%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET617^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:23:23 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 131 ( 31 equ; 0 cnn)
% Maximal formula atoms : 2 ( 6 avg)
% Number of connectives : 192 ( 66 ~; 34 |; 46 &; 46 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 2 con; 0-4 aty)
% Number of variables : 34 ( 29 ^; 4 !; 1 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vOR: $o > $o > $o ).
thf(func_def_2,type,
vAND: $o > $o > $o ).
thf(func_def_3,type,
vNOT: $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_8,type,
sK0: a > $o ).
thf(f1,conjecture,
! [X0: a > $o] :
( ( X0
= ( ^ [X1: a] :
( ( ~ ( X0 @ X1 )
& $false )
| ( ~ $false
& ( X0 @ X1 ) ) ) ) )
& ( ( ^ [X1: a] :
( ( ( X0 @ X1 )
& ~ $false )
| ( $false
& ~ ( X0 @ X1 ) ) ) )
= X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_92_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o] :
( ( X0
= ( ^ [X1: a] :
( ( ~ ( X0 @ X1 )
& $false )
| ( ~ $false
& ( X0 @ X1 ) ) ) ) )
& ( ( ^ [X1: a] :
( ( ( X0 @ X1 )
& ~ $false )
| ( $false
& ~ ( X0 @ X1 ) ) ) )
= X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o] :
( ( X0
= ( ^ [X1: a] :
( ( ~ ( X0 @ X1 )
& $false )
| ( ~ $false
& ( X0 @ X1 ) ) ) ) )
& ( ( ^ [X2: a] :
( ( ( X0 @ X2 )
& ~ $false )
| ( $false
& ~ ( X0 @ X2 ) ) ) )
= X0 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o] :
( ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ $false )
| ( $false
& ~ ( X0 @ Y0 ) ) ) )
= X0 )
& ( ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& $false )
| ( ~ $false
& ( X0 @ Y0 ) ) ) )
= X0 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o] :
( ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ $false )
| ( $false
& ~ ( X0 @ Y0 ) ) ) )
!= X0 )
| ( ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& $false )
| ( ~ $false
& ( X0 @ Y0 ) ) ) )
!= X0 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| ( $false
& ~ ( sK0 @ Y0 ) ) ) ) )
| ( sK0
!= ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& $false )
| ( ~ $false
& ( sK0 @ Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f5]) ).
thf(f7,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| ( $false
& ~ ( sK0 @ Y0 ) ) ) ) )
| ( sK0
!= ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& $false )
| ( ~ $false
& ( sK0 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& $false )
| ( ~ $false
& ( sK0 @ Y0 ) ) ) ) )
| ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| $false ) ) ) ),
inference(boolean_simplification,[],[f7]) ).
thf(f10,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& $false )
| ( $true
& ( sK0 @ Y0 ) ) ) ) )
| ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| $false ) ) ) ),
inference(boolean_simplification,[],[f9]) ).
thf(f11,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( ~ ( sK0 @ Y0 )
& $false )
| ( sK0 @ Y0 ) ) ) )
| ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| $false ) ) ) ),
inference(boolean_simplification,[],[f10]) ).
thf(f12,plain,
( ( sK0
!= ( ^ [Y0: a] :
( $false
| ( sK0 @ Y0 ) ) ) )
| ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| $false ) ) ) ),
inference(boolean_simplification,[],[f11]) ).
thf(f13,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| $false ) ) )
| ( ( ^ [Y0: a] : ( sK0 @ Y0 ) )
!= sK0 ) ),
inference(boolean_simplification,[],[f12]) ).
thf(f14,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| $false ) ) )
| ( sK0 != sK0 ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
( sK0
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ $false )
| $false ) ) ),
inference(trivial_inequality_removal,[],[f14]) ).
thf(f16,plain,
( sK0
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ $false ) ) ),
inference(boolean_simplification,[],[f15]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& $true ) )
!= sK0 ),
inference(boolean_simplification,[],[f16]) ).
thf(f18,plain,
( ( ^ [Y0: a] : ( sK0 @ Y0 ) )
!= sK0 ),
inference(boolean_simplification,[],[f17]) ).
thf(f19,plain,
sK0 != sK0,
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
$false,
inference(trivial_inequality_removal,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET617^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:34:52 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.29 % (343115)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (343124)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2277897134:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (343124) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-343115-343124"...
% 0.21/0.29 % (343124)...printing done.
% 0.21/0.29 % (343124)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (343124)------------------------------
% 0.21/0.29 % (343124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (343124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (343124)CaDiCaL version: 2.1.3
% 0.21/0.29 % (343124)Termination reason: Refutation
% 0.21/0.29 % (343124)Time elapsed: 0.001 s
% 0.21/0.29 % (343124)Peak memory usage: 11 MB
% 0.21/0.29 % (343124)Instructions burned: 2 (million)
% 0.21/0.29 % (343115)Success in time 0.038 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------