%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM654^1 : 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 : n008.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 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 37 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 108 ( 27 ~; 9 |; 1 &; 58 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 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,
more: nat > nat > $o ).
thf(func_def_4,type,
less: nat > nat > $o ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(f1,axiom,
~ ( more @ x @ y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(f3,axiom,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ( more @ X0 @ X1 )
=> ( less @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10a) ).
thf(f4,conjecture,
( ~ ( less @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10e) ).
thf(f5,negated_conjecture,
~ ( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
~ ( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
~ ( ( ( less @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ( more @ X0 @ X1 )
=> ( less @ X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f9,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( ( more @ X0 @ X1 )
!= $true )
=> ( ( less @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f12,plain,
~ ( more @ x @ y ),
inference(rectify,[],[f1]) ).
thf(f13,plain,
( ( more @ x @ y )
!= $true ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
~ ( ( ( less @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[],[f7]) ).
thf(f15,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( ( more @ X0 @ X1 )
!= $true )
=> ( ( less @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[],[f9]) ).
thf(f17,plain,
( ( more @ x @ y )
!= $true ),
inference(flattening,[],[f13]) ).
thf(f19,plain,
( ( x != y )
& ( ( less @ x @ y )
!= $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f20,plain,
! [X0: nat,X1: nat] :
( ( ( less @ X0 @ X1 )
= $true )
| ( ( more @ X0 @ X1 )
= $true )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f21,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X0 @ X1 )
= $true )
| ( ( less @ X0 @ X1 )
= $true )
| ( X0 = X1 ) ),
inference(flattening,[],[f20]) ).
thf(f22,plain,
( ( less @ x @ y )
!= $true ),
inference(cnf_transformation,[],[f19]) ).
thf(f23,plain,
x != y,
inference(cnf_transformation,[],[f19]) ).
thf(f24,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X0 @ X1 )
= $true )
| ( X0 = X1 )
| ( ( less @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f25,plain,
( ( more @ x @ y )
!= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f30,plain,
( ( ( less @ x @ y )
= $true )
| ( x = y )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f25,f24]) ).
thf(f31,plain,
( ( x = y )
| ( ( less @ x @ y )
= $true ) ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f32,plain,
( ( less @ x @ y )
= $true ),
inference(forward_subsumption_resolution,[],[f31,f23]) ).
thf(f33,plain,
$false,
inference(forward_subsumption_resolution,[],[f32,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM654^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n008.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 12:32:54 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.18/0.27 % (3078673)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.27 % (3078678)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1858739510:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.18/0.27 % (3078678) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3078673-3078678"...
% 0.18/0.27 % (3078678)...printing done.
% 0.18/0.27 % (3078678)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (3078678)------------------------------
% 0.18/0.27 % (3078678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (3078678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (3078678)CaDiCaL version: 2.1.3
% 0.18/0.27 % (3078678)Termination reason: Refutation
% 0.18/0.27 % (3078678)Time elapsed: 0.001 s
% 0.18/0.27 % (3078678)Peak memory usage: 12 MB
% 0.18/0.27 % (3078678)Instructions burned: 1 (million)
% 0.18/0.27 % (3078673)Success in time 0.029 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------