%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n014.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 07:46:03 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 94 ( 35 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 404 ( 15 ~; 8 |; 2 &; 369 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 2 con; 0-5 aty)
% Number of variables : 81 ( 17 ^; 60 !; 4 ?; 81 :)
% 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 > 'type/realax/real' ).
thf(func_def_11,type,
sK2: sK0 > 'type/realax/real' ).
thf(func_def_12,type,
sK3: sK0 > $o ).
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,X4: X0 > X1,X5: X0 > $o] :
( ( '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',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X3 )
=> ( ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_add' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_ADD_') ).
thf(f5,negated_conjecture,
~ ! [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_add' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ! [X3: X0 > X1,X4: X0 > X1,X5: X0 > $o] :
( ( '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 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f7,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
= $true )
=> ! [X3: X0 > X1,X4: X0 > X1,X5: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X5 )
= $true )
=> ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5
@ ^ [Y0: X0] : ( X2 @ ( X3 @ Y0 ) @ ( X4 @ 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: 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_add' @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) )
= ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true )
=> ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/realax/real_add' @ ( X1 @ Y0 ) @ ( X2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ! [X3: X0 > X1,X4: X0 > X1,X5: X0 > $o] :
( ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5
@ ^ [Y0: X0] : ( X2 @ ( X3 @ Y0 ) @ ( X4 @ Y0 ) ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X5 )
!= $true ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f13,plain,
? [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > 'type/realax/real',X3: X0 > $o] :
( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ ( 'const/iterate/sum' @ X0 @ X3 @ X2 ) )
!= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [Y0: X0] : ( 'const/realax/real_add' @ ( X1 @ Y0 ) @ ( X2 @ Y0 ) ) ) )
& ( ( 'const/sets/FINITE' @ X0 @ X3 )
= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f14,plain,
( ( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK2 ) )
!= ( 'const/iterate/sum' @ sK0 @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( sK1 @ Y0 ) @ ( sK2 @ Y0 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK3 ) ) ),
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] :
( 'const/iterate/sum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' ) ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f16,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > X1,X4: X0 > X1,X5: X0 > $o] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X5 )
!= $true )
| ( ( X2 @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X3 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5 @ X4 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X5
@ ^ [Y0: X0] : ( X2 @ ( X3 @ Y0 ) @ ( X4 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f17,plain,
( ( 'const/iterate/monoidal' @ 'type/realax/real' @ 'const/realax/real_add' )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f18,plain,
( $true
= ( 'const/sets/FINITE' @ sK0 @ sK3 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
( ( 'const/realax/real_add' @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK1 ) @ ( 'const/iterate/sum' @ sK0 @ sK3 @ sK2 ) )
!= ( 'const/iterate/sum' @ sK0 @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( sK1 @ Y0 ) @ ( sK2 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f22,plain,
( ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ sK1 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ sK2 ) )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( sK1 @ Y0 ) @ ( sK2 @ Y0 ) ) ) ),
inference(definition_unfolding,[],[f19,f15,f15,f15]) ).
thf(f30,plain,
! [X0: $tType,X2: X0 > 'type/realax/real',X3: X0 > 'type/realax/real',X1: X0 > $o] :
( ( $true != $true )
| ( $true
!= ( 'const/sets/FINITE' @ X0 @ X1 ) )
| ( ( '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 ) )
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1
@ ^ [Y0: X0] : ( 'const/realax/real_add' @ ( X2 @ Y0 ) @ ( X3 @ Y0 ) ) ) ) ),
inference(constrained_superposition,[],[f16,f17]) ).
thf(f33,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_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 ) )
= ( 'const/iterate/iterate' @ X0 @ 'type/realax/real' @ 'const/realax/real_add' @ X1
@ ^ [Y0: X0] : ( 'const/realax/real_add' @ ( X2 @ Y0 ) @ ( X3 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f34,plain,
! [X0: sK0 > 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( $true != $true )
| ( ( 'const/realax/real_add' @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ X0 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ X1 ) )
= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ),
inference(constrained_superposition,[],[f33,f18]) ).
thf(f37,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' @ sK3 @ X0 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3 @ X1 ) )
= ( 'const/iterate/iterate' @ sK0 @ 'type/realax/real' @ 'const/realax/real_add' @ sK3
@ ^ [Y0: sK0] : ( 'const/realax/real_add' @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f38,plain,
$false,
inference(backward_subsumption_resolution,[],[f22,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA099^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.16 % Computer : n014.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 17:41:00 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 Running first-order model finding
% 0.09/0.19 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.25 % (2981529)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (2981536)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4139886250:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.25 % (2981535)% WARNING: option uhcvi not known.
% 0.09/0.25 % (2981535)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1425108330:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.25 % (2981537)dis+10_1_sil=32000:sp=arity:random_seed=827589931:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.25 % (2981538)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1996705190:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.25 % (2981540)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3045687064:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.25 % (2981539)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2977085531:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.25 % (2981535)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25 % (2981538)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25 % (2981535)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.25 % (2981535) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2981529-2981535"...
% 0.09/0.25 % (2981537) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2981529-2981537"...
% 0.09/0.25 % (2981535)...printing done.
% 0.09/0.25 % (2981537)...printing done.
% 0.09/0.25 % (2981535)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.25 % (2981535)------------------------------
% 0.09/0.25 % (2981535)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (2981535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (2981535)CaDiCaL version: 2.1.3
% 0.09/0.25 % (2981535)Termination reason: Refutation
% 0.09/0.25 % (2981535)Time elapsed: 0.005 s
% 0.09/0.25 % (2981535)Peak memory usage: 12 MB
% 0.09/0.25 % (2981535)Instructions burned: 6 (million)
% 0.09/0.25 % (2981529)Success in time 0.047 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------