%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM657^1 : 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 : n017.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 08:18:25 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 166 ( 60 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 227 ( 75 ~; 23 |; 6 &; 96 @)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 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 : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?; 19 :)
% 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,
more: nat > nat > $o ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(f1,axiom,
less @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(f3,axiom,
! [X0: nat,X1: 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(f4,conjecture,
~ ( ~ ( more @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10h) ).
thf(f5,negated_conjecture,
~ ~ ( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f8,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ~ ( more @ X0 @ X1 ) )
=> ~ ~ ( ( ( more @ X0 @ X1 )
=> ~ ( less @ X0 @ X1 ) )
=> ~ ( ( less @ X0 @ X1 )
=> ( X0 != X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f9,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ( ( more @ X0 @ X1 )
!= $true ) )
=> ~ ~ ( ( ( ( more @ X0 @ X1 )
= $true )
=> ( ( less @ X0 @ X1 )
!= $true ) )
=> ~ ( ( ( less @ X0 @ X1 )
= $true )
=> ( X0 != X1 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ~ ( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(rectify,[],[f5]) ).
thf(f11,plain,
~ ~ ( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
less @ x @ y,
inference(rectify,[],[f1]) ).
thf(f13,plain,
( ( less @ x @ y )
= $true ),
inference(fool_elimination,[],[f12]) ).
thf(f15,plain,
! [X1: nat,X0: nat] :
~ ( ( ( X0 = X1 )
=> ( ( more @ X0 @ X1 )
!= $true ) )
=> ( ( ( ( more @ X0 @ X1 )
= $true )
=> ( ( less @ X0 @ X1 )
!= $true ) )
=> ~ ( ( ( less @ X0 @ X1 )
= $true )
=> ( X0 != X1 ) ) ) ),
inference(flattening,[],[f9]) ).
thf(f16,plain,
( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[],[f11]) ).
thf(f17,plain,
! [X1: nat,X0: nat] :
( ( ( X0 != X1 )
| ( ( less @ X0 @ X1 )
!= $true ) )
& ( ( ( less @ X0 @ X1 )
!= $true )
| ( ( more @ X0 @ X1 )
!= $true ) )
& ( ( ( more @ X0 @ X1 )
!= $true )
| ( X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f18,plain,
! [X1: nat,X0: nat] :
( ( ( ( more @ X0 @ X1 )
!= $true )
| ( X0 != X1 ) )
& ( ( X0 != X1 )
| ( ( less @ X0 @ X1 )
!= $true ) )
& ( ( ( less @ X0 @ X1 )
!= $true )
| ( ( more @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( ( more @ x @ y )
= $true )
| ( x = y ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f21,plain,
! [X0: nat,X1: nat] :
( ( ( $true
!= ( more @ X1 @ X0 ) )
| ( X0 != X1 ) )
& ( ( X0 != X1 )
| ( $true
!= ( less @ X1 @ X0 ) ) )
& ( ( $true
!= ( less @ X1 @ X0 ) )
| ( $true
!= ( more @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f23,plain,
( ( ( more @ x @ y )
= $true )
| ( x = y ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f24,plain,
( ( less @ x @ y )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f25,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( more @ X1 @ X0 ) )
| ( $true
!= ( less @ X1 @ X0 ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f26,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true
!= ( less @ X1 @ X0 ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f32,plain,
! [X1: nat] :
( $true
!= ( less @ X1 @ X1 ) ),
inference(equality_resolution,[],[f26]) ).
thf(f34,definition,
( spl0_1
<=> ( ( more @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f35,plain,
( ( ( more @ x @ y )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f37,definition,
( spl0_2
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f38,plain,
( ( x = y )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f39,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f23,f37,f34]) ).
thf(f40,plain,
( ( ( less @ y @ y )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f24,f38]) ).
thf(f41,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f40,f32]) ).
thf(f42,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f41]) ).
thf(f58,plain,
( ( ( less @ x @ y )
!= $true )
| ( $true != $true )
| ~ spl0_1 ),
inference(constrained_superposition,[],[f25,f35]) ).
thf(f62,plain,
( ( ( less @ x @ y )
!= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f63,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f62,f24]) ).
thf(f64,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f63]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f39]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f42]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f64]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f65,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM657^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n017.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 12:27:52 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 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
% 0.07/0.26 % (273733)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.26 % (273743)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=205051457:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.07/0.26 % (273743) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-273733-273743"...
% 0.07/0.26 % (273743)...printing done.
% 0.07/0.26 % (273743)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.26 % (273743)------------------------------
% 0.07/0.26 % (273743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (273743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (273743)CaDiCaL version: 2.1.3
% 0.07/0.26 % (273743)Termination reason: Refutation
% 0.07/0.26 % (273743)Time elapsed: 0.002 s
% 0.07/0.26 % (273743)Peak memory usage: 13 MB
% 0.07/0.26 % (273743)Instructions burned: 3 (million)
% 0.07/0.26 % (273733)Success in time 0.026 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------