%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU921^5 : 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 : n011.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 08:31:57 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 24 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 69 ( 11 ~; 3 |; 2 &; 45 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-4 aty)
% Number of variables : 23 ( 8 ^; 15 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
f: $i > $i ).
thf(func_def_1,type,
g: $i > $i ).
thf(func_def_2,type,
h: $i > $i ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ! [X0: $i,X1: $i] :
( ( ( g @ X0 )
= X1 )
=> ( ( h @ X1 )
= ( f @ X0 ) ) )
=> ( ( ^ [X0: $i] : ( h @ ( g @ X0 ) ) )
= f ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM588LEM2_pme) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i,X1: $i] :
( ( ( g @ X0 )
= X1 )
=> ( ( h @ X1 )
= ( f @ X0 ) ) )
=> ( ( ^ [X0: $i] : ( h @ ( g @ X0 ) ) )
= f ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i,X1: $i] :
( ( ( g @ X0 )
= X1 )
=> ( ( h @ X1 )
= ( f @ X0 ) ) )
=> ( ( ^ [X2: $i] : ( h @ ( g @ X2 ) ) )
= f ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i,X1: $i] :
( ( ( g @ X0 )
= X1 )
=> ( ( h @ X1 )
= ( f @ X0 ) ) )
=> ( f
= ( ^ [Y0: $i] : ( h @ ( g @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( f
!= ( ^ [Y0: $i] : ( h @ ( g @ Y0 ) ) ) )
& ! [X1: $i,X0: $i] :
( ( ( g @ X0 )
!= X1 )
| ( ( h @ X1 )
= ( f @ X0 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( f
!= ( ^ [Y0: $i] : ( h @ ( g @ Y0 ) ) ) )
& ! [X0: $i,X1: $i] :
( ( ( g @ X1 )
!= X0 )
| ( ( f @ X1 )
= ( h @ X0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ( ( g @ X1 )
!= X0 )
| ( ( f @ X1 )
= ( h @ X0 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( f
!= ( ^ [Y0: $i] : ( h @ ( g @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
! [X1: $i] :
( ( h @ ( g @ X1 ) )
= ( f @ X1 ) ),
inference(equality_resolution,[],[f7]) ).
thf(f10,plain,
( ( ^ [Y0: $i] : ( h @ ( g @ Y0 ) )
@ sK0 )
!= ( f @ sK0 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f11,plain,
( ( h @ ( g @ sK0 ) )
!= ( f @ sK0 ) ),
inference(beta-eta_normalization,[],[f10]) ).
thf(f12,plain,
$false,
inference(forward_subsumption_resolution,[],[f11,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU921^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n011.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:46:31 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.28 % (181094)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (181103)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=90169530:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.28 % (181103) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-181094-181103"...
% 0.22/0.28 % (181103)...printing done.
% 0.22/0.28 % (181103)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (181103)------------------------------
% 0.22/0.28 % (181103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (181103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (181103)CaDiCaL version: 2.1.3
% 0.22/0.28 % (181103)Termination reason: Refutation
% 0.22/0.28 % (181103)Time elapsed: 0.001 s
% 0.22/0.28 % (181103)Peak memory usage: 12 MB
% 0.22/0.28 % (181103)Instructions burned: 1 (million)
% 0.22/0.28 % (181094)Success in time 0.035 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------