%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO495^6 : 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 : n009.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 09:12:59 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 : SYO495^6 : 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 % 0.16/0.34 % Computer : n009.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 00:16:59 EDT 2026 % 0.16/0.34 % CPUTime : % 0.32/0.50 %----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.g (-> 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)))))))))))) % 0.38/0.61 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.38/0.61 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.38/0.61 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.61 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.61 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.61 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.61 (define tptp.mbox_s5 () (let ((_let_1 (@var "V" $$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)))))))) % 0.38/0.61 (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))))) % 0.38/0.61 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.38/0.61 (define @t2 () (@var "X" tptp.mu)) % 0.38/0.61 (define @t3 () (_ tptp.g @t2)) % 0.38/0.61 (define @t4 () (_ tptp.f @t2)) % 0.38/0.61 (define @t5 () (@list @t2 @t1)) % 0.38/0.61 (define @t6 () (lambda @t5 (_ (_ (_ tptp.mor @t4) @t3) @t1))) % 0.38/0.61 (define @t7 () (lambda @t5 (_ (_ (_ tptp.mor (_ tptp.mbox_s5 @t4)) (_ tptp.mbox_s5 @t3)) @t1))) % 0.38/0.61 (define @t8 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mforall_ind @t7)) (_ tptp.mbox_s5 (_ tptp.mforall_ind @t6)))))) % 0.38/0.61 (define @t9 () (@var "Y" tptp.mu)) % 0.38/0.61 (define @t10 () (@var "W" $$unsorted)) % 0.38/0.61 (define @t11 () (lambda (@list @t2 @t9 @t10) (= @t2 @t9))) % 0.38/0.61 (define @t12 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.61 (define @t13 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.61 (define @t14 () (lambda (@list @t13 @t12 @t10) (= (_ @t13 @t10) (_ @t12 @t10)))) % 0.38/0.61 (define @t15 () (@var "Phi" (-> $$unsorted Bool))) % 0.38/0.61 (define @t16 () (_ @t15 @t10)) % 0.38/0.61 (define @t17 () (not @t16)) % 0.38/0.61 (define @t18 () (@list @t15 @t10)) % 0.38/0.61 (define @t19 () (lambda @t18 @t17)) % 0.38/0.61 (define @t20 () (@var "Psi" (-> $$unsorted Bool))) % 0.38/0.61 (define @t21 () (_ @t20 @t10)) % 0.38/0.61 (define @t22 () (lambda (@list @t15 @t20 @t10) (or @t16 @t21))) % 0.38/0.61 (define @t23 () (_ tptp.mnot @t20)) % 0.38/0.61 (define @t24 () (_ tptp.mnot @t15)) % 0.38/0.61 (define @t25 () (_ tptp.mor @t24)) % 0.38/0.61 (define @t26 () (@list @t15 @t20 @t1)) % 0.38/0.61 (define @t27 () (lambda @t26 (_ (_ tptp.mnot (_ @t25 @t23)) @t1))) % 0.38/0.61 (define @t28 () (lambda @t26 (_ (_ @t25 @t20) @t1))) % 0.38/0.61 (define @t29 () (lambda @t26 (_ (_ (_ tptp.mor @t23) @t15) @t1))) % 0.38/0.61 (define @t30 () (lambda @t26 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t15) @t20)) (_ (_ tptp.mimplies @t20) @t15)) @t1))) % 0.38/0.61 (define @t31 () (lambda @t26 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t15) @t20)) @t1))) % 0.38/0.61 (define @t32 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.38/0.61 (define @t33 () (_ @t32 @t2)) % 0.38/0.61 (define @t34 () (_ @t33 @t10)) % 0.38/0.61 (define @t35 () (@list @t2)) % 0.38/0.61 (define @t36 () (forall @t35 @t34)) % 0.38/0.61 (define @t37 () (@list @t32 @t10)) % 0.38/0.61 (define @t38 () (lambda @t37 @t36)) % 0.38/0.61 (define @t39 () (@var "P" (-> $$unsorted Bool))) % 0.38/0.61 (define @t40 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.38/0.61 (define @t41 () (_ @t40 @t39)) % 0.38/0.61 (define @t42 () (lambda (@list @t40 @t10) (forall (@list @t39) (_ @t41 @t10)))) % 0.38/0.61 (define @t43 () (lambda (@list @t32 @t1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda @t5 (_ (_ tptp.mnot @t33) @t1)))) @t1))) % 0.38/0.61 (define @t44 () (lambda (@list @t40 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t39 @t1) (_ (_ tptp.mnot @t41) @t1)))) @t1))) % 0.38/0.61 (define @t45 () (@list @t10)) % 0.38/0.61 (define @t46 () (lambda @t45 true)) % 0.38/0.61 (define @t47 () (@var "V" $$unsorted)) % 0.38/0.61 (define @t48 () (_ @t15 @t47)) % 0.38/0.61 (define @t49 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.38/0.61 (define @t50 () (@list @t47)) % 0.38/0.61 (define @t51 () (lambda (@list @t49 @t15 @t10) (forall @t50 (or (not (_ (_ @t49 @t10) @t47)) @t48)))) % 0.38/0.61 (define @t52 () (lambda (@list @t49 @t15 @t1) (_ (_ tptp.mnot (_ (_ tptp.mbox @t49) @t24)) @t1))) % 0.38/0.61 (define @t53 () (@var "S" $$unsorted)) % 0.38/0.61 (define @t54 () (_ @t49 @t53)) % 0.38/0.61 (define @t55 () (@list @t53)) % 0.38/0.61 (define @t56 () (@list @t49)) % 0.38/0.61 (define @t57 () (lambda @t56 (forall @t55 (_ @t54 @t53)))) % 0.38/0.61 (define @t58 () (@var "T" $$unsorted)) % 0.38/0.61 (define @t59 () (_ @t49 @t58)) % 0.38/0.61 (define @t60 () (_ @t54 @t58)) % 0.38/0.61 (define @t61 () (lambda @t56 (forall (@list @t53 @t58) (=> @t60 (_ @t59 @t53))))) % 0.38/0.61 (define @t62 () (@list @t58)) % 0.38/0.61 (define @t63 () (lambda @t56 (forall @t55 (exists @t62 @t60)))) % 0.38/0.61 (define @t64 () (@var "U" $$unsorted)) % 0.38/0.61 (define @t65 () (_ @t54 @t64)) % 0.38/0.61 (define @t66 () (_ @t59 @t64)) % 0.38/0.61 (define @t67 () (@list @t53 @t58 @t64)) % 0.38/0.61 (define @t68 () (lambda @t56 (forall @t67 (=> (and @t60 @t66) @t65)))) % 0.38/0.61 (define @t69 () (and @t60 @t65)) % 0.38/0.61 (define @t70 () (lambda @t56 (forall @t67 (=> @t69 @t66)))) % 0.38/0.61 (define @t71 () (= @t58 @t64)) % 0.38/0.61 (define @t72 () (lambda @t56 (forall @t67 (=> @t69 @t71)))) % 0.38/0.61 (define @t73 () (@list @t64)) % 0.38/0.61 (define @t74 () (lambda @t56 (forall @t55 (exists @t62 (and @t60 (forall @t73 (=> @t65 @t71))))))) % 0.38/0.61 (define @t75 () (_ @t49 @t64)) % 0.38/0.61 (define @t76 () (_ @t75 @t58)) % 0.38/0.61 (define @t77 () (lambda @t56 (forall @t67 (=> @t60 (exists @t73 (and @t65 @t76)))))) % 0.38/0.61 (define @t78 () (lambda @t56 (forall @t67 (=> @t69 (or @t66 @t71 @t76))))) % 0.38/0.61 (define @t79 () (lambda @t56 (forall @t67 (=> @t69 (exists @t50 (and (_ @t59 @t47) (_ @t75 @t47))))))) % 0.38/0.61 (define @t80 () (forall @t45 @t16)) % 0.38/0.61 (define @t81 () (@list @t15)) % 0.38/0.61 (define @t82 () (lambda @t81 @t80)) % 0.38/0.61 (define @t83 () (lambda @t81 (forall @t45 @t17))) % 0.38/0.61 (define @t84 () (lambda @t81 (exists @t45 @t16))) % 0.38/0.61 (define @t85 () (lambda @t81 (exists @t45 @t17))) % 0.38/0.61 (define @t86 () (_ (_ tptp.rel_s5 @t10) @t47)) % 0.38/0.61 (define @t87 () (not @t86)) % 0.38/0.61 (define @t88 () (or @t87 @t48)) % 0.38/0.61 (define @t89 () (forall @t50 @t88)) % 0.38/0.61 (define @t90 () (lambda @t18 @t89)) % 0.38/0.61 (define @t91 () (lambda (@list @t15 @t1) (_ (_ tptp.mnot (_ tptp.mbox_s5 @t24)) @t1))) % 0.38/0.61 (define @t92 () (@var "BOUND_VARIABLE_8578" $$unsorted)) % 0.38/0.61 (define @t93 () (@var "BOUND_VARIABLE_8580" tptp.mu)) % 0.38/0.61 (define @t94 () (tptp.g @t93 @t92)) % 0.38/0.61 (define @t95 () (tptp.f @t93 @t92)) % 0.38/0.61 (define @t96 () (not (tptp.rel_s5 @t10 @t92))) % 0.38/0.61 (define @t97 () (@var "BOUND_VARIABLE_8494" $$unsorted)) % 0.38/0.61 (define @t98 () (tptp.g @t2 @t97)) % 0.38/0.61 (define @t99 () (not (tptp.rel_s5 @t10 @t97))) % 0.38/0.61 (define @t100 () (@var "BOUND_VARIABLE_8488" $$unsorted)) % 0.38/0.61 (define @t101 () (tptp.f @t2 @t100)) % 0.38/0.61 (define @t102 () (not (tptp.rel_s5 @t10 @t100))) % 0.38/0.61 (define @t103 () (or @t102 @t101 @t99 @t98)) % 0.38/0.61 (define @t104 () (@list @t2 @t100 @t97)) % 0.38/0.61 (define @t105 () (forall @t104 @t103)) % 0.38/0.61 (define @t106 () (not @t105)) % 0.38/0.61 (define @t107 () (or @t106 @t96 @t95 @t94)) % 0.38/0.61 (define @t108 () (or @t96 @t95 @t94)) % 0.38/0.61 (define @t109 () (or @t106 @t108)) % 0.38/0.61 (define @t110 () (@list @t10 @t92 @t93)) % 0.38/0.61 (define @t111 () (forall @t110 @t109)) % 0.38/0.61 (define @t112 () (@list @t92 @t93)) % 0.38/0.61 (define @t113 () (forall @t112 @t109)) % 0.38/0.61 (define @t114 () (forall @t112 @t108)) % 0.38/0.61 (define @t115 () (@var "BOUND_VARIABLE_8552" tptp.mu)) % 0.38/0.61 (define @t116 () (or @t106 @t114)) % 0.38/0.61 (define @t117 () (tptp.g @t115 @t47)) % 0.38/0.61 (define @t118 () (tptp.f @t115 @t47)) % 0.38/0.61 (define @t119 () (tptp.rel_s5 @t10 @t47)) % 0.38/0.61 (define @t120 () (not @t119)) % 0.38/0.61 (define @t121 () (or @t120 @t118 @t117)) % 0.38/0.61 (define @t122 () (@list @t47 @t115)) % 0.38/0.61 (define @t123 () (forall @t122 @t121)) % 0.38/0.61 (define @t124 () (or @t106 @t123)) % 0.38/0.61 (define @t125 () (not (tptp.rel_s5 @t1 @t47))) % 0.38/0.61 (define @t126 () (forall @t122 (or @t125 @t118 @t117))) % 0.38/0.61 (define @t127 () (forall @t104 (or (not (tptp.rel_s5 @t1 @t100)) @t101 (not (tptp.rel_s5 @t1 @t97)) @t98))) % 0.38/0.61 (define @t128 () (not @t127)) % 0.38/0.61 (define @t129 () (@list @t1)) % 0.38/0.61 (define @t130 () (lambda @t129 (or @t128 @t126))) % 0.38/0.61 (define @t131 () (_ @t130 @t10)) % 0.38/0.61 (define @t132 () (forall @t45 @t131)) % 0.38/0.61 (define @t133 () (_ @t15 @t10)) % 0.38/0.61 (define @t134 () (lambda @t81 (forall @t45 @t133))) % 0.38/0.61 (define @t135 () (lambda @t45 @t123)) % 0.38/0.61 (define @t136 () (_ @t135 @t1)) % 0.38/0.61 (define @t137 () (or @t128 @t136)) % 0.38/0.61 (define @t138 () (lambda @t129 @t137)) % 0.38/0.61 (define @t139 () (_ @t20 @t1)) % 0.38/0.61 (define @t140 () (@list @t20 @t1)) % 0.38/0.61 (define @t141 () (or @t118 @t117)) % 0.38/0.61 (define @t142 () (or @t120 @t141)) % 0.38/0.61 (define @t143 () (forall @t122 @t142)) % 0.38/0.61 (define @t144 () (@list @t115)) % 0.38/0.61 (define @t145 () (forall @t144 @t142)) % 0.38/0.61 (define @t146 () (forall @t144 @t141)) % 0.38/0.61 (define @t147 () (or @t120 @t146)) % 0.38/0.61 (define @t148 () (tptp.g @t2 @t47)) % 0.38/0.61 (define @t149 () (tptp.f @t2 @t47)) % 0.38/0.61 (define @t150 () (forall @t35 (or @t149 @t148))) % 0.38/0.61 (define @t151 () (tptp.g @t2 @t10)) % 0.38/0.61 (define @t152 () (tptp.f @t2 @t10)) % 0.38/0.61 (define @t153 () (lambda @t45 (forall @t35 (or @t152 @t151)))) % 0.38/0.61 (define @t154 () (_ @t153 @t47)) % 0.38/0.61 (define @t155 () (or @t120 @t154)) % 0.38/0.61 (define @t156 () (forall @t50 @t155)) % 0.38/0.61 (define @t157 () (lambda @t45 @t156)) % 0.38/0.61 (define @t158 () (_ @t15 @t47)) % 0.38/0.61 (define @t159 () (lambda @t18 (forall @t50 (or @t120 @t158)))) % 0.38/0.61 (define @t160 () (_ @t3 @t10)) % 0.38/0.61 (define @t161 () (_ @t4 @t10)) % 0.38/0.61 (define @t162 () (or @t161 @t160)) % 0.38/0.61 (define @t163 () (or (_ @t4 @t1) (_ @t3 @t1))) % 0.38/0.61 (define @t164 () (lambda @t5 @t163)) % 0.38/0.61 (define @t165 () (_ @t164 @t2 @t10)) % 0.38/0.61 (define @t166 () (forall @t35 @t165)) % 0.38/0.61 (define @t167 () (lambda @t45 @t166)) % 0.38/0.61 (define @t168 () (_ @t32 @t2 @t10)) % 0.38/0.61 (define @t169 () (lambda @t37 (forall @t35 @t168))) % 0.38/0.61 (define @t170 () (lambda @t45 @t162)) % 0.38/0.61 (define @t171 () (@list @t20 @t10)) % 0.38/0.61 (define @t172 () (lambda @t171 (or @t161 @t21))) % 0.38/0.61 (define @t173 () (_ @t22 @t4)) % 0.38/0.61 (define @t174 () (lambda @t5 (_ (_ @t173 @t3) @t1))) % 0.38/0.61 (define @t175 () (lambda @t45 @t105)) % 0.38/0.61 (define @t176 () (_ @t175 @t1)) % 0.38/0.61 (define @t177 () (not @t176)) % 0.38/0.61 (define @t178 () (or @t177 @t139)) % 0.38/0.61 (define @t179 () (lambda @t140 @t178)) % 0.38/0.61 (define @t180 () (or (not (_ @t15 @t1)) @t139)) % 0.38/0.61 (define @t181 () (lambda @t26 @t180)) % 0.38/0.61 (define @t182 () (or @t99 @t98)) % 0.38/0.61 (define @t183 () (or @t102 @t101)) % 0.38/0.61 (define @t184 () (or @t183 @t182)) % 0.38/0.61 (define @t185 () (forall @t104 @t184)) % 0.38/0.61 (define @t186 () (forall (@list @t100 @t97) @t184)) % 0.38/0.61 (define @t187 () (forall (@list @t97) @t182)) % 0.38/0.61 (define @t188 () (@list @t47)) % 0.38/0.61 (define @t189 () (forall (@list @t100) @t183)) % 0.38/0.61 (define @t190 () (or @t189 @t187)) % 0.38/0.61 (define @t191 () (forall @t50 (or @t120 @t148))) % 0.38/0.61 (define @t192 () (forall @t50 (or @t120 @t149))) % 0.38/0.61 (define @t193 () (or @t192 @t191)) % 0.38/0.61 (define @t194 () (or (forall @t50 (or @t125 @t149)) (forall @t50 (or @t125 @t148)))) % 0.38/0.61 (define @t195 () (lambda @t5 @t194)) % 0.38/0.61 (define @t196 () (_ @t195 @t2 @t10)) % 0.38/0.61 (define @t197 () (forall @t35 @t196)) % 0.38/0.61 (define @t198 () (lambda @t45 @t197)) % 0.38/0.61 (define @t199 () (lambda @t45 @t191)) % 0.38/0.61 (define @t200 () (_ @t199 @t10)) % 0.38/0.61 (define @t201 () (or @t192 @t200)) % 0.38/0.61 (define @t202 () (lambda @t45 @t201)) % 0.38/0.61 (define @t203 () (_ @t3 @t47)) % 0.38/0.61 (define @t204 () (or @t120 @t203)) % 0.38/0.61 (define @t205 () (_ @t3 @t47)) % 0.38/0.61 (define @t206 () (or @t120 @t205)) % 0.38/0.61 (define @t207 () (forall @t50 @t206)) % 0.38/0.61 (define @t208 () (lambda @t45 @t207)) % 0.38/0.61 (define @t209 () (_ @t159 @t3)) % 0.38/0.61 (define @t210 () (lambda @t45 @t192)) % 0.38/0.61 (define @t211 () (_ @t210 @t10)) % 0.38/0.61 (define @t212 () (or @t211 @t21)) % 0.38/0.61 (define @t213 () (lambda @t171 @t212)) % 0.38/0.61 (define @t214 () (_ @t4 @t47)) % 0.38/0.61 (define @t215 () (or @t120 @t214)) % 0.38/0.61 (define @t216 () (_ @t4 @t47)) % 0.38/0.61 (define @t217 () (or @t120 @t216)) % 0.38/0.61 (define @t218 () (forall @t50 @t217)) % 0.38/0.61 (define @t219 () (lambda @t45 @t218)) % 0.38/0.61 (define @t220 () (_ @t159 @t4)) % 0.38/0.61 (define @t221 () (lambda @t5 (_ (_ (_ @t22 @t220) @t209) @t1))) % 0.38/0.61 (define @t222 () (or @t17 @t21)) % 0.38/0.61 (define @t223 () (lambda @t45 @t222)) % 0.38/0.61 (define @t224 () (lambda @t45 @t17)) % 0.38/0.61 (define @t225 () (_ @t224 @t10)) % 0.38/0.61 (define @t226 () (or @t225 @t21)) % 0.38/0.61 (define @t227 () (lambda @t171 @t226)) % 0.38/0.61 (define @t228 () (forall @t110 @t107)) % 0.38/0.61 (define @t229 () (@quantifiers_skolemize @t228 0)) % 0.38/0.61 (define @t230 () (forall @t104 (or (not (tptp.rel_s5 @t229 @t100)) @t101 (not (tptp.rel_s5 @t229 @t97)) @t98))) % 0.38/0.61 (define @t231 () (@quantifiers_skolemize @t228 1)) % 0.38/0.61 (define @t232 () (@quantifiers_skolemize @t228 2)) % 0.38/0.61 (define @t233 () (tptp.g @t232 @t231)) % 0.38/0.61 (define @t234 () (tptp.f @t232 @t231)) % 0.38/0.61 (define @t235 () (tptp.rel_s5 @t229 @t231)) % 0.38/0.61 (define @t236 () (not @t235)) % 0.38/0.61 (define @t237 () (not @t230)) % 0.38/0.61 (define @t238 () (or @t237 @t236 @t234 @t233)) % 0.38/0.61 (define @t239 () (@list true)) % 0.38/0.61 (define @t240 () (@list @t238)) % 0.38/0.61 (define @t241 () (or @t236 @t234 @t236 @t233)) % 0.38/0.61 (define @t242 () (not @t241)) % 0.38/0.61 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.38/0.61 (assume @p2 (_ tptp.mreflexive tptp.rel_s5)) % 0.38/0.61 (assume @p3 (_ tptp.mtransitive tptp.rel_s5)) % 0.38/0.61 (assume @p4 (_ tptp.msymmetric tptp.rel_s5)) % 0.38/0.61 (assume @p5 @t8) % 0.38/0.61 (assume @p6 true) % 0.38/0.61 (step @p7 (= tptp.meq_ind @t11) :rule refl :args (@t11)) % 0.38/0.61 (step @p8 (= tptp.meq_prop @t14) :rule refl :args (@t14)) % 0.38/0.61 (step @p9 (= tptp.mnot @t19) :rule refl :args (@t19)) % 0.38/0.61 (step @p10 (= tptp.mor @t22) :rule refl :args (@t22)) % 0.38/0.61 (step @p11 (= tptp.mand @t27) :rule refl :args (@t27)) % 0.38/0.61 (step @p12 (= tptp.mimplies @t28) :rule refl :args (@t28)) % 0.38/0.61 (step @p13 (= tptp.mimplied @t29) :rule refl :args (@t29)) % 0.38/0.61 (step @p14 (= tptp.mequiv @t30) :rule refl :args (@t30)) % 0.38/0.61 (step @p15 (= tptp.mxor @t31) :rule refl :args (@t31)) % 0.38/0.61 (step @p16 (= tptp.mforall_ind @t38) :rule refl :args (@t38)) % 0.38/0.61 (step @p17 (= tptp.mforall_prop @t42) :rule refl :args (@t42)) % 0.38/0.61 (step @p18 (= tptp.mexists_ind @t43) :rule refl :args (@t43)) % 0.38/0.61 (step @p19 (= tptp.mexists_prop @t44) :rule refl :args (@t44)) % 0.38/0.61 (step @p20 (= tptp.mtrue @t46) :rule refl :args (@t46)) % 0.38/0.61 (step @p21 (= tptp.mbox @t51) :rule refl :args (@t51)) % 0.38/0.61 (step @p22 (= tptp.mdia @t52) :rule refl :args (@t52)) % 0.38/0.61 (step @p23 (= tptp.mreflexive @t57) :rule refl :args (@t57)) % 0.38/0.61 (step @p24 (= tptp.msymmetric @t61) :rule refl :args (@t61)) % 0.38/0.61 (step @p25 (= tptp.mserial @t63) :rule refl :args (@t63)) % 0.38/0.61 (step @p26 (= tptp.mtransitive @t68) :rule refl :args (@t68)) % 0.38/0.61 (step @p27 (= tptp.meuclidean @t70) :rule refl :args (@t70)) % 0.38/0.61 (step @p28 (= tptp.mpartially_functional @t72) :rule refl :args (@t72)) % 0.38/0.61 (step @p29 (= tptp.mfunctional @t74) :rule refl :args (@t74)) % 0.38/0.61 (step @p30 (= tptp.mweakly_dense @t77) :rule refl :args (@t77)) % 0.38/0.61 (step @p31 (= tptp.mweakly_connected @t78) :rule refl :args (@t78)) % 0.38/0.61 (step @p32 (= tptp.mweakly_directed @t79) :rule refl :args (@t79)) % 0.38/0.61 (step @p33 (= tptp.mvalid @t82) :rule refl :args (@t82)) % 0.38/0.61 (step @p34 (= tptp.minvalid @t83) :rule refl :args (@t83)) % 0.38/0.61 (step @p35 (= tptp.msatisfiable @t84) :rule refl :args (@t84)) % 0.38/0.61 (step @p36 (= tptp.mcountersatisfiable @t85) :rule refl :args (@t85)) % 0.38/0.61 (step @p37 (= tptp.mbox_s5 @t90) :rule refl :args (@t90)) % 0.38/0.61 (step @p38 (= tptp.mdia_s5 @t91) :rule refl :args (@t91)) % 0.38/0.61 (step @p39 :rule aci_norm :args ((= @t109 @t107))) % 0.38/0.61 (step @p40 :rule cong :premises (@p39) :args (@t111)) % 0.38/0.61 (step @p41 :rule quant-merge-prenex :args ((= (forall @t45 @t113) @t111))) % 0.38/0.61 (step @p42 :rule alpha_equiv :args (@t114 (@list @t92 @t93) (@list @t47 @t115))) % 0.38/0.61 (step @p43 :rule refl :args (@t106)) % 0.38/0.61 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t116)) % 0.38/0.61 (step @p45 :rule quant-miniscope-or :args ((= @t113 @t116))) % 0.38/0.61 (step @p46 :rule trans :premises (@p45 @p44)) % 0.38/0.61 (step @p47 :rule symm :premises (@p46)) % 0.38/0.61 (step @p48 :rule cong :premises (@p47) :args ((forall @t45 @t124))) % 0.38/0.61 (step @p49 :rule trans :premises (@p48 @p41)) % 0.38/0.61 (step @p50 :rule trans :premises (@p49 @p40)) % 0.38/0.61 (step @p51 :rule beta-reduce :args ((= @t131 @t124))) % 0.38/0.61 (step @p52 :rule cong :premises (@p51) :args (@t132)) % 0.38/0.61 (step @p53 :rule trans :premises (@p52 @p50)) % 0.38/0.61 (step @p54 :rule beta-reduce :args ((= (_ @t134 @t130) @t132))) % 0.38/0.61 (step @p55 :rule trans :premises (@p54 @p53)) % 0.38/0.61 (step @p56 :rule beta-reduce :args ((= @t136 @t126))) % 0.38/0.61 (step @p57 :rule refl :args (@t128)) % 0.38/0.61 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t137)) % 0.38/0.61 (step @p59 :rule cong :premises (@p58) :args (@t138)) % 0.38/0.61 (step @p60 :rule beta-reduce :args ((= (_ (lambda @t140 (or @t128 @t139)) @t135) @t138))) % 0.38/0.61 (step @p61 :rule trans :premises (@p60 @p59)) % 0.38/0.61 (step @p62 :rule aci_norm :args ((= @t142 @t121))) % 0.38/0.61 (step @p63 :rule cong :premises (@p62) :args (@t143)) % 0.38/0.61 (step @p64 :rule quant-merge-prenex :args ((= (forall @t50 @t145) @t143))) % 0.38/0.61 (step @p65 :rule alpha_equiv :args (@t146 (@list @t115) (@list @t2))) % 0.38/0.61 (step @p66 :rule refl :args (@t120)) % 0.38/0.61 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t147)) % 0.38/0.61 (step @p68 :rule quant-miniscope-or :args ((= @t145 @t147))) % 0.38/0.61 (step @p69 :rule trans :premises (@p68 @p67)) % 0.38/0.61 (step @p70 :rule symm :premises (@p69)) % 0.38/0.61 (step @p71 :rule cong :premises (@p70) :args ((forall @t50 (or @t120 @t150)))) % 0.38/0.61 (step @p72 :rule trans :premises (@p71 @p64)) % 0.38/0.61 (step @p73 :rule trans :premises (@p72 @p63)) % 0.38/0.61 (step @p74 :rule beta-reduce :args ((= @t154 @t150))) % 0.38/0.61 (step @p75 :rule refl :args (@t120)) % 0.38/0.61 (step @p76 :rule nary_cong :premises (@p75 @p74) :args (@t155)) % 0.38/0.61 (step @p77 :rule cong :premises (@p76) :args (@t156)) % 0.38/0.61 (step @p78 :rule trans :premises (@p77 @p73)) % 0.38/0.61 (step @p79 :rule cong :premises (@p78) :args (@t157)) % 0.38/0.61 (step @p80 :rule beta-reduce :args ((= (_ @t159 @t153) @t157))) % 0.38/0.61 (step @p81 :rule trans :premises (@p80 @p79)) % 0.38/0.61 (step @p82 :rule refl :args (@t151)) % 0.38/0.61 (step @p83 :rule refl :args (@t160)) % 0.38/0.61 (step @p84 :rule cong :premises (@p83 @p82) :args ((= @t160 @t151))) % 0.38/0.61 (step @p85 :rule symm :premises (@p84)) % 0.38/0.61 (step @p86 :rule eq_resolve :premises (@p83 @p85)) % 0.38/0.61 (step @p87 :rule refl :args (@t152)) % 0.38/0.61 (step @p88 :rule refl :args (@t161)) % 0.38/0.61 (step @p89 :rule cong :premises (@p88 @p87) :args ((= @t161 @t152))) % 0.38/0.61 (step @p90 :rule symm :premises (@p89)) % 0.38/0.61 (step @p91 :rule eq_resolve :premises (@p88 @p90)) % 0.38/0.61 (step @p92 :rule nary_cong :premises (@p91 @p86) :args (@t162)) % 0.38/0.61 (step @p93 :rule cong :premises (@p92) :args ((forall @t35 @t162))) % 0.38/0.61 (step @p94 :rule beta-reduce :args ((= @t165 @t162))) % 0.38/0.61 (step @p95 :rule cong :premises (@p94) :args (@t166)) % 0.38/0.61 (step @p96 :rule trans :premises (@p95 @p93)) % 0.38/0.61 (step @p97 :rule cong :premises (@p96) :args (@t167)) % 0.38/0.61 (step @p98 :rule beta-reduce :args ((= (_ @t169 @t164) @t167))) % 0.38/0.61 (step @p99 :rule trans :premises (@p98 @p97)) % 0.38/0.61 (step @p100 :rule beta-reduce :args ((= (_ @t170 @t1) @t163))) % 0.38/0.61 (step @p101 :rule refl :args (@t1)) % 0.38/0.61 (step @p102 :rule beta-reduce :args ((= (_ @t172 @t3) @t170))) % 0.38/0.61 (step @p103 :rule refl :args (@t3)) % 0.38/0.61 (step @p104 :rule beta-reduce :args ((= @t173 @t172))) % 0.38/0.61 (step @p105 :rule ho_cong :premises (@p104 @p103)) % 0.38/0.61 (step @p106 :rule trans :premises (@p105 @p102)) % 0.38/0.61 (step @p107 :rule ho_cong :premises (@p106 @p101)) % 0.38/0.61 (step @p108 :rule trans :premises (@p107 @p100)) % 0.38/0.61 (step @p109 :rule cong :premises (@p108) :args (@t174)) % 0.38/0.61 (step @p110 :rule refl :args (@t169)) % 0.38/0.61 (step @p111 :rule ho_cong :premises (@p110 @p109)) % 0.38/0.61 (step @p112 :rule trans :premises (@p111 @p99)) % 0.38/0.61 (step @p113 :rule refl :args (@t159)) % 0.38/0.61 (step @p114 :rule ho_cong :premises (@p113 @p112)) % 0.38/0.61 (step @p115 :rule trans :premises (@p114 @p81)) % 0.38/0.61 (step @p116 :rule refl :args (@t139)) % 0.38/0.61 (step @p117 :rule beta-reduce :args ((= @t176 @t127))) % 0.38/0.61 (step @p118 :rule cong :premises (@p117) :args (@t177)) % 0.38/0.61 (step @p119 :rule nary_cong :premises (@p118 @p116) :args (@t178)) % 0.38/0.61 (step @p120 :rule cong :premises (@p119) :args (@t179)) % 0.38/0.61 (step @p121 :rule beta-reduce :args ((= (_ @t181 @t175) @t179))) % 0.38/0.61 (step @p122 :rule trans :premises (@p121 @p120)) % 0.38/0.61 (step @p123 :rule aci_norm :args ((= @t184 @t103))) % 0.38/0.61 (step @p124 :rule cong :premises (@p123) :args (@t185)) % 0.38/0.61 (step @p125 :rule quant-merge-prenex :args ((= (forall @t35 @t186) @t185))) % 0.38/0.61 (step @p126 :rule alpha_equiv :args (@t187 (@list @t97) @t188)) % 0.38/0.61 (step @p127 :rule alpha_equiv :args (@t189 (@list @t100) @t188)) % 0.38/0.61 (step @p128 :rule nary_cong :premises (@p127 @p126) :args (@t190)) % 0.38/0.61 (step @p129 :rule quant-miniscope-or :args ((= @t186 @t190))) % 0.38/0.61 (step @p130 :rule trans :premises (@p129 @p128)) % 0.38/0.61 (step @p131 :rule symm :premises (@p130)) % 0.38/0.61 (step @p132 :rule cong :premises (@p131) :args ((forall @t35 @t193))) % 0.38/0.61 (step @p133 :rule trans :premises (@p132 @p125)) % 0.38/0.61 (step @p134 :rule trans :premises (@p133 @p124)) % 0.38/0.61 (step @p135 :rule beta-reduce :args ((= @t196 @t193))) % 0.38/0.61 (step @p136 :rule cong :premises (@p135) :args (@t197)) % 0.38/0.61 (step @p137 :rule trans :premises (@p136 @p134)) % 0.38/0.61 (step @p138 :rule cong :premises (@p137) :args (@t198)) % 0.38/0.61 (step @p139 :rule beta-reduce :args ((= (_ @t169 @t195) @t198))) % 0.38/0.61 (step @p140 :rule trans :premises (@p139 @p138)) % 0.38/0.61 (step @p141 :rule beta-reduce :args ((= (_ (lambda @t45 @t193) @t1) @t194))) % 0.38/0.61 (step @p142 :rule beta-reduce :args ((= @t200 @t191))) % 0.38/0.61 (step @p143 :rule refl :args (@t192)) % 0.38/0.61 (step @p144 :rule nary_cong :premises (@p143 @p142) :args (@t201)) % 0.38/0.61 (step @p145 :rule cong :premises (@p144) :args (@t202)) % 0.38/0.61 (step @p146 :rule beta-reduce :args ((= (_ (lambda @t171 (or @t192 @t21)) @t199) @t202))) % 0.38/0.61 (step @p147 :rule trans :premises (@p146 @p145)) % 0.38/0.61 (step @p148 :rule refl :args (@t148)) % 0.38/0.61 (step @p149 :rule refl :args (@t203)) % 0.38/0.61 (step @p150 :rule cong :premises (@p149 @p148) :args ((= @t203 @t148))) % 0.38/0.61 (step @p151 :rule symm :premises (@p150)) % 0.38/0.61 (step @p152 :rule eq_resolve :premises (@p149 @p151)) % 0.38/0.61 (step @p153 :rule nary_cong :premises (@p66 @p152) :args (@t204)) % 0.38/0.61 (step @p154 :rule cong :premises (@p153) :args ((forall @t50 @t204))) % 0.38/0.61 (step @p155 :rule refl :args (@t205)) % 0.38/0.61 (step @p156 :rule nary_cong :premises (@p75 @p155) :args (@t206)) % 0.38/0.61 (step @p157 :rule cong :premises (@p156) :args (@t207)) % 0.38/0.61 (step @p158 :rule trans :premises (@p157 @p154)) % 0.38/0.61 (step @p159 :rule cong :premises (@p158) :args (@t208)) % 0.38/0.61 (step @p160 :rule beta-reduce :args ((= @t209 @t208))) % 0.38/0.61 (step @p161 :rule trans :premises (@p160 @p159)) % 0.38/0.61 (step @p162 :rule refl :args (@t21)) % 0.38/0.61 (step @p163 :rule beta-reduce :args ((= @t211 @t192))) % 0.38/0.61 (step @p164 :rule nary_cong :premises (@p163 @p162) :args (@t212)) % 0.38/0.61 (step @p165 :rule cong :premises (@p164) :args (@t213)) % 0.38/0.61 (step @p166 :rule beta-reduce :args ((= (_ @t22 @t210) @t213))) % 0.38/0.61 (step @p167 :rule trans :premises (@p166 @p165)) % 0.38/0.61 (step @p168 :rule refl :args (@t149)) % 0.38/0.61 (step @p169 :rule refl :args (@t214)) % 0.38/0.61 (step @p170 :rule cong :premises (@p169 @p168) :args ((= @t214 @t149))) % 0.38/0.61 (step @p171 :rule symm :premises (@p170)) % 0.38/0.61 (step @p172 :rule eq_resolve :premises (@p169 @p171)) % 0.38/0.61 (step @p173 :rule nary_cong :premises (@p66 @p172) :args (@t215)) % 0.38/0.61 (step @p174 :rule cong :premises (@p173) :args ((forall @t50 @t215))) % 0.38/0.61 (step @p175 :rule refl :args (@t216)) % 0.38/0.61 (step @p176 :rule nary_cong :premises (@p75 @p175) :args (@t217)) % 0.38/0.61 (step @p177 :rule cong :premises (@p176) :args (@t218)) % 0.38/0.61 (step @p178 :rule trans :premises (@p177 @p174)) % 0.38/0.61 (step @p179 :rule cong :premises (@p178) :args (@t219)) % 0.38/0.61 (step @p180 :rule beta-reduce :args ((= @t220 @t219))) % 0.38/0.61 (step @p181 :rule trans :premises (@p180 @p179)) % 0.38/0.61 (step @p182 :rule refl :args (@t22)) % 0.38/0.61 (step @p183 :rule ho_cong :premises (@p182 @p181)) % 0.38/0.61 (step @p184 :rule trans :premises (@p183 @p167)) % 0.38/0.61 (step @p185 :rule ho_cong :premises (@p184 @p161)) % 0.38/0.61 (step @p186 :rule trans :premises (@p185 @p147)) % 0.38/0.61 (step @p187 :rule ho_cong :premises (@p186 @p101)) % 0.38/0.61 (step @p188 :rule trans :premises (@p187 @p141)) % 0.38/0.61 (step @p189 :rule cong :premises (@p188) :args (@t221)) % 0.38/0.61 (step @p190 :rule ho_cong :premises (@p110 @p189)) % 0.38/0.61 (step @p191 :rule trans :premises (@p190 @p140)) % 0.38/0.61 (step @p192 :rule refl :args (@t181)) % 0.38/0.61 (step @p193 :rule ho_cong :premises (@p192 @p191)) % 0.38/0.61 (step @p194 :rule trans :premises (@p193 @p122)) % 0.38/0.61 (step @p195 :rule ho_cong :premises (@p194 @p115)) % 0.38/0.61 (step @p196 :rule trans :premises (@p195 @p61)) % 0.38/0.61 (step @p197 :rule refl :args (@t134)) % 0.38/0.61 (step @p198 :rule ho_cong :premises (@p197 @p196)) % 0.38/0.61 (step @p199 :rule trans :premises (@p198 @p55)) % 0.38/0.61 (step @p200 :rule cong :premises (@p199) :args ((not (_ @t134 (_ (_ @t181 (_ @t169 @t221)) (_ @t159 (_ @t169 @t174))))))) % 0.38/0.61 (step @p201 :rule refl :args (@t4)) % 0.38/0.61 (step @p202 :rule ho_cong :premises (@p10 @p201)) % 0.38/0.61 (step @p203 :rule ho_cong :premises (@p202 @p103)) % 0.38/0.61 (step @p204 :rule ho_cong :premises (@p203 @p101)) % 0.38/0.61 (step @p205 :rule cong :premises (@p204) :args (@t6)) % 0.38/0.61 (step @p206 :rule refl :args (@t168)) % 0.38/0.61 (step @p207 :rule refl :args (@t34)) % 0.38/0.61 (step @p208 :rule cong :premises (@p207 @p206) :args ((= @t34 @t168))) % 0.38/0.61 (step @p209 :rule symm :premises (@p208)) % 0.38/0.61 (step @p210 :rule eq_resolve :premises (@p207 @p209)) % 0.38/0.61 (step @p211 :rule cong :premises (@p210) :args (@t36)) % 0.38/0.61 (step @p212 :rule cong :premises (@p211) :args (@t38)) % 0.38/0.61 (step @p213 :rule trans :premises (@p16 @p212)) % 0.38/0.61 (step @p214 :rule ho_cong :premises (@p213 @p205)) % 0.38/0.61 (step @p215 :rule refl :args (@t158)) % 0.38/0.61 (step @p216 :rule refl :args (@t48)) % 0.38/0.61 (step @p217 :rule cong :premises (@p216 @p215) :args ((= @t48 @t158))) % 0.38/0.61 (step @p218 :rule symm :premises (@p217)) % 0.38/0.61 (step @p219 :rule eq_resolve :premises (@p216 @p218)) % 0.38/0.61 (step @p220 :rule refl :args (@t119)) % 0.38/0.61 (step @p221 :rule refl :args (@t86)) % 0.38/0.61 (step @p222 :rule cong :premises (@p221 @p220) :args ((= @t86 @t119))) % 0.38/0.61 (step @p223 :rule symm :premises (@p222)) % 0.38/0.61 (step @p224 :rule eq_resolve :premises (@p221 @p223)) % 0.38/0.61 (step @p225 :rule cong :premises (@p224) :args (@t87)) % 0.38/0.61 (step @p226 :rule nary_cong :premises (@p225 @p219) :args (@t88)) % 0.38/0.61 (step @p227 :rule cong :premises (@p226) :args (@t89)) % 0.38/0.61 (step @p228 :rule cong :premises (@p227) :args (@t90)) % 0.38/0.61 (step @p229 :rule trans :premises (@p37 @p228)) % 0.38/0.61 (step @p230 :rule ho_cong :premises (@p229 @p214)) % 0.38/0.61 (step @p231 :rule ho_cong :premises (@p229 @p103)) % 0.38/0.61 (step @p232 :rule ho_cong :premises (@p229 @p201)) % 0.38/0.61 (step @p233 :rule ho_cong :premises (@p10 @p232)) % 0.38/0.61 (step @p234 :rule ho_cong :premises (@p233 @p231)) % 0.38/0.61 (step @p235 :rule ho_cong :premises (@p234 @p101)) % 0.38/0.61 (step @p236 :rule cong :premises (@p235) :args (@t7)) % 0.38/0.61 (step @p237 :rule ho_cong :premises (@p213 @p236)) % 0.38/0.61 (step @p238 :rule beta-reduce :args ((= (_ @t223 @t1) @t180))) % 0.38/0.61 (step @p239 :rule beta-reduce :args ((= (_ (lambda @t171 @t222) @t20) @t223))) % 0.38/0.61 (step @p240 :rule refl :args (@t20)) % 0.38/0.61 (step @p241 :rule beta-reduce :args ((= @t225 @t17))) % 0.38/0.61 (step @p242 :rule nary_cong :premises (@p241 @p162) :args (@t226)) % 0.38/0.61 (step @p243 :rule cong :premises (@p242) :args (@t227)) % 0.38/0.61 (step @p244 :rule beta-reduce :args ((= (_ @t22 @t224) @t227))) % 0.38/0.61 (step @p245 :rule trans :premises (@p244 @p243)) % 0.38/0.61 (step @p246 :rule beta-reduce :args ((= (_ @t19 @t15) @t224))) % 0.38/0.61 (step @p247 :rule ho_cong :premises (@p182 @p246)) % 0.38/0.61 (step @p248 :rule trans :premises (@p247 @p245)) % 0.38/0.61 (step @p249 :rule ho_cong :premises (@p248 @p240)) % 0.38/0.61 (step @p250 :rule trans :premises (@p249 @p239)) % 0.38/0.61 (step @p251 :rule ho_cong :premises (@p250 @p101)) % 0.38/0.61 (step @p252 :rule trans :premises (@p251 @p238)) % 0.38/0.61 (step @p253 :rule refl :args (@t15)) % 0.38/0.61 (step @p254 :rule ho_cong :premises (@p9 @p253)) % 0.38/0.61 (step @p255 :rule ho_cong :premises (@p10 @p254)) % 0.38/0.61 (step @p256 :rule ho_cong :premises (@p255 @p240)) % 0.38/0.61 (step @p257 :rule ho_cong :premises (@p256 @p101)) % 0.38/0.61 (step @p258 :rule trans :premises (@p257 @p252)) % 0.38/0.61 (step @p259 :rule cong :premises (@p258) :args (@t28)) % 0.38/0.61 (step @p260 :rule trans :premises (@p12 @p259)) % 0.38/0.61 (step @p261 :rule ho_cong :premises (@p260 @p237)) % 0.38/0.61 (step @p262 :rule ho_cong :premises (@p261 @p230)) % 0.38/0.61 (step @p263 :rule refl :args (@t133)) % 0.38/0.61 (step @p264 :rule refl :args (@t16)) % 0.38/0.61 (step @p265 :rule cong :premises (@p264 @p263) :args ((= @t16 @t133))) % 0.38/0.61 (step @p266 :rule symm :premises (@p265)) % 0.38/0.61 (step @p267 :rule eq_resolve :premises (@p264 @p266)) % 0.38/0.61 (step @p268 :rule cong :premises (@p267) :args (@t80)) % 0.38/0.61 (step @p269 :rule cong :premises (@p268) :args (@t82)) % 0.38/0.61 (step @p270 :rule trans :premises (@p33 @p269)) % 0.38/0.61 (step @p271 :rule ho_cong :premises (@p270 @p262)) % 0.38/0.61 (step @p272 :rule cong :premises (@p271) :args (@t8)) % 0.38/0.61 (step @p273 :rule trans :premises (@p272 @p200)) % 0.38/0.61 (step @p274 :rule eq_resolve :premises (@p5 @p273)) % 0.38/0.61 (step @p275 :rule skolemize :premises (@p274)) % 0.38/0.61 (step @p276 :rule bool-double-not-elim :args (@t230)) % 0.38/0.61 (step @p277 :rule refl :args (@t238)) % 0.38/0.61 (step @p278 :rule nary_cong :premises (@p277 @p276) :args ((or @t238 (not @t237)))) % 0.38/0.61 (step @p279 :rule cnf_or_neg :args (@t238 0)) % 0.38/0.61 (step @p280 :rule eq_resolve :premises (@p279 @p278)) % 0.38/0.61 (step @p281 :rule reordering :premises (@p280) :args ((or @t230 @t238))) % 0.38/0.61 (step @p282 :rule chain_m_resolution :premises (@p281 @p275) :args (@t230 @t239 @t240)) % 0.38/0.61 (step @p283 :rule cnf_or_neg :args (@t238 3)) % 0.38/0.61 (step @p284 :rule chain_m_resolution :premises (@p283 @p275) :args ((not @t233) @t239 @t240)) % 0.38/0.61 (step @p285 :rule cnf_or_neg :args (@t238 2)) % 0.38/0.61 (step @p286 :rule chain_m_resolution :premises (@p285 @p275) :args ((not @t234) @t239 @t240)) % 0.38/0.61 (step @p287 :rule bool-double-not-elim :args (@t235)) % 0.38/0.61 (step @p288 :rule nary_cong :premises (@p277 @p287) :args ((or @t238 (not @t236)))) % 0.38/0.61 (step @p289 :rule cnf_or_neg :args (@t238 1)) % 0.38/0.61 (step @p290 :rule eq_resolve :premises (@p289 @p288)) % 0.38/0.61 (step @p291 :rule reordering :premises (@p290) :args ((or @t235 @t238))) % 0.38/0.61 (step @p292 :rule chain_m_resolution :premises (@p291 @p275) :args (@t235 @t239 @t240)) % 0.38/0.61 (step @p293 :rule cnf_or_pos :args (@t241)) % 0.38/0.61 (step @p294 :rule factoring :premises (@p293)) % 0.38/0.61 (step @p295 :rule reordering :premises (@p294) :args ((or @t236 @t234 @t233 @t242))) % 0.38/0.61 (step @p296 :rule chain_m_resolution :premises (@p295 @p292 @p286 @p284) :args (@t242 (@list false true true) (@list @t235 @t234 @t233))) % 0.38/0.61 (assume-push @p303 @t230) % 0.38/0.61 (step @p298 :rule instantiate :premises (@p282) :args ((@list @t232 @t231 @t231))) % 0.38/0.61 (step-pop @p304 :rule scope :premises (@p298)) % 0.38/0.61 (step @p299 :rule process_scope :premises (@p304) :args (@t241)) % 0.38/0.61 (step @p301 :rule implies_elim :premises (@p299)) % 0.38/0.61 (step @p302 false :rule chain_m_resolution :premises (@p301 @p296 @p282) :args (false (@list true false) (@list @t241 @t230))) % 0.38/0.61 ) % 0.38/0.61 % SZS output end Proof % 0.38/0.61 % cvc5 exiting %------------------------------------------------------------------------------