%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO131^5 : 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 : n003.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 08:46:40 AM UTC 2026
% Result : Theorem 0.25s 0.34s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 60 ( 9 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 94 ( 11 ~; 3 |; 1 &; 74 @)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn 2 !; 4 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
f: $i > $i ).
thf(func_def_1,type,
cR: $i > $i > $o ).
thf(func_def_3,type,
g: $i > $i ).
thf(f1,conjecture,
( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
=> ? [X0: $i] : ( cR @ X0 @ ( f @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXAMPLE1) ).
thf(f2,negated_conjecture,
~ ( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
=> ? [X0: $i] : ( cR @ X0 @ ( f @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
=> ? [X0: $i] : ( cR @ X0 @ ( f @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
= $true )
=> ? [X0: $i] :
( ( cR @ X0 @ ( f @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X0: $i] :
( ( cR @ X0 @ ( f @ X0 ) )
!= $true )
& ( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
= $true ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f7,plain,
! [X0: $i] :
( ( cR @ X0 @ ( f @ X0 ) )
!= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f10,definition,
( spl0_1
<=> ( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f12,plain,
( ( ( cR @ ( g @ ( f @ a ) ) @ ( f @ ( g @ ( f @ a ) ) ) )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f10]) ).
thf(f13,plain,
spl0_1,
inference(avatar_split_clause,[],[f6,f10]) ).
thf(f14,plain,
( ( $true != $true )
| ~ spl0_1 ),
inference(superposition,[],[f7,f12]) ).
thf(f15,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f14]) ).
thf(f16,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f15]) ).
cnf(s1,plain,
spl0_1,
inference(sat_conversion,[],[f13]) ).
cnf(s2,plain,
~ spl0_1,
inference(sat_conversion,[],[f16]) ).
cnf(s3,plain,
$false,
inference(rat,[],[s1,s2]) ).
thf(f17,plain,
$false,
inference(avatar_sat_refutation,[],[s3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO131^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 % Computer : n003.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 16:36:29 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.29 Running higher-order theorem proving
% 0.25/0.30 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
% 0.25/0.34 % (2716751)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.34 % (2716759)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=2362484826: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)
% 0.25/0.34 % (2716759) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2716751-2716759"...
% 0.25/0.34 % (2716759)...printing done.
% 0.25/0.34 % (2716759)Refutation found. Thanks to Tanya!
% 0.25/0.34 % SZS status Theorem for theBenchmark
% 0.25/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.34 % (2716759)------------------------------
% 0.25/0.34 % (2716759)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.34 % (2716759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.34 % (2716759)CaDiCaL version: 2.1.3
% 0.25/0.34 % (2716759)Termination reason: Refutation
% 0.25/0.34 % (2716759)Time elapsed: 0.002 s
% 0.25/0.34 % (2716759)Peak memory usage: 13 MB
% 0.25/0.34 % (2716759)Instructions burned: 1 (million)
% 0.25/0.34 % (2716751)Success in time 0.03 s
% 0.25/0.34 % Vampire exiting
%------------------------------------------------------------------------------