%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM699^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:18:36 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 18 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 89 ( 11 ~; 4 |; 0 &; 71 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: nat ).
thf(func_def_1,type,
y: nat ).
thf(func_def_2,type,
less: nat > nat > $o ).
thf(func_def_4,type,
lessis: nat > nat > $o ).
thf(func_def_5,type,
suc: nat > nat ).
thf(func_def_6,type,
pl: nat > nat > nat ).
thf(func_def_7,type,
n_1: nat ).
thf(f1,axiom,
less @ y @ x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(f2,axiom,
! [X0: nat,X1: nat] :
( ( less @ X1 @ X0 )
=> ( lessis @ ( pl @ X1 @ n_1 ) @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz25b) ).
thf(f3,axiom,
! [X0: nat] :
( ( pl @ X0 @ n_1 )
= ( suc @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz4a) ).
thf(f4,conjecture,
lessis @ ( suc @ y ) @ x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz25c) ).
thf(f5,negated_conjecture,
~ ( lessis @ ( suc @ y ) @ x ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
less @ y @ x,
inference(rectify,[],[f1]) ).
thf(f7,plain,
( ( less @ y @ x )
= $true ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
~ ( lessis @ ( suc @ y ) @ x ),
inference(rectify,[],[f5]) ).
thf(f9,plain,
( ( lessis @ ( suc @ y ) @ x )
!= $true ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: nat,X1: nat] :
( ( less @ X1 @ X0 )
=> ( lessis @ ( pl @ X1 @ n_1 ) @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
! [X1: nat,X0: nat] :
( ( ( less @ X1 @ X0 )
= $true )
=> ( ( lessis @ ( pl @ X1 @ n_1 ) @ X0 )
= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( ( lessis @ ( suc @ y ) @ x )
!= $true ),
inference(flattening,[],[f9]) ).
thf(f13,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ ( pl @ X1 @ n_1 ) @ X0 )
= $true )
| ( ( less @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f14,plain,
( ( less @ y @ x )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f15,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ ( pl @ X1 @ n_1 ) @ X0 )
= $true )
| ( ( less @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f16,plain,
( ( lessis @ ( suc @ y ) @ x )
!= $true ),
inference(cnf_transformation,[],[f12]) ).
thf(f17,plain,
! [X0: nat] :
( ( pl @ X0 @ n_1 )
= ( suc @ X0 ) ),
inference(cnf_transformation,[],[f3]) ).
thf(f19,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ ( suc @ X1 ) @ X0 )
= $true )
| ( ( less @ X1 @ X0 )
!= $true ) ),
inference(forward_demodulation,[],[f15,f17]) ).
thf(f20,plain,
( ( ( less @ y @ x )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f16,f19]) ).
thf(f21,plain,
( ( less @ y @ x )
!= $true ),
inference(trivial_inequality_removal,[],[f20]) ).
thf(f22,plain,
$false,
inference(forward_subsumption_resolution,[],[f21,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM699^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 12:43:41 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.30 % (19164)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (19175)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (19175)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
% 0.21/0.30 % (19173)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3331434700:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (19170)lrs+10_16_si=on:nwc=1.5:random_seed=3527609112:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (19171)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2373349838:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (19169)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=464568764:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (19174)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2293820837:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (19172)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1662070357:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.30 % (19175)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3403950534:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (19171) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-19164-19171"...
% 0.21/0.30 % (19170) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-19164-19170"...
% 0.21/0.30 % (19169) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-19164-19169"...
% 0.21/0.30 % (19173) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-19164-19173"...
% 0.21/0.30 % (19174) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-19164-19174"...
% 0.21/0.30 % (19172) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-19164-19172"...
% 0.21/0.30 % (19173)...printing done.
% 0.21/0.30 % (19169)...printing done.
% 0.21/0.30 % (19170)...printing done.
% 0.21/0.30 % (19171)...printing done.
% 0.21/0.30 % (19175) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-19164-19175"...
% 0.21/0.30 % (19174)...printing done.
% 0.21/0.30 % (19173)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (19173)------------------------------
% 0.21/0.30 % (19173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (19173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (19173)CaDiCaL version: 2.1.3
% 0.21/0.30 % (19173)Termination reason: Refutation
% 0.21/0.30 % (19173)Time elapsed: 0.002 s
% 0.21/0.30 % (19173)Peak memory usage: 12 MB
% 0.21/0.30 % (19173)Instructions burned: 1 (million)
% 0.21/0.30 % (19164)Success in time 0.045 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------