%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM653^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:18:24 AM UTC 2026
% Result : Theorem 0.25s 0.34s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 129 ( 53 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 184 ( 57 ~; 13 |; 4 &; 86 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% 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(f1,axiom,
( ~ ( less @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
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/sandbox2/benchmark/theBenchmark.p',satz10b) ).
thf(f4,conjecture,
~ ( more @ x @ y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10d) ).
thf(f5,negated_conjecture,
~ ~ ( more @ x @ y ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( ( ( less @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[],[f6]) ).
thf(f10,plain,
~ ~ ( more @ x @ y ),
inference(rectify,[],[f5]) ).
thf(f11,plain,
~ ( ( ( more @ x @ y )
!= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,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(f13,plain,
! [X0: nat,X1: nat] :
~ ( ( ( X0 = X1 )
=> ( ( more @ X1 @ X0 )
!= $true ) )
=> ~ ~ ( ( ( ( more @ X1 @ X0 )
= $true )
=> ( $true
!= ( less @ X1 @ X0 ) ) )
=> ~ ( ( $true
= ( less @ X1 @ X0 ) )
=> ( X0 != X1 ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ( ( less @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[],[f7]) ).
thf(f16,plain,
( ( more @ x @ y )
= $true ),
inference(flattening,[],[f11]) ).
thf(f17,plain,
! [X1: nat,X0: nat] :
~ ( ( ( X0 = X1 )
=> ( ( more @ X1 @ X0 )
!= $true ) )
=> ( ( ( ( more @ X1 @ X0 )
= $true )
=> ( $true
!= ( less @ X1 @ X0 ) ) )
=> ~ ( ( $true
= ( less @ X1 @ X0 ) )
=> ( X0 != X1 ) ) ) ),
inference(flattening,[],[f13]) ).
thf(f18,plain,
! [X1: nat,X0: nat] :
( ( ( $true
!= ( less @ X1 @ X0 ) )
| ( X0 != X1 ) )
& ( ( $true
!= ( less @ X1 @ X0 ) )
| ( ( more @ X1 @ X0 )
!= $true ) )
& ( ( ( more @ X1 @ X0 )
!= $true )
| ( X0 != X1 ) ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f19,plain,
! [X0: nat,X1: nat] :
( ( ( $true
!= ( less @ X1 @ X0 ) )
| ( X0 != X1 ) )
& ( ( $true
!= ( less @ X1 @ X0 ) )
| ( ( more @ X1 @ X0 )
!= $true ) )
& ( ( ( more @ X1 @ X0 )
!= $true )
| ( X0 != X1 ) ) ),
inference(flattening,[],[f18]) ).
thf(f20,plain,
( ( ( less @ x @ y )
= $true )
| ( x = y ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f22,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X1 @ X0 )
!= $true )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f23,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( less @ X1 @ X0 ) )
| ( ( more @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f26,plain,
( ( more @ x @ y )
= $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f27,plain,
( ( ( less @ x @ y )
= $true )
| ( x = y ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f30,plain,
! [X1: nat] :
( ( more @ X1 @ X1 )
!= $true ),
inference(equality_resolution,[],[f22]) ).
thf(f32,plain,
( ( x = y )
| ( $true != $true )
| ( ( more @ x @ y )
!= $true ) ),
inference(superposition,[],[f23,f27]) ).
thf(f33,plain,
( ( ( more @ x @ y )
!= $true )
| ( x = y ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f34,plain,
x = y,
inference(forward_subsumption_resolution,[],[f33,f26]) ).
thf(f35,plain,
( $true
= ( more @ y @ y ) ),
inference(superposition,[],[f26,f34]) ).
thf(f36,plain,
$false,
inference(forward_subsumption_resolution,[],[f35,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM653^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.25 % Computer : n013.cluster.edu
% 0.12/0.25 % Model : x86_64 x86_64
% 0.12/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.25 % Memory : 8046.5625MB
% 0.12/0.25 % OS : Linux 6.8.0-71-generic
% 0.12/0.25 % CPULimit : 300
% 0.12/0.25 % WCLimit : 300
% 0.12/0.25 % DateTime : Tue Sep 29 12:31:22 UTC 2026
% 0.12/0.25 % CPUTime :
% 0.12/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.29 Running higher-order theorem proving
% 0.12/0.30 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.25/0.34 % (2032099)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.34 % (2032108)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2782994759:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.25/0.34 % (2032108) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2032099-2032108"...
% 0.25/0.34 % (2032108)...printing done.
% 0.25/0.34 % (2032108)Refutation found. Thanks to Tanya!
% 0.25/0.34 % SZS status Theorem for theBenchmark
% 0.25/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.34 % (2032108)------------------------------
% 0.25/0.34 % (2032108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.34 % (2032108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.34 % (2032108)CaDiCaL version: 2.1.3
% 0.25/0.34 % (2032108)Termination reason: Refutation
% 0.25/0.34 % (2032108)Time elapsed: 0.002 s
% 0.25/0.34 % (2032108)Peak memory usage: 12 MB
% 0.25/0.34 % (2032108)Instructions burned: 2 (million)
% 0.25/0.34 % (2032099)Success in time 0.024 s
% 0.25/0.34 % Vampire exiting
%------------------------------------------------------------------------------