TSTP Solution File: SEV282^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV282^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.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 : Thu Aug 31 19:22:06 EDT 2023
% Result : Theorem 0.21s 0.52s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV282^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 03:12:49 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 % File : SEV282^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% 0.21/0.52 % Domain : Set Theory
% 0.21/0.52 % Problem : TPS problem TTTP6100
% 0.21/0.52 % Version : Especial.
% 0.21/0.52 % English :
% 0.21/0.52
% 0.21/0.52 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.52 % Source : [Bro09]
% 0.21/0.52 % Names : tps_000 [Bro09]
% 0.21/0.52 % : TTTP6100 [TPS]
% 0.21/0.52
% 0.21/0.52 % Status : Theorem
% 0.21/0.52 % Rating : 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v6.2.0
% 0.21/0.52 % Syntax : Number of formulae : 7 ( 3 unt; 3 typ; 3 def)
% 0.21/0.52 % Number of atoms : 11 ( 4 equ; 0 cnn)
% 0.21/0.52 % Maximal formula atoms : 2 ( 2 avg)
% 0.21/0.52 % Number of connectives : 17 ( 2 ~; 0 |; 3 &; 10 @)
% 0.21/0.52 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.21/0.52 % Maximal formula depth : 2 ( 1 avg)
% 0.21/0.52 % Number of types : 2 ( 0 usr)
% 0.21/0.52 % Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% 0.21/0.52 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.21/0.52 % Number of variables : 9 ( 5 ^; 2 !; 2 ?; 9 :)
% 0.21/0.52 % SPC : TH0_THM_EQU_NAR
% 0.21/0.52
% 0.21/0.52 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.52 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.52 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.52 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.52 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.21/0.52 % : v6.2.0 - Reordered definitions.
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 thf(cNAT_type,type,
% 0.21/0.52 cNAT: ( ( $i > $o ) > $o ) > $o ).
% 0.21/0.52
% 0.21/0.52 thf(cSUCC_type,type,
% 0.21/0.52 cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 0.21/0.52
% 0.21/0.52 thf(cZERO_type,type,
% 0.21/0.52 cZERO: ( $i > $o ) > $o ).
% 0.21/0.52
% 0.21/0.52 thf(cZERO_def,definition,
% 0.21/0.52 ( cZERO
% 0.21/0.52 = ( ^ [Xp: $i > $o] :
% 0.21/0.52 ~ ? [Xx: $i] : ( Xp @ Xx ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(cSUCC_def,definition,
% 0.21/0.52 ( cSUCC
% 0.21/0.52 = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
% 0.21/0.52 ? [Xx: $i] :
% 0.21/0.52 ( ( Xp @ Xx )
% 0.21/0.52 & ( Xn
% 0.21/0.52 @ ^ [Xt: $i] :
% 0.21/0.52 ( ( Xt != Xx )
% 0.21/0.52 & ( Xp @ Xt ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(cNAT_def,definition,
% 0.21/0.52 ( cNAT
% 0.21/0.52 = ( ^ [Xn: ( $i > $o ) > $o] :
% 0.21/0.52 ! [Xp: ( ( $i > $o ) > $o ) > $o] :
% 0.21/0.52 ( ( ( Xp @ cZERO )
% 0.21/0.52 & ! [Xx: ( $i > $o ) > $o] :
% 0.21/0.52 ( ( Xp @ Xx )
% 0.21/0.52 => ( Xp @ ( cSUCC @ Xx ) ) ) )
% 0.21/0.52 => ( Xp @ Xn ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(cTTTP6100,conjecture,
% 0.21/0.52 cNAT @ cZERO ).
% 0.21/0.52
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.YbZpVIZGY1/cvc5---1.0.5_4389.p...
% 0.21/0.52 (declare-sort $$unsorted 0)
% 0.21/0.52 (declare-fun tptp.cNAT ((-> (-> $$unsorted Bool) Bool)) Bool)
% 0.21/0.52 (declare-fun tptp.cSUCC ((-> (-> $$unsorted Bool) Bool) (-> $$unsorted Bool)) Bool)
% 0.21/0.52 (declare-fun tptp.cZERO ((-> $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (not (exists ((Xx $$unsorted)) (@ Xp Xx))))))
% 0.21/0.52 (assert (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt)))))))))
% 0.21/0.52 (assert (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (=> (and (@ Xp tptp.cZERO) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (=> (@ Xp Xx) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))))))
% 0.21/0.52 (assert (not (@ tptp.cNAT tptp.cZERO)))
% 0.21/0.52 (set-info :filename cvc5---1.0.5_4389)
% 0.21/0.52 (check-sat-assuming ( true ))
% 0.21/0.52 ------- get file name : TPTP file name is SEV282^5
% 0.21/0.52 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_4389.smt2...
% 0.21/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.52 % SZS status Theorem for SEV282^5
% 0.21/0.52 % SZS output start Proof for SEV282^5
% 0.21/0.52 (
% 0.21/0.52 (let ((_let_1 (not (@ tptp.cNAT tptp.cZERO)))) (let ((_let_2 (= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (=> (and (@ Xp tptp.cZERO) (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (=> (@ Xp Xx) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))))))) (let ((_let_3 (= tptp.cSUCC (lambda ((Xn (-> (-> $$unsorted Bool) Bool)) (Xp (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xp Xx) (@ Xn (lambda ((Xt $$unsorted)) (and (not (= Xt Xx)) (@ Xp Xt)))))))))) (let ((_let_4 (= tptp.cZERO (lambda ((Xp (-> $$unsorted Bool))) (not (exists ((Xx $$unsorted)) (@ Xp Xx))))))) (let ((_let_5 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_6 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_6 _let_5) :args ((= tptp.cNAT (lambda ((Xn (-> (-> $$unsorted Bool) Bool))) (forall ((Xp (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ Xp tptp.cZERO)) (not (forall ((Xx (-> (-> $$unsorted Bool) Bool))) (or (not (@ Xp Xx)) (@ Xp (@ tptp.cSUCC Xx))))) (@ Xp Xn))))) SB_DEFAULT SBA_FIXPOINT))) _let_6 _let_5) :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (_let_4 _let_3 _let_2 _let_1 true)))))))))
% 0.21/0.52 )
% 0.21/0.52 % SZS output end Proof for SEV282^5
% 0.21/0.52 % cvc5---1.0.5 exiting
% 0.21/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------