 0.36/0.60 (step @p48 :rule cong :premises (@p47) :args ((forall @t44 @t114))) % 0.36/0.60 (step @p49 :rule trans :premises (@p48 @p41)) % 0.36/0.60 (step @p50 :rule trans :premises (@p49 @p40)) % 0.36/0.60 (step @p51 :rule beta-reduce :args ((= @t121 @t114))) % 0.36/0.60 (step @p52 :rule cong :premises (@p51) :args (@t122)) % 0.36/0.60 (step @p53 :rule trans :premises (@p52 @p50)) % 0.36/0.60 (step @p54 :rule beta-reduce :args ((= (_ @t124 @t120) @t122))) % 0.36/0.60 (step @p55 :rule trans :premises (@p54 @p53)) % 0.36/0.60 (step @p56 :rule beta-reduce :args ((= @t126 @t117))) % 0.36/0.60 (step @p57 :rule refl :args (@t118)) % 0.36/0.60 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t127)) % 0.36/0.60 (step @p59 :rule cong :premises (@p58) :args (@t128)) % 0.36/0.60 (step @p60 :rule beta-reduce :args ((= (_ (lambda @t130 (or @t118 @t129)) @t125) @t128))) % 0.36/0.60 (step @p61 :rule trans :premises (@p60 @p59)) % 0.36/0.60 (step @p62 :rule beta-reduce :args ((= @t132 @t110))) % 0.36/0.60 (step @p63 :rule cong :premises (@p62) :args (@t133)) % 0.36/0.60 (step @p64 :rule cong :premises (@p63) :args (@t134)) % 0.36/0.60 (step @p65 :rule beta-reduce :args ((= (_ @t136 @t131) @t134))) % 0.36/0.60 (step @p66 :rule trans :premises (@p65 @p64)) % 0.36/0.60 (step @p67 :rule beta-reduce :args ((= (_ (lambda @t119 @t116) @t1) @t116))) % 0.36/0.60 (step @p68 :rule refl :args (@t1)) % 0.36/0.60 (step @p69 :rule refl :args (@t108)) % 0.36/0.60 (step @p70 :rule refl :args (@t137)) % 0.36/0.60 (step @p71 :rule cong :premises (@p70 @p69) :args ((= @t137 @t108))) % 0.36/0.60 (step @p72 :rule symm :premises (@p71)) % 0.36/0.60 (step @p73 :rule eq_resolve :premises (@p70 @p72)) % 0.36/0.60 (step @p74 :rule cong :premises (@p73) :args (@t138)) % 0.36/0.60 (step @p75 :rule refl :args (@t115)) % 0.36/0.60 (step @p76 :rule nary_cong :premises (@p75 @p74) :args (@t139)) % 0.36/0.60 (step @p77 :rule cong :premises (@p76) :args ((forall @t49 @t139))) % 0.36/0.60 (step @p78 :rule refl :args (@t140)) % 0.36/0.60 (step @p79 :rule cong :premises (@p78) :args (@t141)) % 0.36/0.60 (step @p80 :rule refl :args (@t115)) % 0.36/0.60 (step @p81 :rule nary_cong :premises (@p80 @p79) :args (@t142)) % 0.36/0.60 (step @p82 :rule cong :premises (@p81) :args (@t143)) % 0.36/0.60 (step @p83 :rule trans :premises (@p82 @p77)) % 0.36/0.60 (step @p84 :rule cong :premises (@p83) :args (@t144)) % 0.36/0.60 (step @p85 :rule cong :premises (@p84) :args (@t145)) % 0.36/0.60 (step @p86 :rule beta-reduce :args ((= @t150 @t145))) % 0.36/0.60 (step @p87 :rule trans :premises (@p86 @p85)) % 0.36/0.60 (step @p88 :rule ho_cong :premises (@p87 @p68)) % 0.36/0.60 (step @p89 :rule trans :premises (@p88 @p67)) % 0.36/0.60 (step @p90 :rule cong :premises (@p89) :args (@t151)) % 0.36/0.60 (step @p91 :rule refl :args (@t136)) % 0.36/0.60 (step @p92 :rule ho_cong :premises (@p91 @p90)) % 0.36/0.60 (step @p93 :rule trans :premises (@p92 @p66)) % 0.36/0.60 (step @p94 :rule refl :args (@t129)) % 0.36/0.60 (step @p95 :rule bool-double-not-elim :args (@t118)) % 0.36/0.60 (step @p96 :rule beta-reduce :args ((= @t154 @t152))) % 0.36/0.60 (step @p97 :rule cong :premises (@p96) :args (@t155)) % 0.36/0.60 (step @p98 :rule trans :premises (@p97 @p95)) % 0.36/0.60 (step @p99 :rule nary_cong :premises (@p98 @p94) :args (@t156)) % 0.36/0.60 (step @p100 :rule cong :premises (@p99) :args (@t157)) % 0.36/0.60 (step @p101 :rule beta-reduce :args ((= (_ @t159 @t153) @t157))) % 0.36/0.60 (step @p102 :rule trans :premises (@p101 @p100)) % 0.36/0.60 (step @p103 :rule beta-reduce :args ((= @t162 @t112))) % 0.36/0.60 (step @p104 :rule cong :premises (@p103) :args (@t163)) % 0.36/0.60 (step @p105 :rule nary_cong :premises (@p80 @p104) :args (@t164)) % 0.36/0.60 (step @p106 :rule cong :premises (@p105) :args (@t165)) % 0.36/0.60 (step @p107 :rule cong :premises (@p106) :args (@t166)) % 0.36/0.60 (step @p108 :rule cong :premises (@p107) :args (@t167)) % 0.36/0.60 (step @p109 :rule beta-reduce :args ((= (_ @t149 @t161) @t167))) % 0.36/0.60 (step @p110 :rule trans :premises (@p109 @p108)) % 0.36/0.60 (step @p111 :rule refl :args (@t160)) % 0.36/0.60 (step @p112 :rule refl :args (@t168)) % 0.36/0.60 (step @p113 :rule cong :premises (@p112 @p111) :args ((= @t168 @t160))) % 0.36/0.60 (step @p114 :rule symm :premises (@p113)) % 0.36/0.60 (step @p115 :rule eq_resolve :premises (@p112 @p114)) % 0.36/0.60 (step @p116 :rule cong :premises (@p115) :args ((forall @t34 @t168))) % 0.36/0.60 (step @p117 :rule beta-reduce :args ((= @t169 @t168))) % 0.36/0.60 (step @p118 :rule cong :premises (@p117) :args (@t170)) % 0.36/0.60 (step @p119 :rule trans :premises (@p118 @p116)) % 0.36/0.60 (step @p120 :rule cong :premises (@p119) :args (@t171)) % 0.36/0.60 (step @p121 :rule beta-reduce :args ((= @t172 @t171))) % 0.36/0.60 (step @p122 :rule trans :premises (@p121 @p120)) % 0.36/0.60 (step @p123 :rule refl :args (@t149)) % 0.36/0.60 (step @p124 :rule ho_cong :premises (@p123 @p122)) % 0.36/0.60 (step @p125 :rule trans :premises (@p124 @p110)) % 0.36/0.60 (step @p126 :rule refl :args (@t159)) % 0.36/0.60 (step @p127 :rule ho_cong :premises (@p126 @p125)) % 0.36/0.60 (step @p128 :rule trans :premises (@p127 @p102)) % 0.36/0.60 (step @p129 :rule ho_cong :premises (@p128 @p93)) % 0.36/0.60 (step @p130 :rule trans :premises (@p129 @p61)) % 0.36/0.60 (step @p131 :rule refl :args (@t124)) % 0.36/0.60 (step @p132 :rule ho_cong :premises (@p131 @p130)) % 0.36/0.60 (step @p133 :rule trans :premises (@p132 @p55)) % 0.36/0.60 (step @p134 :rule cong :premises (@p133) :args ((not (_ @t124 (_ (_ @t159 (_ @t149 @t172)) (_ @t136 @t151)))))) % 0.36/0.60 (step @p135 :rule refl :args (@t3)) % 0.36/0.60 (step @p136 :rule beta-reduce :args ((= (_ (lambda @t44 (not @t173)) @t1) @t148))) % 0.36/0.60 (step @p137 :rule beta-reduce :args ((= @t175 @t173))) % 0.36/0.60 (step @p138 :rule cong :premises (@p137) :args (@t176)) % 0.36/0.60 (step @p139 :rule cong :premises (@p138) :args (@t177)) % 0.36/0.60 (step @p140 :rule beta-reduce :args ((= (_ @t18 @t174) @t177))) % 0.36/0.60 (step @p141 :rule trans :premises (@p140 @p139)) % 0.36/0.60 (step @p142 :rule refl :args (@t146)) % 0.36/0.60 (step @p143 :rule refl :args (@t47)) % 0.36/0.60 (step @p144 :rule cong :premises (@p143 @p142) :args ((= @t47 @t146))) % 0.36/0.60 (step @p145 :rule symm :premises (@p144)) % 0.36/0.60 (step @p146 :rule eq_resolve :premises (@p143 @p145)) % 0.36/0.60 (step @p147 :rule cong :premises (@p146) :args (@t178)) % 0.36/0.60 (step @p148 :rule refl :args (@t97)) % 0.36/0.60 (step @p149 :rule nary_cong :premises (@p148 @p147) :args (@t179)) % 0.36/0.60 (step @p150 :rule cong :premises (@p149) :args ((forall @t49 @t179))) % 0.36/0.60 (step @p151 :rule beta-reduce :args ((= @t181 @t178))) % 0.36/0.60 (step @p152 :rule refl :args (@t97)) % 0.36/0.60 (step @p153 :rule nary_cong :premises (@p152 @p151) :args (@t182)) % 0.36/0.60 (step @p154 :rule cong :premises (@p153) :args (@t183)) % 0.36/0.60 (step @p155 :rule trans :premises (@p154 @p150)) % 0.36/0.60 (step @p156 :rule cong :premises (@p155) :args (@t184)) % 0.36/0.60 (step @p157 :rule beta-reduce :args ((= (_ @t185 @t180) @t184))) % 0.36/0.60 (step @p158 :rule trans :premises (@p157 @p156)) % 0.36/0.60 (step @p159 :rule beta-reduce :args ((= (_ @t18 @t14) @t180))) % 0.36/0.60 (step @p160 :rule refl :args (@t185)) % 0.36/0.60 (step @p161 :rule ho_cong :premises (@p160 @p159)) % 0.36/0.60 (step @p162 :rule trans :premises (@p161 @p158)) % 0.36/0.60 (step @p163 :rule refl :args (@t18)) % 0.36/0.60 (step @p164 :rule ho_cong :premises (@p163 @p162)) % 0.36/0.60 (step @p165 :rule trans :premises (@p164 @p141)) % 0.36/0.60 (step @p166 :rule ho_cong :premises (@p165 @p68)) % 0.36/0.60 (step @p167 :rule trans :premises (@p166 @p136)) % 0.36/0.60 (step @p168 :rule refl :args (@t14)) % 0.36/0.60 (step @p169 :rule ho_cong :premises (@p9 @p168)) % 0.36/0.60 (step @p170 :rule refl :args (@t96)) % 0.36/0.60 (step @p171 :rule refl :args (@t85)) % 0.36/0.60 (step @p172 :rule cong :premises (@p171 @p170) :args ((= @t85 @t96))) % 0.36/0.60 (step @p173 :rule symm :premises (@p172)) % 0.36/0.60 (step @p174 :rule eq_resolve :premises (@p171 @p173)) % 0.36/0.60 (step @p175 :rule cong :premises (@p174) :args (@t86)) % 0.36/0.60 (step @p176 :rule nary_cong :premises (@p175 @p146) :args (@t87)) % 0.36/0.60 (step @p177 :rule cong :premises (@p176) :args (@t88)) % 0.36/0.60 (step @p178 :rule cong :premises (@p177) :args (@t89)) % 0.36/0.60 (step @p179 :rule trans :premises (@p37 @p178)) % 0.36/0.60 (step @p180 :rule ho_cong :premises (@p179 @p169)) % 0.36/0.60 (step @p181 :rule ho_cong :premises (@p9 @p180)) % 0.36/0.60 (step @p182 :rule ho_cong :premises (@p181 @p68)) % 0.36/0.60 (step @p183 :rule trans :premises (@p182 @p167)) % 0.36/0.60 (step @p184 :rule cong :premises (@p183) :args (@t91)) % 0.36/0.60 (step @p185 :rule trans :premises (@p38 @p184)) % 0.36/0.60 (step @p186 :rule ho_cong :premises (@p185 @p135)) % 0.36/0.60 (step @p187 :rule ho_cong :premises (@p186 @p68)) % 0.36/0.60 (step @p188 :rule cong :premises (@p187) :args (@t5)) % 0.36/0.60 (step @p189 :rule refl :args (@t135)) % 0.36/0.60 (step @p190 :rule refl :args (@t33)) % 0.36/0.60 (step @p191 :rule cong :premises (@p190 @p189) :args ((= @t33 @t135))) % 0.36/0.60 (step @p192 :rule symm :premises (@p191)) % 0.36/0.60 (step @p193 :rule eq_resolve :premises (@p190 @p192)) % 0.36/0.60 (step @p194 :rule cong :premises (@p193) :args (@t35)) % 0.36/0.60 (step @p195 :rule cong :premises (@p194) :args (@t37)) % 0.36/0.60 (step @p196 :rule trans :premises (@p16 @p195)) % 0.36/0.60 (step @p197 :rule ho_cong :premises (@p196 @p188)) % 0.36/0.60 (step @p198 :rule refl :args (@t6)) % 0.36/0.60 (step @p199 :rule ho_cong :premises (@p196 @p198)) % 0.36/0.60 (step @p200 :rule ho_cong :premises (@p185 @p199)) % 0.36/0.60 (step @p201 :rule beta-reduce :args ((= (_ @t187 @t1) @t158))) % 0.36/0.60 (step @p202 :rule beta-reduce :args ((= (_ (lambda @t188 @t186) @t19) @t187))) % 0.36/0.60 (step @p203 :rule refl :args (@t19)) % 0.36/0.60 (step @p204 :rule refl :args (@t20)) % 0.36/0.60 (step @p205 :rule beta-reduce :args ((= @t189 @t16))) % 0.36/0.60 (step @p206 :rule nary_cong :premises (@p205 @p204) :args (@t190)) % 0.36/0.60 (step @p207 :rule cong :premises (@p206) :args (@t191)) % 0.36/0.60 (step @p208 :rule beta-reduce :args ((= (_ @t21 @t180) @t191))) % 0.36/0.60 (step @p209 :rule trans :premises (@p208 @p207)) % 0.36/0.60 (step @p210 :rule refl :args (@t21)) % 0.36/0.60 (step @p211 :rule ho_cong :premises (@p210 @p159)) % 0.36/0.60 (step @p212 :rule trans :premises (@p211 @p209)) % 0.36/0.60 (step @p213 :rule ho_cong :premises (@p212 @p203)) % 0.36/0.60 (step @p214 :rule trans :premises (@p213 @p202)) % 0.36/0.60 (step @p215 :rule ho_cong :premises (@p214 @p68)) % 0.36/0.60 (step @p216 :rule trans :premises (@p215 @p201)) % 0.36/0.60 (step @p217 :rule ho_cong :premises (@p10 @p169)) % 0.36/0.60 (step @p218 :rule ho_cong :premises (@p217 @p203)) % 0.36/0.60 (step @p219 :rule ho_cong :premises (@p218 @p68)) % 0.36/0.60 (step @p220 :rule trans :premises (@p219 @p216)) % 0.36/0.60 (step @p221 :rule cong :premises (@p220) :args (@t27)) % 0.36/0.60 (step @p222 :rule trans :premises (@p12 @p221)) % 0.36/0.60 (step @p223 :rule ho_cong :premises (@p222 @p200)) % 0.36/0.60 (step @p224 :rule ho_cong :premises (@p223 @p197)) % 0.36/0.60 (step @p225 :rule refl :args (@t123)) % 0.36/0.60 (step @p226 :rule refl :args (@t15)) % 0.36/0.60 (step @p227 :rule cong :premises (@p226 @p225) :args ((= @t15 @t123))) % 0.36/0.60 (step @p228 :rule symm :premises (@p227)) % 0.36/0.60 (step @p229 :rule eq_resolve :premises (@p226 @p228)) % 0.36/0.60 (step @p230 :rule cong :premises (@p229) :args (@t79)) % 0.36/0.60 (step @p231 :rule cong :premises (@p230) :args (@t81)) % 0.36/0.60 (step @p232 :rule trans :premises (@p33 @p231)) % 0.36/0.60 (step @p233 :rule ho_cong :premises (@p232 @p224)) % 0.36/0.60 (step @p234 :rule cong :premises (@p233) :args (@t7)) % 0.36/0.60 (step @p235 :rule trans :premises (@p234 @p134)) % 0.36/0.60 (step @p236 :rule eq_resolve :premises (@p5 @p235)) % 0.36/0.60 (step @p237 :rule skolemize :premises (@p236)) % 0.36/0.60 (step @p238 :rule bool-double-not-elim :args (@t194)) % 0.36/0.60 (step @p239 :rule refl :args (@t202)) % 0.36/0.60 (step @p240 :rule nary_cong :premises (@p239 @p238) :args ((or @t202 (not @t195)))) % 0.36/0.60 (step @p241 :rule cnf_or_neg :args (@t202 2)) % 0.36/0.60 (step @p242 :rule eq_resolve :premises (@p241 @p240)) % 0.36/0.60 (step @p243 :rule reordering :premises (@p242) :args ((or @t194 @t202))) % 0.36/0.60 (step @p244 :rule chain_m_resolution :premises (@p243 @p237) :args (@t194 @t203 @t204)) % 0.36/0.60 (step @p245 :rule bool-double-not-elim :args (@t200)) % 0.36/0.60 (step @p246 :rule nary_cong :premises (@p239 @p245) :args ((or @t202 (not @t201)))) % 0.36/0.60 (step @p247 :rule cnf_or_neg :args (@t202 0)) % 0.36/0.60 (step @p248 :rule eq_resolve :premises (@p247 @p246)) % 0.36/0.60 (step @p249 :rule reordering :premises (@p248) :args ((or @t200 @t202))) % 0.36/0.60 (step @p250 :rule chain_m_resolution :premises (@p249 @p237) :args (@t200 @t203 @t204)) % 0.36/0.60 (step @p251 :rule instantiate :premises (@p250) :args ((@list @t193))) % 0.36/0.60 (step @p252 :rule bool-double-not-elim :args (@t197)) % 0.36/0.60 (step @p253 :rule nary_cong :premises (@p239 @p252) :args ((or @t202 (not @t198)))) % 0.36/0.60 (step @p254 :rule cnf_or_neg :args (@t202 1)) % 0.36/0.60 (step @p255 :rule eq_resolve :premises (@p254 @p253)) % 0.36/0.60 (step @p256 :rule reordering :premises (@p255) :args ((or @t197 @t202))) % 0.36/0.60 (step @p257 :rule chain_m_resolution :premises (@p256 @p237) :args (@t197 @t203 @t204)) % 0.36/0.60 (step @p258 :rule cnf_or_pos :args (@t207)) % 0.36/0.60 (step @p259 :rule reordering :premises (@p258) :args ((or @t198 @t206 (not @t207)))) % 0.36/0.60 (step @p260 :rule chain_m_resolution :premises (@p259 @p257 @p251) :args (@t206 (@list false false) (@list @t197 @t207))) % 0.36/0.60 (assume-push @p267 @t194) % 0.36/0.60 (step @p262 :rule instantiate :premises (@p244) :args ((@list @t199))) % 0.36/0.60 (step-pop @p268 :rule scope :premises (@p262)) % 0.36/0.60 (step @p263 :rule process_scope :premises (@p268) :args (@t205)) % 0.36/0.60 (step @p265 :rule implies_elim :premises (@p263)) % 0.36/0.60 (step @p266 false :rule chain_m_resolution :premises (@p265 @p260 @p244) :args (false (@list true false) (@list @t205 @t194))) % 0.36/0.60 ) % 0.36/0.60 % SZS output end Proof % 0.36/0.61 % cvc5 exiting %------------------------------------------------------------------------------