TSTP Solution File: SEV258^5 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV258^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n017.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 17:58:06 EDT 2024
% Result : Theorem 0.44s 0.62s
% Output : Proof 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.17 % Problem : SEV258^5 : TPTP v8.2.0. Released v4.0.0.
% 0.18/0.18 % Command : do_cvc5 %s %d
% 0.19/0.41 % Computer : n017.cluster.edu
% 0.19/0.41 % Model : x86_64 x86_64
% 0.19/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.41 % Memory : 8042.1875MB
% 0.19/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.41 % CPULimit : 300
% 0.19/0.41 % WCLimit : 300
% 0.19/0.41 % DateTime : Mon May 27 12:35:54 EDT 2024
% 0.19/0.41 % CPUTime :
% 0.44/0.60 %----Proving TH0
% 0.44/0.62 --- Run --ho-elim --full-saturate-quant at 10...
% 0.44/0.62 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.5FT1bbVUxD/cvc5---1.0.5_10241.smt2
% 0.44/0.62 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.5FT1bbVUxD/cvc5---1.0.5_10241.smt2
% 0.44/0.62 (assume a0 (not (and (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) false)) true)) (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) (not false))) true)) (forall ((K (-> (-> tptp.a Bool) Bool)) (R (-> tptp.a Bool))) (=> (and (forall ((Xx (-> tptp.a Bool))) (=> (@ K Xx) true)) (= R (lambda ((Xx tptp.a)) (exists ((S (-> tptp.a Bool))) (and (@ K S) (@ S Xx)))))) true)) (forall ((Y (-> tptp.a Bool)) (Z (-> tptp.a Bool)) (S (-> tptp.a Bool))) (=> (and true true (= S (lambda ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))) true)))))
% 0.44/0.62 (assume a1 true)
% 0.44/0.62 (step t1 (cl (not (= (not (and (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) false)) true)) (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) (not false))) true)) (forall ((K (-> (-> tptp.a Bool) Bool)) (R (-> tptp.a Bool))) (=> (and (forall ((Xx (-> tptp.a Bool))) (=> (@ K Xx) true)) (= R (lambda ((Xx tptp.a)) (exists ((S (-> tptp.a Bool))) (and (@ K S) (@ S Xx)))))) true)) (forall ((Y (-> tptp.a Bool)) (Z (-> tptp.a Bool)) (S (-> tptp.a Bool))) (=> (and true true (= S (lambda ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))) true)))) false)) (not (not (and (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) false)) true)) (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) (not false))) true)) (forall ((K (-> (-> tptp.a Bool) Bool)) (R (-> tptp.a Bool))) (=> (and (forall ((Xx (-> tptp.a Bool))) (=> (@ K Xx) true)) (= R (lambda ((Xx tptp.a)) (exists ((S (-> tptp.a Bool))) (and (@ K S) (@ S Xx)))))) true)) (forall ((Y (-> tptp.a Bool)) (Z (-> tptp.a Bool)) (S (-> tptp.a Bool))) (=> (and true true (= S (lambda ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))) true))))) false) :rule equiv_pos2)
% 0.44/0.62 (anchor :step t2 :args ((R (-> tptp.a Bool)) (:= R R)))
% 0.44/0.62 (step t2.t1 (cl (= R R)) :rule refl)
% 0.44/0.62 (step t2.t2 (cl (= (=> (= R (lambda ((Xx tptp.a)) false)) true) true)) :rule all_simplify)
% 0.44/0.62 (step t2 (cl (= (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) false)) true)) (forall ((R (-> tptp.a Bool))) true))) :rule bind)
% 0.44/0.62 (step t3 (cl (= (forall ((R (-> tptp.a Bool))) true) true)) :rule all_simplify)
% 0.44/0.62 (step t4 (cl (= (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) false)) true)) true)) :rule trans :premises (t2 t3))
% 0.44/0.62 (anchor :step t5 :args ((R (-> tptp.a Bool)) (:= R R)))
% 0.44/0.62 (step t5.t1 (cl (= R R)) :rule refl)
% 0.44/0.62 (step t5.t2 (cl (= (=> (= R (lambda ((Xx tptp.a)) (not false))) true) true)) :rule all_simplify)
% 0.44/0.62 (step t5 (cl (= (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) (not false))) true)) (forall ((R (-> tptp.a Bool))) true))) :rule bind)
% 0.44/0.62 (step t6 (cl (= (forall ((R (-> tptp.a Bool))) true) true)) :rule all_simplify)
% 0.44/0.62 (step t7 (cl (= (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) (not false))) true)) true)) :rule trans :premises (t5 t6))
% 0.44/0.62 (anchor :step t8 :args ((K (-> (-> tptp.a Bool) Bool)) (:= K K) (R (-> tptp.a Bool)) (:= R R)))
% 0.44/0.62 (step t8.t1 (cl (= K K)) :rule refl)
% 0.44/0.62 (step t8.t2 (cl (= R R)) :rule refl)
% 0.44/0.62 (step t8.t3 (cl (= (=> (and (forall ((Xx (-> tptp.a Bool))) (=> (@ K Xx) true)) (= R (lambda ((Xx tptp.a)) (exists ((S (-> tptp.a Bool))) (and (@ K S) (@ S Xx)))))) true) true)) :rule all_simplify)
% 0.44/0.62 (step t8 (cl (= (forall ((K (-> (-> tptp.a Bool) Bool)) (R (-> tptp.a Bool))) (=> (and (forall ((Xx (-> tptp.a Bool))) (=> (@ K Xx) true)) (= R (lambda ((Xx tptp.a)) (exists ((S (-> tptp.a Bool))) (and (@ K S) (@ S Xx)))))) true)) (forall ((K (-> (-> tptp.a Bool) Bool)) (R (-> tptp.a Bool))) true))) :rule bind)
% 0.44/0.62 (step t9 (cl (= (forall ((K (-> (-> tptp.a Bool) Bool)) (R (-> tptp.a Bool))) true) true)) :rule all_simplify)
% 0.44/0.62 (step t10 (cl (= (forall ((K (-> (-> tptp.a Bool) Bool)) (R (-> tptp.a Bool))) (=> (and (forall ((Xx (-> tptp.a Bool))) (=> (@ K Xx) true)) (= R (lambda ((Xx tptp.a)) (exists ((S (-> tptp.a Bool))) (and (@ K S) (@ S Xx)))))) true)) true)) :rule trans :premises (t8 t9))
% 0.44/0.63 (anchor :step t11 :args ((Y (-> tptp.a Bool)) (:= Y Y) (Z (-> tptp.a Bool)) (:= Z Z) (S (-> tptp.a Bool)) (:= S S)))
% 0.44/0.63 (step t11.t1 (cl (= Y Y)) :rule refl)
% 0.44/0.63 (step t11.t2 (cl (= Z Z)) :rule refl)
% 0.44/0.63 (step t11.t3 (cl (= S S)) :rule refl)
% 0.44/0.63 (step t11.t4 (cl (= (=> (and true true (= S (lambda ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))) true) true)) :rule all_simplify)
% 0.44/0.63 (step t11 (cl (= (forall ((Y (-> tptp.a Bool)) (Z (-> tptp.a Bool)) (S (-> tptp.a Bool))) (=> (and true true (= S (lambda ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))) true)) (forall ((Y (-> tptp.a Bool)) (Z (-> tptp.a Bool)) (S (-> tptp.a Bool))) true))) :rule bind)
% 0.44/0.63 (step t12 (cl (= (forall ((Y (-> tptp.a Bool)) (Z (-> tptp.a Bool)) (S (-> tptp.a Bool))) true) true)) :rule all_simplify)
% 0.44/0.63 (step t13 (cl (= (forall ((Y (-> tptp.a Bool)) (Z (-> tptp.a Bool)) (S (-> tptp.a Bool))) (=> (and true true (= S (lambda ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))) true)) true)) :rule trans :premises (t11 t12))
% 0.44/0.63 (step t14 (cl (= (and (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) false)) true)) (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) (not false))) true)) (forall ((K (-> (-> tptp.a Bool) Bool)) (R (-> tptp.a Bool))) (=> (and (forall ((Xx (-> tptp.a Bool))) (=> (@ K Xx) true)) (= R (lambda ((Xx tptp.a)) (exists ((S (-> tptp.a Bool))) (and (@ K S) (@ S Xx)))))) true)) (forall ((Y (-> tptp.a Bool)) (Z (-> tptp.a Bool)) (S (-> tptp.a Bool))) (=> (and true true (= S (lambda ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))) true))) (and true true true true))) :rule cong :premises (t4 t7 t10 t13))
% 0.44/0.63 (step t15 (cl (= (and true true true true) true)) :rule all_simplify)
% 0.44/0.63 (step t16 (cl (= (and (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) false)) true)) (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) (not false))) true)) (forall ((K (-> (-> tptp.a Bool) Bool)) (R (-> tptp.a Bool))) (=> (and (forall ((Xx (-> tptp.a Bool))) (=> (@ K Xx) true)) (= R (lambda ((Xx tptp.a)) (exists ((S (-> tptp.a Bool))) (and (@ K S) (@ S Xx)))))) true)) (forall ((Y (-> tptp.a Bool)) (Z (-> tptp.a Bool)) (S (-> tptp.a Bool))) (=> (and true true (= S (lambda ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))) true))) true)) :rule trans :premises (t14 t15))
% 0.44/0.63 (step t17 (cl (= (not (and (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) false)) true)) (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) (not false))) true)) (forall ((K (-> (-> tptp.a Bool) Bool)) (R (-> tptp.a Bool))) (=> (and (forall ((Xx (-> tptp.a Bool))) (=> (@ K Xx) true)) (= R (lambda ((Xx tptp.a)) (exists ((S (-> tptp.a Bool))) (and (@ K S) (@ S Xx)))))) true)) (forall ((Y (-> tptp.a Bool)) (Z (-> tptp.a Bool)) (S (-> tptp.a Bool))) (=> (and true true (= S (lambda ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))) true)))) (not true))) :rule cong :premises (t16))
% 0.44/0.63 (step t18 (cl (= (not true) false)) :rule all_simplify)
% 0.44/0.63 (step t19 (cl (= (not (and (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) false)) true)) (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) (not false))) true)) (forall ((K (-> (-> tptp.a Bool) Bool)) (R (-> tptp.a Bool))) (=> (and (forall ((Xx (-> tptp.a Bool))) (=> (@ K Xx) true)) (= R (lambda ((Xx tptp.a)) (exists ((S (-> tptp.a Bool))) (and (@ K S) (@ S Xx)))))) true)) (forall ((Y (-> tptp.a Bool)) (Z (-> tptp.a Bool)) (S (-> tptp.a Bool))) (=> (and true true (= S (lambda ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))) true)))) false)) :rule trans :premises (t17 t18))
% 0.44/0.63 (step t20 (cl false) :rule resolution :premises (t1 t19 a0))
% 0.44/0.63 (step t21 (cl (not false)) :rule false)
% 0.44/0.63 (step t22 (cl) :rule resolution :premises (t20 t21))
% 0.44/0.63
% 0.44/0.63 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.5FT1bbVUxD/cvc5---1.0.5_10241.smt2
% 0.44/0.63 % cvc5---1.0.5 exiting
% 0.44/0.63 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------