%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA099^1 : 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 : n017.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 07:45:54 AM UTC 2026
% Result : Theorem 0.24s 0.35s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 108 ( 41 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 471 ( 19 ~; 10 |; 3 &; 429 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 2 con; 0-5 aty)
% Number of variables : 95 ( 21 ^; 66 !; 8 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/realax/real_add': '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/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_4,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK1: sK0 > $o ).
thf(func_def_11,type,
sK2: sK0 > 'type/realax/real' ).
thf(func_def_12,type,
sK3: sK0 > 'type/realax/real' ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/sum_') ).
thf(f2,axiom,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ! [X3: X0 > X1,X5: X0 > $o,X4: X0 > X1] :
( ( 'const/sets/FINITE' @ X0 @ X5 )
=> ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5
@ ^ [X6: X0] : ( X2 @ ( X3 @ X6 ) @ ( X4 @ X6 ) ) )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_OP_') ).
thf(f3,axiom,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_REAL_ADD_') ).
thf(f4,conjecture,
! [X0: $tType,X1: X0 > 'type/realax/real',X3: X0 > $o,X2: X0 > 'type/realax/real'] :
( ( 'const/sets/FINITE' @ X0 @ X3 )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_add' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_ADD_') ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X3: X0 > $o,X2: X0 > 'type/realax/real'] :
( ( 'const/sets/FINITE' @ X0 @ X3 )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_add' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( 'const/sets/FINITE' @ X0 @ X2 )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) )
= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [X4: X0] : ( 'const/realax/real_add' @ ( X1 @ X4 ) @ ( X3 @ X4 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) )
= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [Y0: X0] : ( 'const/realax/real_add' @ ( X1 @ Y0 ) @ ( X3 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add',
inference(rectify,[],[f3]) ).
thf(f9,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ! [X3: X0 > X1,X4: X0 > $o,X5: X0 > X1] :
( ( 'const/sets/FINITE' @ X0 @ X4 )
=> ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4
@ ^ [X6: X0] : ( X2 @ ( X3 @ X6 ) @ ( X5 @ X6 ) ) )
= ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
= $true )
=> ! [X3: X0 > X1,X5: X0 > X1,X4: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true )
=> ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4
@ ^ [Y0: X0] : ( X2 @ ( X3 @ Y0 ) @ ( X5 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
? [X0: $tType,X2: X0 > $o,X1: X0 > 'type/realax/real',X3: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) )
!= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [Y0: X0] : ( 'const/realax/real_add' @ ( X1 @ Y0 ) @ ( X3 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f13,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ! [X5: X0 > X1,X4: X0 > $o,X3: X0 > X1] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true )
| ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4
@ ^ [Y0: X0] : ( X2 @ ( X3 @ Y0 ) @ ( X5 @ Y0 ) ) ) ) ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f14,plain,
! [X0: $tType,X1: $tType,X2: X0 > X0 > X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X2 )
!= $true )
| ! [X3: X1 > X0,X4: X1 > $o,X5: X1 > X0] :
( ( $true
!= ( 'const/sets/FINITE' @ X1 @ X4 ) )
| ( ( X2 @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X4 @ X5 ) @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X4 @ X3 ) )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X4
@ ^ [Y0: X1] : ( X2 @ ( X5 @ Y0 ) @ ( X3 @ Y0 ) ) ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f15,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > 'type/realax/real',X3: X0 > 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
& ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X1 @ X2 ) @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) )
!= ( 'const/iterate/sum' @ X0 @ X1
@ ^ [Y0: X0] : ( 'const/realax/real_add' @ ( X2 @ Y0 ) @ ( X3 @ Y0 ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f16,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ sK1 )
= $true )
& ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK2 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK3 ) )
!= ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( sK2 @ Y0 ) @ ( sK3 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f15]) ).
thf(f17,plain,
! [X1: $tType,X0: $tType,X2: X0 > X0 > X0,X3: X1 > X0,X4: X1 > $o,X5: X1 > X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X2 )
!= $true )
| ( $true
!= ( 'const/sets/FINITE' @ X1 @ X4 ) )
| ( ( X2 @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X4 @ X5 ) @ ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X4 @ X3 ) )
= ( 'const/iterate/iterate' @ X1 @ X0 @ X2 @ X4
@ ^ [Y0: X1] : ( X2 @ ( X5 @ Y0 ) @ ( X3 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f18,plain,
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK2 ) @ ( 'const/iterate/sum' @ sK0 @ sK1 @ sK3 ) )
!= ( 'const/iterate/sum' @ sK0 @ sK1
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( sK2 @ Y0 ) @ ( sK3 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f19,plain,
( ( 'const/sets/FINITE' @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f20,plain,
! [X0: $tType] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f21,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f24,plain,
( ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ sK2 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ sK3 ) )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( sK2 @ Y0 ) @ ( sK3 @ Y0 ) ) ) ),
inference(definition_unfolding,[],[f18,f20,f20,f20]) ).
thf(f25,plain,
! [X0: $tType,X2: X0 > 'type/realax/real',X3: X0 > 'type/realax/real',X1: X0 > $o] :
( ( ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1
@ ^ [Y0: X0] : ( 'const/realax/real_add' @ ( X2 @ Y0 ) @ ( X3 @ Y0 ) ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1 @ X2 ) @ ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1 @ X3 ) ) )
| ( $true != $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true ) ),
inference(constrained_superposition,[],[f17,f21]) ).
thf(f26,plain,
! [X0: $tType,X2: X0 > 'type/realax/real',X3: X0 > 'type/realax/real',X1: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1
@ ^ [Y0: X0] : ( 'const/realax/real_add' @ ( X2 @ Y0 ) @ ( X3 @ Y0 ) ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1 @ X2 ) @ ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1 @ X3 ) ) ) ),
inference(trivial_inequality_removal,[],[f25]) ).
thf(f27,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ X0 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ X1 ) )
= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f26,f19]) ).
thf(f28,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ X0 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1 @ X1 ) )
= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ),
inference(trivial_inequality_removal,[],[f27]) ).
thf(f29,plain,
( ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( sK2 @ Y0 ) @ ( sK3 @ Y0 ) ) )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK1
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( sK2 @ Y0 ) @ ( sK3 @ Y0 ) ) ) ),
inference(constrained_superposition,[],[f24,f28]) ).
thf(f30,plain,
$false,
inference(trivial_inequality_removal,[],[f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA099^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n017.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 17:36:38 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.25 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.30 Running higher-order theorem proving
% 0.24/0.31 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
% 0.24/0.35 % (657170)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.35 % (657177)lrs+10_16_si=on:nwc=1.5:random_seed=2648964436:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.35 % (657176)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3276525597:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.35 % (657177) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-657170-657177"...
% 0.24/0.35 % (657176) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-657170-657176"...
% 0.24/0.35 % (657177)...printing done.
% 0.24/0.35 % (657177)Refutation found. Thanks to Tanya!
% 0.24/0.35 % SZS status Theorem for theBenchmark
% 0.24/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.35 % (657177)------------------------------
% 0.24/0.35 % (657177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.35 % (657177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.35 % (657177)CaDiCaL version: 2.1.3
% 0.24/0.35 % (657177)Termination reason: Refutation
% 0.24/0.35 % (657177)Time elapsed: 0.004 s
% 0.24/0.35 % (657177)Peak memory usage: 12 MB
% 0.24/0.35 % (657177)Instructions burned: 5 (million)
% 0.24/0.35 % (657170)Success in time 0.028 s
% 0.24/0.36 % Vampire exiting
%------------------------------------------------------------------------------