%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM660^1 : 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 : n026.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 08:18:26 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 103 ( 35 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 114 ( 29 ~; 12 |; 1 &; 58 @)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 12 !; 0 ?; 12 :)
% 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(f1,axiom,
( ~ ( more @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(f2,axiom,
! [X0: nat,X1: nat] :
( ( more @ X0 @ X1 )
=> ( less @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz11) ).
thf(f3,conjecture,
( ~ ( less @ y @ x )
=> ( y = x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13) ).
thf(f4,negated_conjecture,
~ ( ~ ( less @ y @ x )
=> ( y = x ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: nat,X1: nat] :
( ( more @ X0 @ X1 )
=> ( less @ X1 @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
! [X0: nat,X1: nat] :
( ( ( more @ X0 @ X1 )
= $true )
=> ( ( less @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( ~ ( less @ y @ x )
=> ( y = x ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( ( less @ y @ x )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( ( more @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[],[f6]) ).
thf(f12,plain,
~ ( ( ( less @ y @ x )
!= $true )
=> ( x = y ) ),
inference(flattening,[],[f10]) ).
thf(f13,plain,
! [X1: nat,X0: nat] :
( ( ( less @ X1 @ X0 )
= $true )
| ( ( more @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f14,plain,
( ( ( less @ y @ x )
!= $true )
& ( x != y ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f15,plain,
( ( x = y )
| ( ( more @ x @ y )
= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f16,plain,
! [X0: nat,X1: nat] :
( ( ( less @ X0 @ X1 )
= $true )
| ( $true
!= ( more @ X1 @ X0 ) ) ),
inference(rectify,[],[f13]) ).
thf(f17,plain,
( ( x = y )
| ( ( more @ x @ y )
= $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f18,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( more @ X1 @ X0 ) )
| ( ( less @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f19,plain,
x != y,
inference(cnf_transformation,[],[f14]) ).
thf(f20,plain,
( ( less @ y @ x )
!= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f24,definition,
( spl0_1
<=> ( ( more @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f26,plain,
( ( ( more @ x @ y )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f28,definition,
( spl0_2
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f31,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f17,f28,f24]) ).
thf(f32,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f19,f28]) ).
thf(f33,plain,
( ( ( less @ y @ x )
= $true )
| ( $true != $true )
| ~ spl0_1 ),
inference(constrained_superposition,[],[f18,f26]) ).
thf(f34,plain,
( ( ( less @ y @ x )
= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f35,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f34,f20]) ).
thf(f36,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f35]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f32]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f36]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f37,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM660^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 12:35:43 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.08/0.26 % (533239)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.26 % (533245)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=293843714:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.26 % (533245) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-533239-533245"...
% 0.08/0.26 % (533245)...printing done.
% 0.08/0.26 % (533245)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (533245)------------------------------
% 0.08/0.26 % (533245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (533245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (533245)CaDiCaL version: 2.1.3
% 0.08/0.26 % (533245)Termination reason: Refutation
% 0.08/0.26 % (533245)Time elapsed: 0.001 s
% 0.08/0.26 % (533245)Peak memory usage: 12 MB
% 0.08/0.26 % (533245)Instructions burned: 1 (million)
% 0.08/0.26 % (533239)Success in time 0.016 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------