%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU858^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:31:49 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 30 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 85 ( 11 ~; 11 |; 11 &; 42 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 2 con; 0-4 aty)
% Number of variables : 49 ( 26 ^; 21 !; 2 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vOR: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
sK0: ( a > $o ) > $o ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(f1,conjecture,
! [X0: ( a > $o ) > $o] :
( ( ( X0
@ ^ [X1: a] : $false )
& ! [X2: a > $o,X1: a] :
( ( X0 @ X2 )
=> ( X0
@ ^ [X3: a] :
( ( X3 = X1 )
| ( X2 @ X3 ) ) ) ) )
=> ( X0
@ ^ [X1: a] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM163_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > $o ) > $o] :
( ( ( X0
@ ^ [X1: a] : $false )
& ! [X2: a > $o,X1: a] :
( ( X0 @ X2 )
=> ( X0
@ ^ [X3: a] :
( ( X3 = X1 )
| ( X2 @ X3 ) ) ) ) )
=> ( X0
@ ^ [X1: a] : $false ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: ( a > $o ) > $o] :
( ( ( X0
@ ^ [X1: a] : $false )
& ! [X2: a > $o,X3: a] :
( ( X0 @ X2 )
=> ( X0
@ ^ [X4: a] :
( ( X3 = X4 )
| ( X2 @ X4 ) ) ) ) )
=> ( X0
@ ^ [X5: a] : $false ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: ( a > $o ) > $o] :
( ( ( ( X0
@ ^ [Y0: a] : $false )
= $true )
& ! [X2: a > $o,X3: a] :
( ( ( X0 @ X2 )
= $true )
=> ( ( X0
@ ^ [Y0: a] :
( ( X2 @ Y0 )
| ( X3 = Y0 ) ) )
= $true ) ) )
=> ( ( X0
@ ^ [Y0: a] : $false )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: ( a > $o ) > $o] :
( ( ( ( X0
@ ^ [Y0: a] : $false )
= $true )
& ! [X2: a,X1: a > $o] :
( ( ( X0 @ X1 )
= $true )
=> ( $true
= ( X0
@ ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 = Y0 ) ) ) ) ) )
=> ( ( X0
@ ^ [Y0: a] : $false )
= $true ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X0: ( a > $o ) > $o] :
( ( ( X0
@ ^ [Y0: a] : $false )
!= $true )
& ( ( X0
@ ^ [Y0: a] : $false )
= $true )
& ! [X1: a > $o,X2: a] :
( ( $true
= ( X0
@ ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 = Y0 ) ) ) )
| ( ( X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: ( a > $o ) > $o] :
( ! [X1: a > $o,X2: a] :
( ( $true
= ( X0
@ ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 = Y0 ) ) ) )
| ( ( X0 @ X1 )
!= $true ) )
& ( ( X0
@ ^ [Y0: a] : $false )
= $true )
& ( ( X0
@ ^ [Y0: a] : $false )
!= $true ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ! [X1: a > $o,X2: a] :
( ( $true
= ( sK0
@ ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 = Y0 ) ) ) )
| ( ( sK0 @ X1 )
!= $true ) )
& ( ( sK0
@ ^ [Y0: a] : $false )
= $true )
& ( ( sK0
@ ^ [Y0: a] : $false )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f7]) ).
thf(f9,plain,
( ( sK0
@ ^ [Y0: a] : $false )
!= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( sK0
@ ^ [Y0: a] : $false )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
$false,
inference(forward_subsumption_resolution,[],[f9,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU858^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n020.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:41:05 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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
% 0.09/0.26 % (1142884)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.26 % (1142896)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2566738036:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.09/0.26 % (1142896) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1142884-1142896"...
% 0.09/0.26 % (1142896)...printing done.
% 0.09/0.26 % (1142896)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.26 % (1142896)------------------------------
% 0.21/0.26 % (1142896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.26 % (1142896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.26 % (1142896)CaDiCaL version: 2.1.3
% 0.21/0.26 % (1142896)Termination reason: Refutation
% 0.21/0.26 % (1142896)Time elapsed: 0.001 s
% 0.21/0.26 % (1142896)Peak memory usage: 12 MB
% 0.21/0.26 % (1142896)Instructions burned: 1 (million)
% 0.21/0.26 % (1142884)Success in time 0.024 s
% 0.21/0.26 % Vampire exiting
%------------------------------------------------------------------------------