%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA123^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 07:45:58 AM UTC 2026
% Result : Theorem 0.06s 0.25s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 9 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 26 ( 6 ~; 0 |; 0 &; 20 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 2 con; 0-4 aty)
% Number of variables : 11 ( 8 ^; 3 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
'const/trivia/I':
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_1,type,
'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(f1,axiom,
( 'const/iterate/polynomial_function'
@ ^ [X0: 'type/realax/real'] : X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_ID_') ).
thf(f2,axiom,
! [X0: $tType] :
( ( ( ^ [X1: X0] : X1 )
= 'const/trivia/I' )
@ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/trivia/I_DEF_') ).
thf(f3,conjecture,
'const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real',
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_I_') ).
thf(f4,negated_conjecture,
~ ( 'const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real' ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $tType] :
( 'const/trivia/I'
@ ( X0
= ( ^ [Y0: X0] : Y0 ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f6,plain,
~ ( 'const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real' ),
inference(rectify,[],[f4]) ).
thf(f7,plain,
( ( 'const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real' )
!= $true ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( 'const/iterate/polynomial_function'
@ ^ [X0: 'type/realax/real'] : X0 ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( ( 'const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real' )
!= $true ),
inference(flattening,[],[f7]) ).
thf(f11,plain,
( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : Y0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
! [X0: $tType] :
( 'const/trivia/I'
@ ( X0
= ( ^ [Y0: X0] : Y0 ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f13,plain,
( ( 'const/iterate/polynomial_function' @ 'const/trivia/I' @ 'type/realax/real' )
!= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f16,plain,
( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : Y0 ) ),
inference(definition_unfolding,[],[f13,f12]) ).
thf(f17,plain,
$false,
inference(forward_subsumption_resolution,[],[f16,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA123^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n018.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 17:47:11 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.20 Running higher-order theorem proving
% 0.06/0.22 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
% 0.06/0.25 % (409650)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.06/0.25 % (409655)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1605749062:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.06/0.25 % (409655) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-409650-409655"...
% 0.06/0.25 % (409655)...printing done.
% 0.06/0.25 % (409655)Refutation found. Thanks to Tanya!
% 0.06/0.25 % SZS status Theorem for theBenchmark
% 0.06/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.25 % (409655)------------------------------
% 0.06/0.25 % (409655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.25 % (409655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.25 % (409655)CaDiCaL version: 2.1.3
% 0.06/0.25 % (409655)Termination reason: Refutation
% 0.06/0.25 % (409655)Time elapsed: 0.001 s
% 0.06/0.25 % (409655)Peak memory usage: 12 MB
% 0.06/0.25 % (409650)Success in time 0.027 s
% 0.06/0.25 % Vampire exiting
%------------------------------------------------------------------------------