%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM700^1 : 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 : 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 08:18:36 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 138 ( 40 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 185 ( 27 ~; 11 |; 0 &; 136 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 0 ^; 38 !; 0 ?; 38 :)
% 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_3,type,
pl: nat > nat > nat ).
thf(func_def_4,type,
n_1: nat ).
thf(func_def_6,type,
lessis: nat > nat > $o ).
thf(func_def_7,type,
more: nat > nat > $o ).
thf(func_def_8,type,
moreis: nat > nat > $o ).
thf(f1,axiom,
less @ y @ ( pl @ x @ n_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(f2,axiom,
! [X1: nat,X0: nat] :
( ~ ( more @ X0 @ X1 )
=> ( lessis @ X0 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10e) ).
thf(f3,axiom,
! [X1: nat,X0: nat] :
( ( less @ X0 @ X1 )
=> ~ ( moreis @ X0 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10h) ).
thf(f4,axiom,
! [X1: nat,X0: nat] :
( ( more @ X1 @ X0 )
=> ( moreis @ X1 @ ( pl @ X0 @ n_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz25) ).
thf(f5,conjecture,
lessis @ y @ x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz26) ).
thf(f6,negated_conjecture,
~ ( lessis @ y @ x ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
~ ( lessis @ y @ x ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( lessis @ y @ x )
!= $true ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: nat,X1: nat] :
( ( less @ X1 @ X0 )
=> ~ ( moreis @ X1 @ X0 ) ),
inference(rectify,[],[f3]) ).
thf(f10,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( less @ X1 @ X0 ) )
=> ( ( moreis @ X1 @ X0 )
!= $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: nat,X1: nat] :
( ~ ( more @ X1 @ X0 )
=> ( lessis @ X1 @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X1 @ X0 )
!= $true )
=> ( ( lessis @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
less @ y @ ( pl @ x @ n_1 ),
inference(rectify,[],[f1]) ).
thf(f14,plain,
( ( less @ y @ ( pl @ x @ n_1 ) )
= $true ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: nat,X1: nat] :
( ( more @ X0 @ X1 )
=> ( moreis @ X0 @ ( pl @ X1 @ n_1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X0 @ X1 )
= $true )
=> ( ( moreis @ X0 @ ( pl @ X1 @ n_1 ) )
= $true ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ( lessis @ y @ x )
!= $true ),
inference(flattening,[],[f8]) ).
thf(f18,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( less @ X1 @ X0 ) )
=> ( ( moreis @ X1 @ X0 )
!= $true ) ),
inference(flattening,[],[f10]) ).
thf(f19,plain,
! [X1: nat,X0: nat] :
( ( ( more @ X1 @ X0 )
!= $true )
=> ( ( lessis @ X1 @ X0 )
= $true ) ),
inference(flattening,[],[f12]) ).
thf(f20,plain,
! [X1: nat,X0: nat] :
( ( $true
!= ( less @ X1 @ X0 ) )
| ( ( moreis @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f18]) ).
thf(f21,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X1 @ X0 )
= $true )
| ( ( more @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f22,plain,
! [X1: nat,X0: nat] :
( ( ( moreis @ X0 @ ( pl @ X1 @ n_1 ) )
= $true )
| ( ( more @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f23,plain,
! [X0: nat,X1: nat] :
( ( ( moreis @ X1 @ ( pl @ X0 @ n_1 ) )
= $true )
| ( ( more @ X1 @ X0 )
!= $true ) ),
inference(rectify,[],[f22]) ).
thf(f24,plain,
! [X0: nat,X1: nat] :
( ( ( less @ X0 @ X1 )
!= $true )
| ( ( moreis @ X0 @ X1 )
!= $true ) ),
inference(rectify,[],[f20]) ).
thf(f25,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X1 @ X0 )
!= $true )
| ( ( moreis @ X1 @ ( pl @ X0 @ n_1 ) )
= $true ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f26,plain,
( ( lessis @ y @ x )
!= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f27,plain,
! [X0: nat,X1: nat] :
( ( ( moreis @ X0 @ X1 )
!= $true )
| ( ( less @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f28,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X1 @ X0 )
= $true )
| ( ( more @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f29,plain,
( ( less @ y @ ( pl @ x @ n_1 ) )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f32,plain,
( ( $true != $true )
| ( $true
= ( more @ y @ x ) ) ),
inference(constrained_superposition,[],[f26,f28]) ).
thf(f33,plain,
( $true
= ( more @ y @ x ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f34,plain,
( ( ( moreis @ y @ ( pl @ x @ n_1 ) )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f25,f33]) ).
thf(f35,plain,
( ( moreis @ y @ ( pl @ x @ n_1 ) )
= $true ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f36,plain,
( ( ( less @ y @ ( pl @ x @ n_1 ) )
!= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f27,f35]) ).
thf(f37,plain,
( ( less @ y @ ( pl @ x @ n_1 ) )
!= $true ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f38,plain,
$false,
inference(forward_subsumption_resolution,[],[f37,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM700^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n006.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 12:41:09 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.22/0.28 % (658319)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (658326)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2973825592:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.28 % (658326) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-658319-658326"...
% 0.22/0.28 % (658326)...printing done.
% 0.22/0.28 % (658326)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (658326)------------------------------
% 0.22/0.28 % (658326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (658326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (658326)CaDiCaL version: 2.1.3
% 0.22/0.28 % (658326)Termination reason: Refutation
% 0.22/0.28 % (658326)Time elapsed: 0.002 s
% 0.22/0.28 % (658326)Peak memory usage: 12 MB
% 0.22/0.28 % (658326)Instructions burned: 2 (million)
% 0.22/0.28 % (658319)Success in time 0.032 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------