%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA106^1 : 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 : n002.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 07:45:55 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 83 ( 25 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 369 ( 12 ~; 4 |; 0 &; 350 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 84 ( 18 ^; 58 !; 8 ?; 84 :)
% 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/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/realax/real_sub': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
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_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
sK0: 'type/nums/num' > 'type/realax/real' ).
thf(func_def_10,type,
sK1: 'type/nums/num' > 'type/realax/real' ).
thf(func_def_11,type,
sK2: 'type/nums/num' ).
thf(func_def_12,type,
sK3: 'type/nums/num' ).
thf(f1,axiom,
! [X0: $tType,X2: X0 > 'type/realax/real',X1: X0 > 'type/realax/real',X3: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X3 )
=> ( ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_sub' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_SUB_') ).
thf(f2,axiom,
! [X1: 'type/nums/num',X0: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/FINITE_NUMSEG_') ).
thf(f3,conjecture,
! [X0: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( X0 @ X4 ) @ ( X1 @ X4 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ X0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_SUB_NUMSEG_') ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( X0 @ X4 ) @ ( X1 @ X4 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ X0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 ) @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
! [X1: 'type/nums/num',X0: 'type/nums/num'] :
( $true
= ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X0 ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X3 )
=> ( ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_sub' @ ( X2 @ X4 ) @ ( X1 @ X4 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
! [X0: $tType,X3: X0 > $o,X2: X0 > 'type/realax/real',X1: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
=> ( ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/realax/real_sub' @ ( X2 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num',X2: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X1 )
@ ^ [X4: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( X0 @ X4 ) @ ( X2 @ X4 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X1 ) @ X0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X1 ) @ X2 ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ! [X2: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num',X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X1 ) @ X0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X1 ) @ X2 ) )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X1 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( X0 @ Y0 ) @ ( X2 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $tType,X3: X0 > $o,X2: X0 > 'type/realax/real',X1: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
!= $true )
| ( ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/realax/real_sub' @ ( X2 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
? [X0: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X1 ) @ X0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X1 ) @ X2 ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X1 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( X0 @ Y0 ) @ ( X2 @ Y0 ) ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f13,plain,
? [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X2 ) @ X0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X2 ) @ X1 ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X3 @ X2 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( sK0 @ Y0 ) @ ( sK1 @ Y0 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f13]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: X0 > 'type/realax/real'] :
( ( $true
!= ( 'const/sets/FINITE' @ X0 @ X1 ) )
| ( ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) )
= ( 'const/iterate/sum' @ X0 @ X1
@ ^ [Y0: X0] : ( 'const/realax/real_sub' @ ( X2 @ Y0 ) @ ( X3 @ Y0 ) ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f16,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) )
= $true ),
inference(rectify,[],[f6]) ).
thf(f17,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( sK0 @ Y0 ) @ ( sK1 @ Y0 ) ) )
!= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK0 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK1 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f18,plain,
! [X0: $tType,X2: X0 > 'type/realax/real',X3: X0 > 'type/realax/real',X1: X0 > $o] :
( ( $true
!= ( 'const/sets/FINITE' @ X0 @ X1 ) )
| ( ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) )
= ( 'const/iterate/sum' @ X0 @ X1
@ ^ [Y0: X0] : ( 'const/realax/real_sub' @ ( X2 @ Y0 ) @ ( X3 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f19,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) )
= $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
! [X2: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num' > 'type/realax/real',X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( X2 @ Y0 ) @ ( X3 @ Y0 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) @ X2 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) @ X3 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f18,f19]) ).
thf(f23,plain,
! [X2: 'type/nums/num' > 'type/realax/real',X3: 'type/nums/num' > 'type/realax/real',X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( X2 @ Y0 ) @ ( X3 @ Y0 ) ) )
= ( 'const/realax/real_sub' @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) @ X2 ) @ ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f22]) ).
thf(f24,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( sK0 @ Y0 ) @ ( sK1 @ Y0 ) ) )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 )
@ ^ [Y0: 'type/nums/num'] : ( 'const/realax/real_sub' @ ( sK0 @ Y0 ) @ ( sK1 @ Y0 ) ) ) ),
inference(constrained_superposition,[],[f17,f23]) ).
thf(f25,plain,
$false,
inference(trivial_inequality_removal,[],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA106^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n002.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 17:44:22 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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
% 0.19/0.26 % (1627181)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.26 % (1627188)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=856882870:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.26 % (1627188) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1627181-1627188"...
% 0.19/0.26 % (1627188)...printing done.
% 0.19/0.26 % (1627188)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 % (1627188)------------------------------
% 0.19/0.26 % (1627188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (1627188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (1627188)CaDiCaL version: 2.1.3
% 0.19/0.26 % (1627188)Termination reason: Refutation
% 0.19/0.26 % (1627188)Time elapsed: 0.002 s
% 0.19/0.26 % (1627188)Peak memory usage: 12 MB
% 0.19/0.26 % (1627188)Instructions burned: 4 (million)
% 0.19/0.26 % (1627181)Success in time 0.033 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------