TSTP Solution File: SEU858^5 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU858^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n011.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 May 29 17:55:19 EDT 2024
% Result : Theorem 0.25s 0.57s
% Output : Proof 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.16 % Problem : SEU858^5 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.17 % Command : do_cvc5 %s %d
% 0.18/0.39 % Computer : n011.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Mon May 27 11:52:39 EDT 2024
% 0.18/0.39 % CPUTime :
% 0.25/0.55 %----Proving TH0
% 0.25/0.57 --- Run --ho-elim --full-saturate-quant at 10...
% 0.25/0.57 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.zXP0rH19X5/cvc5---1.0.5_32591.smt2
% 0.25/0.57 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.zXP0rH19X5/cvc5---1.0.5_32591.smt2
% 0.25/0.57 (assume a0 (not (forall ((Xw (-> (-> tptp.a Bool) Bool))) (=> (and (@ Xw (lambda ((Xx tptp.a)) false)) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xt Xx))))))) (@ Xw (lambda ((Xx tptp.a)) false))))))
% 0.25/0.57 (assume a1 true)
% 0.25/0.57 (step t1 (cl (not (= (not (forall ((Xw (-> (-> tptp.a Bool) Bool))) (=> (and (@ Xw (lambda ((Xx tptp.a)) false)) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xt Xx))))))) (@ Xw (lambda ((Xx tptp.a)) false))))) false)) (not (not (forall ((Xw (-> (-> tptp.a Bool) Bool))) (=> (and (@ Xw (lambda ((Xx tptp.a)) false)) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xt Xx))))))) (@ Xw (lambda ((Xx tptp.a)) false)))))) false) :rule equiv_pos2)
% 0.25/0.57 (anchor :step t2 :args ((Xw (-> (-> tptp.a Bool) Bool)) (:= Xw Xw)))
% 0.25/0.57 (step t2.t1 (cl (= Xw Xw)) :rule refl)
% 0.25/0.57 (step t2.t2 (cl (= Xw Xw)) :rule refl)
% 0.25/0.57 (step t2.t3 (cl (= (lambda ((Xx tptp.a)) false) (lambda ((BOUND_VARIABLE_766 tptp.a)) false))) :rule all_simplify)
% 0.25/0.57 (step t2.t4 (cl (= (@ Xw (lambda ((Xx tptp.a)) false)) (@ Xw (lambda ((BOUND_VARIABLE_766 tptp.a)) false)))) :rule cong :premises (t2.t2 t2.t3))
% 0.25/0.57 (anchor :step t2.t5 :args ((Xr (-> tptp.a Bool)) (:= Xr Xr) (Xx tptp.a) (:= Xx Xx)))
% 0.25/0.57 (step t2.t5.t1 (cl (= Xr Xr)) :rule refl)
% 0.25/0.57 (step t2.t5.t2 (cl (= Xx Xx)) :rule refl)
% 0.25/0.57 (step t2.t5.t3 (cl (= (@ Xw Xr) (@ Xw Xr))) :rule refl)
% 0.25/0.57 (anchor :step t2.t5.t4 :args ((Xt tptp.a) (:= Xt Xt)))
% 0.25/0.57 (step t2.t5.t4.t1 (cl (= Xt Xt)) :rule refl)
% 0.25/0.57 (step t2.t5.t4.t2 (cl (= (@ Xr Xt) (@ Xr Xt))) :rule refl)
% 0.25/0.57 (step t2.t5.t4.t3 (cl (= (= Xt Xx) (= Xx Xt))) :rule all_simplify)
% 0.25/0.57 (step t2.t5.t4.t4 (cl (= (or (@ Xr Xt) (= Xt Xx)) (or (@ Xr Xt) (= Xx Xt)))) :rule cong :premises (t2.t5.t4.t2 t2.t5.t4.t3))
% 0.25/0.57 (step t2.t5.t4 (cl (= (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xt Xx))) (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xx Xt))))) :rule bind)
% 0.25/0.57 (step t2.t5.t5 (cl (= (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xt Xx)))) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xx Xt)))))) :rule cong :premises (t2.t2 t2.t5.t4))
% 0.25/0.57 (step t2.t5.t6 (cl (= (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xt Xx))))) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xx Xt))))))) :rule cong :premises (t2.t5.t3 t2.t5.t5))
% 0.25/0.57 (step t2.t5 (cl (= (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xt Xx)))))) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xx Xt)))))))) :rule bind)
% 0.25/0.57 (step t2.t6 (cl (= (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xx Xt)))))) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (or (not (@ Xw Xr)) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xx Xt)))))))) :rule all_simplify)
% 0.25/0.57 (step t2.t7 (cl (= (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xt Xx)))))) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (or (not (@ Xw Xr)) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xx Xt)))))))) :rule trans :premises (t2.t5 t2.t6))
% 0.25/0.57 (step t2.t8 (cl (= (and (@ Xw (lambda ((Xx tptp.a)) false)) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xt Xx))))))) (and (@ Xw (lambda ((BOUND_VARIABLE_766 tptp.a)) false)) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (or (not (@ Xw Xr)) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xx Xt))))))))) :rule cong :premises (t2.t4 t2.t7))
% 0.25/0.57 (step t2.t9 (cl (= (lambda ((Xx tptp.a)) false) (lambda ((BOUND_VARIABLE_766 tptp.a)) false))) :rule all_simplify)
% 0.25/0.57 (step t2.t10 (cl (= (@ Xw (lambda ((Xx tptp.a)) false)) (@ Xw (lambda ((BOUND_VARIABLE_766 tptp.a)) false)))) :rule cong :premises (t2.t2 t2.t9))
% 0.25/0.57 (step t2.t11 (cl (= (=> (and (@ Xw (lambda ((Xx tptp.a)) false)) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xt Xx))))))) (@ Xw (lambda ((Xx tptp.a)) false))) (=> (and (@ Xw (lambda ((BOUND_VARIABLE_766 tptp.a)) false)) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (or (not (@ Xw Xr)) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xx Xt))))))) (@ Xw (lambda ((BOUND_VARIABLE_766 tptp.a)) false))))) :rule cong :premises (t2.t8 t2.t10))
% 0.25/0.57 (step t2 (cl (= (forall ((Xw (-> (-> tptp.a Bool) Bool))) (=> (and (@ Xw (lambda ((Xx tptp.a)) false)) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xt Xx))))))) (@ Xw (lambda ((Xx tptp.a)) false)))) (forall ((Xw (-> (-> tptp.a Bool) Bool))) (=> (and (@ Xw (lambda ((BOUND_VARIABLE_766 tptp.a)) false)) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (or (not (@ Xw Xr)) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xx Xt))))))) (@ Xw (lambda ((BOUND_VARIABLE_766 tptp.a)) false)))))) :rule bind)
% 0.25/0.57 (step t3 (cl (= (forall ((Xw (-> (-> tptp.a Bool) Bool))) (=> (and (@ Xw (lambda ((BOUND_VARIABLE_766 tptp.a)) false)) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (or (not (@ Xw Xr)) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xx Xt))))))) (@ Xw (lambda ((BOUND_VARIABLE_766 tptp.a)) false)))) (forall ((Xw (-> (-> tptp.a Bool) Bool))) true))) :rule all_simplify)
% 0.25/0.57 (step t4 (cl (= (forall ((Xw (-> (-> tptp.a Bool) Bool))) true) true)) :rule all_simplify)
% 0.25/0.57 (step t5 (cl (= (forall ((Xw (-> (-> tptp.a Bool) Bool))) (=> (and (@ Xw (lambda ((BOUND_VARIABLE_766 tptp.a)) false)) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (or (not (@ Xw Xr)) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xx Xt))))))) (@ Xw (lambda ((BOUND_VARIABLE_766 tptp.a)) false)))) true)) :rule trans :premises (t3 t4))
% 0.25/0.57 (step t6 (cl (= (forall ((Xw (-> (-> tptp.a Bool) Bool))) (=> (and (@ Xw (lambda ((Xx tptp.a)) false)) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xt Xx))))))) (@ Xw (lambda ((Xx tptp.a)) false)))) true)) :rule trans :premises (t2 t5))
% 0.25/0.57 (step t7 (cl (= (not (forall ((Xw (-> (-> tptp.a Bool) Bool))) (=> (and (@ Xw (lambda ((Xx tptp.a)) false)) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xt Xx))))))) (@ Xw (lambda ((Xx tptp.a)) false))))) (not true))) :rule cong :premises (t6))
% 0.25/0.57 (step t8 (cl (= (not true) false)) :rule all_simplify)
% 0.25/0.57 (step t9 (cl (= (not (forall ((Xw (-> (-> tptp.a Bool) Bool))) (=> (and (@ Xw (lambda ((Xx tptp.a)) false)) (forall ((Xr (-> tptp.a Bool)) (Xx tptp.a)) (=> (@ Xw Xr) (@ Xw (lambda ((Xt tptp.a)) (or (@ Xr Xt) (= Xt Xx))))))) (@ Xw (lambda ((Xx tptp.a)) false))))) false)) :rule trans :premises (t7 t8))
% 0.25/0.57 (step t10 (cl false) :rule resolution :premises (t1 t9 a0))
% 0.25/0.57 (step t11 (cl (not false)) :rule false)
% 0.25/0.57 (step t12 (cl) :rule resolution :premises (t10 t11))
% 0.25/0.57
% 0.25/0.57 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.zXP0rH19X5/cvc5---1.0.5_32591.smt2
% 0.25/0.57 % cvc5---1.0.5 exiting
% 0.25/0.57 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------