%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO291^5 : 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 : n026.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 08:47:22 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 11 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 48 ( 6 ~; 2 |; 9 &; 27 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 7 ( 1 ^; 6 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cQ: $i > $o ).
thf(func_def_3,type,
f: $i > $i ).
thf(func_def_4,type,
cR: $i > $o ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ! [X0: $i > $o] : ( X0 @ y )
=> ( ( cR @ ( f @ x ) )
& ( cQ @ y )
& ( cR @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTEST3) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i > $o] : ( X0 @ y )
=> ( ( cR @ ( f @ x ) )
& ( cQ @ y )
& ( cR @ x ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i > $o] : ( X0 @ y )
=> ( ( cR @ ( f @ x ) )
& ( cQ @ y )
& ( cR @ x ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i > $o] :
( ( X0 @ y )
= $true )
=> ( ( ( cQ @ y )
= $true )
& ( ( cR @ x )
= $true )
& ( ( cR @ ( f @ x ) )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X0: $i > $o] :
( ( X0 @ y )
= $true )
& ( ( ( cR @ x )
!= $true )
| ( ( cQ @ y )
!= $true )
| ( ( cR @ ( f @ x ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f7,plain,
! [X0: $i > $o] :
( ( X0 @ y )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f21,plain,
( ( ^ [Y0: $i] : $false
@ y )
= $true ),
inference(primitive_instantiation,[],[f7]) ).
thf(f25,plain,
$false = $true,
inference(beta-eta_normalization,[],[f21]) ).
thf(f26,plain,
$false,
inference(trivial_inequality_removal,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO291^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n026.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:46:13 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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
% 0.21/0.29 % (848984)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (848991)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=188302501:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (848989)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3897979238:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (848990)lrs+10_16_si=on:nwc=1.5:random_seed=3503814786:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (848992)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=3168751245: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)
% 0.21/0.29 % (848993)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=467545758:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (848989) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-848984-848989"...
% 0.21/0.29 % (848991) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-848984-848991"...
% 0.21/0.29 % (848990) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-848984-848990"...
% 0.21/0.29 % (848993) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-848984-848993"...
% 0.21/0.29 % (848992) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-848984-848992"...
% 0.21/0.29 % (848989)...printing done.
% 0.21/0.29 % (848991)...printing done.
% 0.21/0.29 % (848993)...printing done.
% 0.21/0.29 % (848990)...printing done.
% 0.21/0.29 % (848992)...printing done.
% 0.21/0.29 % (848991)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (848991)------------------------------
% 0.21/0.29 % (848991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (848991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (848991)CaDiCaL version: 2.1.3
% 0.21/0.29 % (848991)Termination reason: Refutation
% 0.21/0.29 % (848991)Time elapsed: 0.002 s
% 0.21/0.29 % (848991)Peak memory usage: 12 MB
% 0.21/0.29 % (848991)Instructions burned: 1 (million)
% 0.21/0.29 % (848984)Success in time 0.033 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------