%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM663^1 : 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 : 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 08:18:27 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 16 unt; 0 typ; 2 def)
% Number of atoms : 149 ( 43 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 164 ( 35 ~; 25 |; 0 &; 92 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 23 !; 0 ?; 23 :)
% 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,
less: nat > nat > $o ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(f1,axiom,
( ~ ( less @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(f2,axiom,
less @ y @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(f4,axiom,
! [X2: nat,X1: nat,X0: nat] :
( ( less @ X0 @ X1 )
=> ( ( less @ X1 @ X2 )
=> ( less @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz15) ).
thf(f5,conjecture,
less @ x @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16a) ).
thf(f6,negated_conjecture,
~ ( less @ x @ z ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( ( ( less @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( less @ X2 @ X1 )
=> ( ( less @ X1 @ X0 )
=> ( less @ X2 @ X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
! [X0: nat,X2: nat,X1: nat] :
( ( ( less @ X2 @ X1 )
= $true )
=> ( ( ( less @ X1 @ X0 )
= $true )
=> ( ( less @ X2 @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f13,plain,
less @ y @ z,
inference(rectify,[],[f2]) ).
thf(f14,plain,
( ( less @ y @ z )
= $true ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
~ ( less @ x @ z ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
( ( less @ x @ z )
!= $true ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ( ( less @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[],[f8]) ).
thf(f19,plain,
( ( less @ x @ z )
!= $true ),
inference(flattening,[],[f16]) ).
thf(f20,plain,
( ( ( less @ x @ y )
= $true )
| ( x = y ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f21,plain,
! [X0: nat,X2: nat,X1: nat] :
( ( ( less @ X2 @ X0 )
= $true )
| ( ( less @ X1 @ X0 )
!= $true )
| ( ( less @ X2 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f22,plain,
! [X1: nat,X2: nat,X0: nat] :
( ( ( less @ X2 @ X0 )
= $true )
| ( ( less @ X2 @ X1 )
!= $true )
| ( ( less @ X1 @ X0 )
!= $true ) ),
inference(flattening,[],[f21]) ).
thf(f24,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( less @ X1 @ X2 )
= $true )
| ( ( less @ X1 @ X0 )
!= $true )
| ( ( less @ X0 @ X2 )
!= $true ) ),
inference(rectify,[],[f22]) ).
thf(f26,plain,
( ( less @ x @ z )
!= $true ),
inference(cnf_transformation,[],[f19]) ).
thf(f27,plain,
( ( less @ y @ z )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f28,plain,
( ( ( less @ x @ y )
= $true )
| ( x = y ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f29,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( less @ X1 @ X0 )
!= $true )
| ( ( less @ X0 @ X2 )
!= $true )
| ( ( less @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f34,definition,
( spl0_1
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f36,plain,
( ( x = y )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f38,definition,
( spl0_2
<=> ( ( less @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f40,plain,
( ( ( less @ x @ y )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f38]) ).
thf(f41,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f28,f38,f34]) ).
thf(f43,plain,
( ! [X0: nat] :
( ( $true
!= ( less @ y @ X0 ) )
| ( $true != $true )
| ( $true
= ( less @ x @ X0 ) ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f29,f40]) ).
thf(f44,plain,
( ! [X0: nat] :
( ( $true
!= ( less @ y @ X0 ) )
| ( $true
= ( less @ x @ X0 ) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f43]) ).
thf(f46,plain,
( ( ( less @ x @ z )
= $true )
| ( $true != $true )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f44,f27]) ).
thf(f47,plain,
( ( ( less @ x @ z )
= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f48,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f47,f26]) ).
thf(f49,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f48]) ).
thf(f50,plain,
( ( ( less @ y @ z )
!= $true )
| ~ spl0_1 ),
inference(constrained_superposition,[],[f26,f36]) ).
thf(f51,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f50,f27]) ).
thf(f52,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f51]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f41]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f49]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f52]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f53,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM663^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 12:36:33 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.23/0.29 % (3457556)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (3457565)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3306386628:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.29 % (3457565) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3457556-3457565"...
% 0.23/0.29 % (3457565)...printing done.
% 0.23/0.29 % (3457565)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.29 % (3457565)------------------------------
% 0.23/0.29 % (3457565)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (3457565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (3457565)CaDiCaL version: 2.1.3
% 0.23/0.29 % (3457565)Termination reason: Refutation
% 0.23/0.29 % (3457565)Time elapsed: 0.003 s
% 0.23/0.29 % (3457565)Peak memory usage: 13 MB
% 0.23/0.29 % (3457565)Instructions burned: 2 (million)
% 0.23/0.29 % (3457556)Success in time 0.03 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------