%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP001^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:34 AM UTC 2026
% Result : Theorem 0.26s 0.36s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 14 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 15 ( 8 ~; 3 |; 1 &; 0 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 3 con; 0-4 aty)
% Number of variables : 12 ( 12 ^; 0 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
tyop_2Emin_2Ebool: $tType ).
thf(type_def_6,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
c_2Ebool_2E_21:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_2,type,
c_2Emin_2E_3D:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_3,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_4,type,
c_2Ebool_2E_3F:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
c_2Ebool_2ET: $o ).
thf(func_def_6,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_7,type,
c_2Ebool_2E_7E: $o > $o ).
thf(func_def_9,type,
vNOT: $o > $o ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f8,axiom,
( c_2Ebool_2ET
<=> ( ( ^ [X0: $o] : X0 )
= ( ^ [X1: $o] : X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ET__DEF) ).
thf(f9,conjecture,
c_2Ebool_2ET,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(f10,negated_conjecture,
~ c_2Ebool_2ET,
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f21,plain,
( c_2Ebool_2ET
<=> ( ( ^ [X0: $o] : X0 )
= ( ^ [X1: $o] : X1 ) ) ),
inference(rectify,[],[f8]) ).
thf(f22,plain,
( ( ( ^ [Y0: $o] : Y0 )
= ( ^ [Y0: $o] : Y0 ) )
<=> ( c_2Ebool_2ET = $true ) ),
inference(fool_elimination,[],[f21]) ).
thf(f25,plain,
~ c_2Ebool_2ET,
inference(rectify,[],[f10]) ).
thf(f26,plain,
c_2Ebool_2ET != $true,
inference(fool_elimination,[],[f25]) ).
thf(f29,plain,
c_2Ebool_2ET != $true,
inference(flattening,[],[f26]) ).
thf(f44,plain,
( ( ( ( ^ [Y0: $o] : Y0 )
= ( ^ [Y0: $o] : Y0 ) )
| ( c_2Ebool_2ET != $true ) )
& ( ( c_2Ebool_2ET = $true )
| ( ( ^ [Y0: $o] : Y0 )
!= ( ^ [Y0: $o] : Y0 ) ) ) ),
inference(nnf_transformation,[],[f22]) ).
thf(f62,plain,
c_2Ebool_2ET != $true,
inference(cnf_transformation,[],[f29]) ).
thf(f63,plain,
( ( ( ^ [Y0: $o] : Y0 )
!= ( ^ [Y0: $o] : Y0 ) )
| ( c_2Ebool_2ET = $true ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f76,plain,
c_2Ebool_2ET = $true,
inference(trivial_inequality_removal,[],[f63]) ).
thf(f77,plain,
$false,
inference(forward_subsumption_resolution,[],[f76,f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP001^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n008.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 19:18:09 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.30 Running higher-order theorem proving
% 0.26/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.36 % (3604017)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.36 % (3604024)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1216059043:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.26/0.36 % (3604024) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3604017-3604024"...
% 0.26/0.36 % (3604024)...printing done.
% 0.26/0.36 % (3604024)Refutation found. Thanks to Tanya!
% 0.26/0.36 % SZS status Theorem for theBenchmark
% 0.26/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.36 % (3604024)------------------------------
% 0.26/0.36 % (3604024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.36 % (3604024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.36 % (3604024)CaDiCaL version: 2.1.3
% 0.26/0.36 % (3604024)Termination reason: Refutation
% 0.26/0.36 % (3604024)Time elapsed: 0.002 s
% 0.26/0.36 % (3604024)Peak memory usage: 12 MB
% 0.26/0.36 % (3604024)Instructions burned: 2 (million)
% 0.26/0.36 % (3604017)Success in time 0.027 s
% 0.26/0.36 % Vampire exiting
%------------------------------------------------------------------------------