%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM788^1 : 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 : n017.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 08:18:53 AM UTC 2026
% Result : Theorem 0.23s 0.28s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 204 ( 54 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 280 ( 78 ~; 25 |; 6 &; 144 @)
% ( 2 <=>; 25 =>; 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_4,type,
less: rat > rat > $o ).
thf(func_def_5,type,
is: rat > rat > $o ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(f1,axiom,
more @ x0 @ y0,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',satz81b) ).
thf(f4,conjecture,
~ ( ~ ( less @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz81g) ).
thf(f5,negated_conjecture,
~ ~ ( ~ ( less @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
more @ x0 @ y0,
inference(rectify,[],[f1]) ).
thf(f7,plain,
( ( more @ x0 @ y0 )
= $true ),
inference(fool_elimination,[],[f6]) ).
thf(f10,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(f11,plain,
! [X0: rat,X1: rat] :
~ ( ( ( $true
= ( is @ X1 @ X0 ) )
=> ( ( more @ X1 @ X0 )
!= $true ) )
=> ~ ~ ( ( ( ( more @ X1 @ X0 )
= $true )
=> ( $true
!= ( less @ X1 @ X0 ) ) )
=> ~ ( ( $true
= ( less @ X1 @ X0 ) )
=> ( $true
!= ( is @ X1 @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
~ ~ ( ~ ( less @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
~ ~ ( ( ( less @ x0 @ y0 )
!= $true )
=> ( ( is @ x0 @ y0 )
= $true ) ),
inference(fool_elimination,[],[f12]) ).
thf(f15,plain,
! [X0: rat,X1: rat] :
~ ( ( ( $true
= ( is @ X1 @ X0 ) )
=> ( ( more @ X1 @ X0 )
!= $true ) )
=> ( ( ( ( more @ X1 @ X0 )
= $true )
=> ( $true
!= ( less @ X1 @ X0 ) ) )
=> ~ ( ( $true
= ( less @ X1 @ X0 ) )
=> ( $true
!= ( is @ X1 @ X0 ) ) ) ) ),
inference(flattening,[],[f11]) ).
thf(f16,plain,
( ( ( less @ x0 @ y0 )
!= $true )
=> ( ( is @ x0 @ y0 )
= $true ) ),
inference(flattening,[],[f13]) ).
thf(f17,plain,
( ( ( less @ x0 @ y0 )
= $true )
| ( ( is @ x0 @ y0 )
= $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f19,plain,
! [X0: rat,X1: rat] :
( ( ( $true
!= ( less @ X1 @ X0 ) )
| ( $true
!= ( is @ X1 @ X0 ) ) )
& ( ( ( more @ X1 @ X0 )
!= $true )
| ( $true
!= ( less @ X1 @ X0 ) ) )
& ( ( ( more @ X1 @ X0 )
!= $true )
| ( $true
!= ( is @ X1 @ X0 ) ) ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f20,plain,
! [X1: rat,X0: rat] :
( ( ( $true
!= ( less @ X1 @ X0 ) )
| ( $true
!= ( is @ X1 @ X0 ) ) )
& ( ( ( more @ X1 @ X0 )
!= $true )
| ( $true
!= ( is @ X1 @ X0 ) ) )
& ( ( ( more @ X1 @ X0 )
!= $true )
| ( $true
!= ( less @ X1 @ X0 ) ) ) ),
inference(flattening,[],[f19]) ).
thf(f21,plain,
! [X0: rat,X1: rat] :
( ( ( ( less @ X0 @ X1 )
!= $true )
| ( ( is @ X0 @ X1 )
!= $true ) )
& ( ( ( more @ X0 @ X1 )
!= $true )
| ( ( is @ X0 @ X1 )
!= $true ) )
& ( ( ( more @ X0 @ X1 )
!= $true )
| ( ( less @ X0 @ X1 )
!= $true ) ) ),
inference(rectify,[],[f20]) ).
thf(f22,plain,
( ( more @ x0 @ y0 )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f24,plain,
! [X0: rat,X1: rat] :
( ( ( less @ X0 @ X1 )
!= $true )
| ( ( more @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f25,plain,
! [X0: rat,X1: rat] :
( ( ( is @ X0 @ X1 )
!= $true )
| ( ( more @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f27,plain,
( ( ( is @ x0 @ y0 )
= $true )
| ( ( less @ x0 @ y0 )
= $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f32,definition,
( spl0_1
<=> ( ( less @ x0 @ y0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f33,plain,
( ( ( less @ x0 @ y0 )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f35,definition,
( spl0_2
<=> ( ( is @ x0 @ y0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f36,plain,
( ( ( is @ x0 @ y0 )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f37,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f27,f35,f32]) ).
thf(f47,plain,
( ( $true != $true )
| ( ( more @ x0 @ y0 )
!= $true )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f25,f36]) ).
thf(f49,plain,
( ( ( more @ x0 @ y0 )
!= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f47]) ).
thf(f51,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f49,f22]) ).
thf(f52,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f51]) ).
thf(f53,plain,
( ( $true != $true )
| ( ( more @ x0 @ y0 )
!= $true )
| ~ spl0_1 ),
inference(constrained_superposition,[],[f24,f33]) ).
thf(f54,plain,
( ( ( more @ x0 @ y0 )
!= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f55,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f54,f22]) ).
thf(f56,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f55]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f37]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f52]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f57,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM788^1 : 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 : n017.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 12:51:23 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 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
% 0.23/0.28 % (291342)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.28 % (291352)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3961854376:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.28 % (291352) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-291342-291352"...
% 0.23/0.28 % (291352)...printing done.
% 0.23/0.28 % (291352)Refutation found. Thanks to Tanya!
% 0.23/0.28 % SZS status Theorem for theBenchmark
% 0.23/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.28 % (291352)------------------------------
% 0.23/0.28 % (291352)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.28 % (291352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.28 % (291352)CaDiCaL version: 2.1.3
% 0.23/0.28 % (291352)Termination reason: Refutation
% 0.23/0.28 % (291352)Time elapsed: 0.002 s
% 0.23/0.28 % (291352)Peak memory usage: 13 MB
% 0.23/0.28 % (291352)Instructions burned: 3 (million)
% 0.23/0.28 % (291342)Success in time 0.018 s
% 0.23/0.28 % Vampire exiting
%------------------------------------------------------------------------------