%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU843^5 : 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 : n007.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 08:31:47 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 28 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 83 ( 7 ~; 15 |; 4 &; 47 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 32 ( 10 ^; 19 !; 3 ?; 32 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_6,type,
sK0: a > $o ).
thf(func_def_7,type,
sK1: a > $o ).
thf(func_def_8,type,
sK2: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= X0 )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM23_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= X0 )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= X0 )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X0 )
=> ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X0 @ X3 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X0 )
=> ! [X2: a] :
( ( ( X1 @ X2 )
= $true )
=> ( ( X0 @ X2 )
= $true ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ? [X2: a] :
( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) )
& ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X0 ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ( $true
!= ( sK0 @ sK2 ) )
& ( $true
= ( sK1 @ sK2 ) )
& ( sK0
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6]) ).
thf(f8,plain,
( sK0
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( $true
= ( sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( $true
!= ( sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
@ X1 )
= ( sK0 @ X1 ) ),
inference(argument_congruence,[],[f8]) ).
thf(f15,plain,
! [X1: a] :
( ( $true
= ( sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
@ X1 ) ) ),
inference(iff_proxy_clausification,[],[f13]) ).
thf(f16,plain,
! [X1: a] :
( ( $true
= ( sK0 @ X1 ) )
| ( ( ( sK1 @ X1 )
| ( sK0 @ X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f18,plain,
! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f16]) ).
thf(f21,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(constrained_superposition,[],[f18,f9]) ).
thf(f23,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f21]) ).
thf(f25,plain,
$false,
inference(forward_subsumption_resolution,[],[f23,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU843^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:37:41 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.20/0.28 % (3452139)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (3452152)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3176138200:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (3452152) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3452139-3452152"...
% 0.20/0.28 % (3452152)...printing done.
% 0.20/0.28 % (3452152)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (3452152)------------------------------
% 0.20/0.28 % (3452152)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3452152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3452152)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3452152)Termination reason: Refutation
% 0.20/0.28 % (3452152)Time elapsed: 0.001 s
% 0.20/0.28 % (3452152)Peak memory usage: 12 MB
% 0.20/0.28 % (3452152)Instructions burned: 1 (million)
% 0.20/0.28 % (3452139)Success in time 0.036 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------