%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA109^1 : 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 : n001.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 07:45:56 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 30 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 183 ( 14 ~; 7 |; 0 &; 162 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 31 ( 0 ^; 27 !; 4 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
'const/sets/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_2,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_3,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_5,type,
sK0: 'type/nums/num' > 'type/realax/real' ).
thf(func_def_6,type,
sK1: 'type/nums/num' ).
thf(func_def_9,type,
sK2: 'type/nums/num' > 'type/nums/num' ).
thf(func_def_10,type,
sK3: 'type/nums/num' > 'type/nums/num' ).
thf(func_def_11,type,
sK4: 'type/nums/num' > 'type/nums/num' ).
thf(func_def_12,type,
sK5: 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_13,type,
sK6:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(f1,axiom,
! [X0: $tType,X2: X0,X1: X0 > 'type/realax/real'] :
( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) @ X1 )
= ( X1 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_SING_') ).
thf(f2,axiom,
! [X0: 'type/nums/num'] :
( ( 'const/iterate/..' @ X0 @ X0 )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NUMSEG_SING_') ).
thf(f3,conjecture,
! [X1: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
= ( X0 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_SING_NUMSEG_') ).
thf(f4,negated_conjecture,
~ ! [X1: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
= ( X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X0 ) @ X1 )
= ( X1 @ X0 ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X1: 'type/nums/num' > 'type/realax/real',X0: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X0 ) @ X1 )
!= ( X1 @ X0 ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
! [X0: $tType,X1: X0,X2: X0 > 'type/realax/real'] :
( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ) @ X2 )
= ( X2 @ X1 ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
? [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
!= ( X0 @ X1 ) ),
inference(rectify,[],[f6]) ).
thf(f9,plain,
( ( sK0 @ sK1 )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK1 ) @ sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
thf(f10,plain,
! [X0: 'type/nums/num'] :
( ( 'const/iterate/..' @ X0 @ X0 )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num' ) ),
inference(cnf_transformation,[],[f2]) ).
thf(f11,plain,
! [X0: $tType,X2: X0 > 'type/realax/real',X1: X0] :
( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ) @ X2 )
= ( X2 @ X1 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
( ( sK0 @ sK1 )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK1 ) @ sK0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f41,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0 > 'type/realax/real'] :
( ( ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 )
!= ( 'const/sets/INSERT' @ X0 @ X3 @ 'const/sets/EMPTY' @ X0 ) )
| ( ( X1 @ X2 )
= ( X1 @ X3 ) ) ),
inference(constrained_superposition,[],[f11,f11]) ).
thf(f42,plain,
! [X0: 'type/nums/num'] :
( ( ( sK0 @ sK1 )
!= ( sK0 @ X0 ) )
| ( ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num' )
!= ( 'const/iterate/..' @ sK1 @ sK1 ) ) ),
inference(constrained_superposition,[],[f12,f11]) ).
thf(f44,plain,
! [X0: 'type/nums/num'] :
( ( ( sK0 @ sK1 )
!= ( sK0 @ X0 ) )
| ( ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num' )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ sK1 @ 'const/sets/EMPTY' @ 'type/nums/num' ) ) ),
inference(forward_demodulation,[],[f42,f10]) ).
thf(f45,plain,
! [X0: 'type/nums/num'] :
( ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num' )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ sK1 @ 'const/sets/EMPTY' @ 'type/nums/num' ) ),
inference(forward_subsumption_resolution,[],[f44,f41]) ).
thf(f46,plain,
! [X0: 'type/nums/num'] :
( ( 'const/sets/INSERT' @ 'type/nums/num' @ sK1 @ 'const/sets/EMPTY' @ 'type/nums/num' @ ( sK3 @ X0 ) )
!= ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num' @ ( sK3 @ X0 ) ) ),
inference(negative_extensionality,[],[f45]) ).
thf(f50,plain,
! [X0: 'type/nums/num'] :
( ( $true
= ( 'const/sets/INSERT' @ 'type/nums/num' @ sK1 @ 'const/sets/EMPTY' @ 'type/nums/num' @ ( sK3 @ X0 ) ) )
| ( $true
= ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num' @ ( sK3 @ X0 ) ) ) ),
inference(xor_proxy_clausification,[],[f46]) ).
thf(f51,plain,
! [X0: 'type/nums/num'] :
( ( $false
= ( 'const/sets/INSERT' @ 'type/nums/num' @ sK1 @ 'const/sets/EMPTY' @ 'type/nums/num' @ ( sK3 @ X0 ) ) )
| ( $false
= ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num' @ ( sK3 @ X0 ) ) ) ),
inference(xor_proxy_clausification,[],[f46]) ).
thf(f58,plain,
( ( ( 'const/sets/INSERT' @ 'type/nums/num' @ sK1 @ 'const/sets/EMPTY' @ 'type/nums/num' @ ( sK3 @ sK1 ) )
= $true )
| ( $true != $true ) ),
inference(equality_factoring,[],[f50]) ).
thf(f60,plain,
( ( 'const/sets/INSERT' @ 'type/nums/num' @ sK1 @ 'const/sets/EMPTY' @ 'type/nums/num' @ ( sK3 @ sK1 ) )
= $true ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f78,plain,
( ( $false = $true )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f51,f60]) ).
thf(f89,plain,
$false = $true,
inference(duplicate_literal_removal,[],[f78]) ).
thf(f90,plain,
$false,
inference(trivial_inequality_removal,[],[f89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA109^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n001.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 17:50:43 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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
% 0.22/0.29 % (1588069)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (1588079)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=762589919:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (1588079) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1588069-1588079"...
% 0.22/0.29 % (1588080)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (1588080)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.29 % (1588079)...printing done.
% 0.22/0.29 % (1588079)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (1588079)------------------------------
% 0.22/0.29 % (1588079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (1588079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (1588079)CaDiCaL version: 2.1.3
% 0.22/0.29 % (1588079)Termination reason: Refutation
% 0.22/0.29 % (1588079)Time elapsed: 0.004 s
% 0.22/0.29 % (1588079)Peak memory usage: 12 MB
% 0.22/0.29 % (1588079)Instructions burned: 13 (million)
% 0.22/0.29 % (1588069)Success in time 0.031 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------