%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA113^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 07:46:05 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 32 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 317 ( 12 ~; 3 |; 2 &; 293 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 59 ( 14 ^; 42 !; 3 ?; 59 :)
% 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/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_1,type,
'const/nums/_0': 'type/nums/num' ).
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_4,type,
'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_5,type,
'const/arith/-': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_6,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
sK0: 'type/nums/num' > 'type/realax/real' ).
thf(func_def_13,type,
sK1: 'type/nums/num' ).
thf(func_def_14,type,
sK2: 'type/nums/num' ).
thf(f1,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X0 )
=> ( ( 'const/arith/+' @ ( 'const/arith/-' @ X0 @ X1 ) @ X1 )
= X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/SUB_ADD_') ).
thf(f2,axiom,
! [X0: 'type/nums/num'] :
( ( 'const/arith/+' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X0 )
= X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/ADD_CLAUSES_0') ).
thf(f3,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ X2 @ X0 ) @ ( 'const/arith/+' @ X3 @ X0 ) ) @ X1 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ X4 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_OFFSET_') ).
thf(f4,conjecture,
! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X2 )
=> ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [X3: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ X3 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_OFFSET_0_') ).
thf(f5,negated_conjecture,
~ ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X2 )
=> ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [X3: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ X3 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X0 )
=> ( ( 'const/arith/+' @ ( 'const/arith/-' @ X0 @ X1 ) @ X1 )
= X0 ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X1 @ X0 )
= $true )
=> ( ( 'const/arith/+' @ ( 'const/arith/-' @ X0 @ X1 ) @ X1 )
= X0 ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ X2 @ X0 ) @ ( 'const/arith/+' @ X3 @ X0 ) ) @ X1 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [X4: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ X4 @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f9,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ X2 @ X0 ) @ ( 'const/arith/+' @ X3 @ X0 ) ) @ X1 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ X0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( 'const/arith/<=' @ X1 @ X2 )
=> ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [X3: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ X3 @ X1 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f11,plain,
~ ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X1 @ X2 )
= $true )
=> ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ X1 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/+' @ ( 'const/arith/-' @ X0 @ X1 ) @ X1 )
= X0 )
| ( ( 'const/arith/<=' @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f13,plain,
? [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ X2 @ X1 ) )
@ ^ [Y0: 'type/nums/num'] : ( X0 @ ( 'const/arith/+' @ Y0 @ X1 ) ) ) )
& ( ( 'const/arith/<=' @ X1 @ X2 )
= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f14,plain,
( ( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK2 @ sK1 ) )
@ ^ [Y0: 'type/nums/num'] : ( sK0 @ ( 'const/arith/+' @ Y0 @ sK1 ) ) ) )
& ( $true
= ( 'const/arith/<=' @ sK1 @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f13]) ).
thf(f15,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X1 @ X0 )
!= $true )
| ( ( 'const/arith/+' @ ( 'const/arith/-' @ X0 @ X1 ) @ X1 )
= X0 ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
! [X0: 'type/nums/num'] :
( ( 'const/arith/+' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ X0 )
= X0 ),
inference(cnf_transformation,[],[f2]) ).
thf(f17,plain,
! [X2: 'type/nums/num',X3: 'type/nums/num',X0: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ X2 @ X0 ) @ ( 'const/arith/+' @ X3 @ X0 ) ) @ X1 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X3 )
@ ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ X0 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f18,plain,
( $true
= ( 'const/arith/<=' @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ ( 'const/arith/-' @ sK2 @ sK1 ) )
@ ^ [Y0: 'type/nums/num'] : ( sK0 @ ( 'const/arith/+' @ Y0 @ sK1 ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f29,plain,
( ( $true != $true )
| ( sK2
= ( 'const/arith/+' @ ( 'const/arith/-' @ sK2 @ sK1 ) @ sK1 ) ) ),
inference(constrained_superposition,[],[f15,f18]) ).
thf(f32,plain,
( sK2
= ( 'const/arith/+' @ ( 'const/arith/-' @ sK2 @ sK1 ) @ sK1 ) ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f34,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ ( 'const/arith/-' @ sK2 @ sK1 ) )
@ ^ [Y0: 'type/nums/num'] : ( X1 @ ( 'const/arith/+' @ Y0 @ sK1 ) ) )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ X0 @ sK1 ) @ sK2 ) @ X1 ) ),
inference(constrained_superposition,[],[f17,f32]) ).
thf(f38,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ sK1 ) @ sK2 )
@ ^ [Y0: 'type/nums/num'] :
( sK0
@ ( ^ [Y1: 'type/nums/num'] : Y1
@ Y0 ) ) ) ),
inference(constrained_superposition,[],[f19,f34]) ).
thf(f39,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ ( 'const/arith/+' @ ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) @ sK1 ) @ sK2 ) @ sK0 ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 )
!= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK2 ) @ sK0 ) ),
inference(forward_demodulation,[],[f39,f16]) ).
thf(f41,plain,
$false,
inference(trivial_inequality_removal,[],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA113^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n006.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 17:41:54 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.31 % (1076856)Will run a generic schedule for satisfiability detection.
% 0.22/0.31 % (1076862)% WARNING: option uhcvi not known.
% 0.22/0.31 % (1076861)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4059415840_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.31 % (1076864)dis+10_1_sil=32000:sp=arity:random_seed=3989642498:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.31 % (1076863)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1354976139:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.31 % (1076862)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=268596286:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.31 % (1076866)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2743216036:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.31 % (1076862)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.31 % (1076862)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.31 % Exception at run slice level
% 0.22/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.31 % (1076865)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=762091205:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.31 % (1076867)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=359112837:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.31 % (1076865)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.31 % (1076864) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1076856-1076864"...
% 0.22/0.31 % (1076863) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1076856-1076863"...
% 0.22/0.31 % (1076866) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1076856-1076866"...
% 0.22/0.31 % (1076867) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1076856-1076867"...
% 0.22/0.31 % (1076864)...printing done.
% 0.22/0.31 % (1076864)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (1076864)------------------------------
% 0.22/0.31 % (1076864)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1076864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1076864)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1076864)Termination reason: Refutation
% 0.22/0.31 % (1076864)Time elapsed: 0.021 s
% 0.22/0.31 % (1076864)Peak memory usage: 11 MB
% 0.22/0.31 % (1076864)Instructions burned: 6 (million)
% 0.22/0.31 % (1076856)Success in time 0.065 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------