%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM680^1 : 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 : n015.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 08:18:31 AM UTC 2026
% Result : Theorem 0.06s 0.25s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 17 unt; 0 typ; 2 def)
% Number of atoms : 258 ( 89 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 381 ( 85 ~; 39 |; 6 &; 218 @)
% ( 2 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 57 !; 0 ?; 57 :)
% 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,
z: nat ).
thf(func_def_3,type,
more: nat > nat > $o ).
thf(func_def_4,type,
pl: nat > nat > nat ).
thf(func_def_6,type,
less: nat > nat > $o ).
thf(func_def_9,type,
vNOT: $o > $o ).
thf(f1,axiom,
more @ ( pl @ x @ z ) @ ( pl @ y @ z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(f3,axiom,
! [X1: nat,X0: nat] :
~ ( ( ( X0 = X1 )
=> ~ ( more @ X0 @ X1 ) )
=> ~ ~ ( ( ( more @ X0 @ X1 )
=> ~ ( less @ X0 @ X1 ) )
=> ~ ( ( less @ X0 @ X1 )
=> ( X0 != X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10b) ).
thf(f5,axiom,
! [X1: nat,X2: nat,X0: nat] :
( ( less @ X0 @ X1 )
=> ( less @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19c) ).
thf(f6,axiom,
! [X1: nat,X0: nat] :
( ( X0 != X1 )
=> ( ~ ( more @ X0 @ X1 )
=> ( less @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10a) ).
thf(f7,conjecture,
more @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz20a) ).
thf(f8,negated_conjecture,
~ ( more @ x @ y ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
more @ ( pl @ x @ z ) @ ( pl @ y @ z ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( less @ X2 @ X0 )
=> ( less @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) ) ),
inference(rectify,[],[f5]) ).
thf(f12,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
= ( less @ X2 @ X0 ) )
=> ( ( less @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) )
= $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
~ ( more @ x @ y ),
inference(rectify,[],[f8]) ).
thf(f14,plain,
( ( more @ x @ y )
!= $true ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ~ ( more @ X1 @ X0 ) )
=> ~ ~ ( ( ( more @ X1 @ X0 )
=> ~ ( less @ X1 @ X0 ) )
=> ~ ( ( less @ X1 @ X0 )
=> ( X0 != X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f16,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ( $true
!= ( more @ X1 @ X0 ) ) )
=> ~ ~ ( ( ( $true
= ( more @ X1 @ X0 ) )
=> ( $true
!= ( less @ X1 @ X0 ) ) )
=> ~ ( ( $true
= ( less @ X1 @ X0 ) )
=> ( X0 != X1 ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f19,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ( more @ X1 @ X0 )
=> ( less @ X1 @ X0 ) ) ),
inference(rectify,[],[f6]) ).
thf(f20,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( $true
!= ( more @ X1 @ X0 ) )
=> ( $true
= ( less @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
( ( more @ x @ y )
!= $true ),
inference(flattening,[],[f14]) ).
thf(f22,plain,
! [X1: nat,X0: nat] :
~ ( ( ( X0 = X1 )
=> ( $true
!= ( more @ X1 @ X0 ) ) )
=> ( ( ( $true
= ( more @ X1 @ X0 ) )
=> ( $true
!= ( less @ X1 @ X0 ) ) )
=> ~ ( ( $true
= ( less @ X1 @ X0 ) )
=> ( X0 != X1 ) ) ) ),
inference(flattening,[],[f16]) ).
thf(f25,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( $true
!= ( more @ X1 @ X0 ) )
=> ( $true
= ( less @ X1 @ X0 ) ) ) ),
inference(flattening,[],[f20]) ).
thf(f28,plain,
! [X1: nat,X0: nat,X2: nat] :
( ( ( less @ ( pl @ X2 @ X1 ) @ ( pl @ X0 @ X1 ) )
= $true )
| ( $true
!= ( less @ X2 @ X0 ) ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f29,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( less @ X1 @ X0 ) )
| ( $true
= ( more @ X1 @ X0 ) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f25]) ).
thf(f30,plain,
! [X1: nat,X0: nat] :
( ( X0 = X1 )
| ( $true
= ( more @ X1 @ X0 ) )
| ( $true
= ( less @ X1 @ X0 ) ) ),
inference(flattening,[],[f29]) ).
thf(f31,plain,
! [X1: nat,X0: nat] :
( ( ( X0 != X1 )
| ( $true
!= ( less @ X1 @ X0 ) ) )
& ( ( $true
!= ( more @ X1 @ X0 ) )
| ( $true
!= ( less @ X1 @ X0 ) ) )
& ( ( $true
!= ( more @ X1 @ X0 ) )
| ( X0 != X1 ) ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f32,plain,
! [X1: nat,X0: nat] :
( ( ( $true
!= ( more @ X1 @ X0 ) )
| ( $true
!= ( less @ X1 @ X0 ) ) )
& ( ( $true
!= ( more @ X1 @ X0 ) )
| ( X0 != X1 ) )
& ( ( X0 != X1 )
| ( $true
!= ( less @ X1 @ X0 ) ) ) ),
inference(flattening,[],[f31]) ).
thf(f33,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
= ( less @ ( pl @ X2 @ X0 ) @ ( pl @ X1 @ X0 ) ) )
| ( $true
!= ( less @ X2 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f34,plain,
! [X0: nat,X1: nat] :
( ( ( ( more @ X0 @ X1 )
!= $true )
| ( ( less @ X0 @ X1 )
!= $true ) )
& ( ( ( more @ X0 @ X1 )
!= $true )
| ( X0 != X1 ) )
& ( ( X0 != X1 )
| ( ( less @ X0 @ X1 )
!= $true ) ) ),
inference(rectify,[],[f32]) ).
thf(f35,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( ( more @ X0 @ X1 )
= $true )
| ( ( less @ X0 @ X1 )
= $true ) ),
inference(rectify,[],[f30]) ).
thf(f37,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
!= ( less @ X2 @ X1 ) )
| ( $true
= ( less @ ( pl @ X2 @ X0 ) @ ( pl @ X1 @ X0 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f38,plain,
( ( more @ x @ y )
!= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f40,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X0 @ X1 )
!= $true )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f41,plain,
! [X0: nat,X1: nat] :
( ( ( less @ X0 @ X1 )
!= $true )
| ( ( more @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f42,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f44,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X0 @ X1 )
= $true )
| ( ( less @ X0 @ X1 )
= $true )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f48,plain,
! [X1: nat] :
( $true
!= ( more @ X1 @ X1 ) ),
inference(equality_resolution,[],[f40]) ).
thf(f52,plain,
( ( x = y )
| ( $true
= ( less @ x @ y ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f38,f44]) ).
thf(f53,plain,
( ( x = y )
| ( $true
= ( less @ x @ y ) ) ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f55,definition,
( spl0_1
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f57,plain,
( ( x = y )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f59,definition,
( spl0_2
<=> ( $true
= ( less @ x @ y ) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f61,plain,
( ( $true
= ( less @ x @ y ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f62,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f53,f59,f55]) ).
thf(f65,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( ( less @ ( pl @ x @ X0 ) @ ( pl @ y @ X0 ) )
= $true ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f37,f61]) ).
thf(f66,plain,
( ! [X0: nat] :
( ( less @ ( pl @ x @ X0 ) @ ( pl @ y @ X0 ) )
= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f65]) ).
thf(f68,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true
!= ( more @ ( pl @ x @ X0 ) @ ( pl @ y @ X0 ) ) ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f41,f66]) ).
thf(f69,plain,
( ! [X0: nat] :
( $true
!= ( more @ ( pl @ x @ X0 ) @ ( pl @ y @ X0 ) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f72,plain,
( ( $true != $true )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f69,f42]) ).
thf(f74,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f75,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f74]) ).
thf(f76,plain,
( ( $true
= ( more @ ( pl @ x @ z ) @ ( pl @ x @ z ) ) )
| ~ spl0_1 ),
inference(constrained_superposition,[],[f42,f57]) ).
thf(f78,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f76,f48]) ).
thf(f79,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f78]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f62]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f75]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f79]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f80,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM680^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n015.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 12:39:18 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.20 Running higher-order theorem proving
% 0.06/0.21 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
% 0.06/0.25 % (3460583)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.06/0.25 % (3460588)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=936254473:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.06/0.25 % (3460588) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3460583-3460588"...
% 0.06/0.25 % (3460588)...printing done.
% 0.06/0.25 % (3460588)Refutation found. Thanks to Tanya!
% 0.06/0.25 % SZS status Theorem for theBenchmark
% 0.06/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.25 % (3460588)------------------------------
% 0.06/0.25 % (3460588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.25 % (3460588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.25 % (3460588)CaDiCaL version: 2.1.3
% 0.06/0.25 % (3460588)Termination reason: Refutation
% 0.06/0.25 % (3460588)Time elapsed: 0.002 s
% 0.06/0.25 % (3460588)Peak memory usage: 13 MB
% 0.06/0.25 % (3460588)Instructions burned: 5 (million)
% 0.06/0.25 % (3460583)Success in time 0.029 s
% 0.06/0.25 % Vampire exiting
%------------------------------------------------------------------------------