%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET043^5 : 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 : n006.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 08:23:11 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 7 unt; 0 typ; 1 def)
% Number of atoms : 102 ( 24 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 100 ( 28 ~; 12 |; 2 &; 52 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 9 !; 6 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cE: $i > $i > $o ).
thf(f1,conjecture,
~ ? [X0: $i] :
! [X1: $i] :
( ~ ( cE @ X1 @ X1 )
<=> ( cE @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cRUSSELL1) ).
thf(f2,negated_conjecture,
~ ~ ? [X0: $i] :
! [X1: $i] :
( ~ ( cE @ X1 @ X1 )
<=> ( cE @ X1 @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ~ ? [X0: $i] :
! [X1: $i] :
( ~ ( cE @ X1 @ X1 )
<=> ( cE @ X1 @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ~ ? [X0: $i] :
! [X1: $i] :
( ( ( cE @ X1 @ X1 )
!= $true )
<=> ( ( cE @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: $i] :
! [X1: $i] :
( ( ( cE @ X1 @ X0 )
= $true )
<=> ( ( cE @ X1 @ X1 )
!= $true ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X0: $i] :
! [X1: $i] :
( ( ( ( cE @ X1 @ X0 )
= $true )
| ( ( cE @ X1 @ X1 )
= $true ) )
& ( ( ( cE @ X1 @ X1 )
!= $true )
| ( ( cE @ X1 @ X0 )
!= $true ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
! [X1: $i] :
( ( ( $true
= ( cE @ X1 @ sK0 ) )
| ( ( cE @ X1 @ X1 )
= $true ) )
& ( ( ( cE @ X1 @ X1 )
!= $true )
| ( $true
!= ( cE @ X1 @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6]) ).
thf(f8,plain,
! [X1: $i] :
( ( $true
!= ( cE @ X1 @ sK0 ) )
| ( ( cE @ X1 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X1: $i] :
( ( $true
= ( cE @ X1 @ sK0 ) )
| ( ( cE @ X1 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
( ( $true != $true )
| ( $true
= ( cE @ sK0 @ sK0 ) ) ),
inference(equality_factoring,[],[f9]) ).
thf(f13,plain,
( $true
= ( cE @ sK0 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f12]) ).
thf(f15,definition,
( spl1_1
<=> ( $true
= ( cE @ sK0 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f17,plain,
( ( $true
= ( cE @ sK0 @ sK0 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f15]) ).
thf(f18,plain,
spl1_1,
inference(avatar_split_clause,[],[f13,f15]) ).
thf(f19,plain,
( ( $true != $true )
| ( $true != $true )
| ~ spl1_1 ),
inference(superposition,[],[f8,f17]) ).
thf(f20,plain,
( ( $true != $true )
| ~ spl1_1 ),
inference(duplicate_literal_removal,[],[f19]) ).
thf(f21,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f20]) ).
thf(f22,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f21]) ).
cnf(s1,plain,
spl1_1,
inference(sat_conversion,[],[f18]) ).
cnf(s2,plain,
~ spl1_1,
inference(sat_conversion,[],[f22]) ).
cnf(s3,plain,
$false,
inference(rat,[],[s1,s2]) ).
thf(f23,plain,
$false,
inference(avatar_sat_refutation,[],[s3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET043^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n006.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 13:35:40 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 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
% 0.19/0.26 % (715379)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.26 % (715387)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2261974817:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.26 % (715387) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-715379-715387"...
% 0.19/0.26 % (715387)...printing done.
% 0.19/0.26 % (715387)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.26 % (715387)------------------------------
% 0.19/0.26 % (715387)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (715387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (715387)CaDiCaL version: 2.1.3
% 0.19/0.26 % (715387)Termination reason: Refutation
% 0.19/0.26 % (715387)Time elapsed: 0.001 s
% 0.19/0.26 % (715387)Peak memory usage: 13 MB
% 0.19/0.26 % (715387)Instructions burned: 1 (million)
% 0.19/0.26 % (715379)Success in time 0.026 s
% 0.19/0.26 % Vampire exiting
%------------------------------------------------------------------------------