%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM784^1 : 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 : n016.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 08:18:52 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 14 unt; 0 typ; 2 def)
% Number of atoms : 196 ( 54 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 264 ( 71 ~; 19 |; 6 &; 142 @)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 12 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
rat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x0: rat ).
thf(func_def_1,type,
y0: rat ).
thf(func_def_2,type,
more: rat > rat > $o ).
thf(func_def_3,type,
is: rat > rat > $o ).
thf(func_def_5,type,
less: rat > rat > $o ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(f1,axiom,
( ~ ( more @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(f3,axiom,
! [X1: rat,X0: rat] :
~ ( ( ( is @ X0 @ X1 )
=> ~ ( more @ X0 @ X1 ) )
=> ~ ~ ( ( ( more @ X0 @ X1 )
=> ~ ( less @ X0 @ X1 ) )
=> ~ ( ( less @ X0 @ X1 )
=> ~ ( is @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz81b) ).
thf(f4,conjecture,
~ ( less @ x0 @ y0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz81c) ).
thf(f5,negated_conjecture,
~ ~ ( less @ x0 @ y0 ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
! [X0: rat,X1: rat] :
~ ( ( ( is @ X1 @ X0 )
=> ~ ( more @ X1 @ X0 ) )
=> ~ ~ ( ( ( more @ X1 @ X0 )
=> ~ ( less @ X1 @ X0 ) )
=> ~ ( ( less @ X1 @ X0 )
=> ~ ( is @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
! [X0: rat,X1: rat] :
~ ( ( ( $true
= ( is @ X1 @ X0 ) )
=> ( ( more @ X1 @ X0 )
!= $true ) )
=> ~ ~ ( ( ( ( more @ X1 @ X0 )
= $true )
=> ( ( less @ X1 @ X0 )
!= $true ) )
=> ~ ( ( ( less @ X1 @ X0 )
= $true )
=> ( $true
!= ( is @ X1 @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f10,plain,
( ~ ( more @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( ( ( more @ x0 @ y0 )
!= $true )
=> ( ( is @ x0 @ y0 )
= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
~ ~ ( less @ x0 @ y0 ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
~ ( ( ( less @ x0 @ y0 )
!= $true ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
! [X1: rat,X0: rat] :
~ ( ( ( $true
= ( is @ X1 @ X0 ) )
=> ( ( more @ X1 @ X0 )
!= $true ) )
=> ( ( ( ( more @ X1 @ X0 )
= $true )
=> ( ( less @ X1 @ X0 )
!= $true ) )
=> ~ ( ( ( less @ X1 @ X0 )
= $true )
=> ( $true
!= ( is @ X1 @ X0 ) ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f16,plain,
( ( ( more @ x0 @ y0 )
!= $true )
=> ( ( is @ x0 @ y0 )
= $true ) ),
inference(flattening,[],[f11]) ).
thf(f17,plain,
( ( less @ x0 @ y0 )
= $true ),
inference(flattening,[],[f13]) ).
thf(f18,plain,
! [X1: rat,X0: rat] :
( ( ( $true
!= ( is @ X1 @ X0 ) )
| ( ( less @ X1 @ X0 )
!= $true ) )
& ( ( ( less @ X1 @ X0 )
!= $true )
| ( ( more @ X1 @ X0 )
!= $true ) )
& ( ( $true
!= ( is @ X1 @ X0 ) )
| ( ( more @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f19,plain,
! [X1: rat,X0: rat] :
( ( ( ( less @ X1 @ X0 )
!= $true )
| ( ( more @ X1 @ X0 )
!= $true ) )
& ( ( $true
!= ( is @ X1 @ X0 ) )
| ( ( more @ X1 @ X0 )
!= $true ) )
& ( ( $true
!= ( is @ X1 @ X0 ) )
| ( ( less @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[],[f18]) ).
thf(f21,plain,
( ( ( more @ x0 @ y0 )
= $true )
| ( ( is @ x0 @ y0 )
= $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f22,plain,
! [X0: rat,X1: rat] :
( ( ( ( less @ X0 @ X1 )
!= $true )
| ( ( more @ X0 @ X1 )
!= $true ) )
& ( ( ( is @ X0 @ X1 )
!= $true )
| ( ( more @ X0 @ X1 )
!= $true ) )
& ( ( ( is @ X0 @ X1 )
!= $true )
| ( ( less @ X0 @ X1 )
!= $true ) ) ),
inference(rectify,[],[f19]) ).
thf(f23,plain,
! [X0: rat,X1: rat] :
( ( ( less @ X0 @ X1 )
!= $true )
| ( ( is @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f25,plain,
! [X0: rat,X1: rat] :
( ( ( less @ X0 @ X1 )
!= $true )
| ( ( more @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f26,plain,
( ( ( more @ x0 @ y0 )
= $true )
| ( ( is @ x0 @ y0 )
= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f28,plain,
( ( less @ x0 @ y0 )
= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f33,definition,
( spl0_1
<=> ( ( more @ x0 @ y0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f35,plain,
( ( ( more @ x0 @ y0 )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f37,definition,
( spl0_2
<=> ( ( is @ x0 @ y0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f40,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f26,f37,f33]) ).
thf(f41,plain,
( ( $true != $true )
| ( ( is @ x0 @ y0 )
!= $true ) ),
inference(constrained_superposition,[],[f23,f28]) ).
thf(f42,plain,
( ( is @ x0 @ y0 )
!= $true ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f45,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f42,f37]) ).
thf(f46,plain,
( ( ( more @ x0 @ y0 )
!= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f25,f28]) ).
thf(f47,plain,
( ( more @ x0 @ y0 )
!= $true ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f48,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f47,f35]) ).
thf(f49,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f48]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f40]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f45]) ).
cnf(s4,plain,
~ spl0_1,
inference(sat_conversion,[],[f49]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
thf(f50,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM784^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n016.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:00:35 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.21 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
% 0.09/0.25 % (302316)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.25 % (302321)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3778732056:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.09/0.25 % (302321) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-302316-302321"...
% 0.09/0.25 % (302321)...printing done.
% 0.09/0.25 % (302321)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.25 % (302321)------------------------------
% 0.09/0.25 % (302321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (302321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (302321)CaDiCaL version: 2.1.3
% 0.09/0.25 % (302321)Termination reason: Refutation
% 0.09/0.25 % (302321)Time elapsed: 0.002 s
% 0.09/0.25 % (302321)Peak memory usage: 13 MB
% 0.09/0.25 % (302321)Instructions burned: 3 (million)
% 0.09/0.25 % (302316)Success in time 0.025 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------