%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO259^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:47:18 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 145 ( 47 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 179 ( 56 ~; 39 |; 19 &; 63 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 56 ( 2 sgn 35 !; 18 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_4,type,
sK1: $i > $o ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
! [X2: $i,X0: $i,X3: $i > $o,X1: $i] :
? [X5: $i > $o,X4: $i > $o] :
( ( ( X5 @ X1 )
| ( X3 @ X1 ) )
& ( ( X5 @ X0 )
| ( X4 @ X0 ) )
& ( ~ ( X3 @ X2 )
| ( X4 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM125B) ).
thf(f2,negated_conjecture,
~ ! [X2: $i,X0: $i,X3: $i > $o,X1: $i] :
? [X5: $i > $o,X4: $i > $o] :
( ( ( X5 @ X1 )
| ( X3 @ X1 ) )
& ( ( X5 @ X0 )
| ( X4 @ X0 ) )
& ( ~ ( X3 @ X2 )
| ( X4 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i,X1: $i,X2: $i > $o,X3: $i] :
? [X4: $i > $o,X5: $i > $o] :
( ( ( X4 @ X3 )
| ( X2 @ X3 ) )
& ( ( X4 @ X1 )
| ( X5 @ X1 ) )
& ( ~ ( X2 @ X0 )
| ( X5 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i,X2: $i > $o,X3: $i] :
? [X4: $i > $o,X5: $i > $o] :
( ( ( $true
= ( X2 @ X3 ) )
| ( $true
= ( X4 @ X3 ) ) )
& ( ( $true
= ( X4 @ X1 ) )
| ( ( X5 @ X1 )
= $true ) )
& ( ( $true
!= ( X2 @ X0 ) )
| ( ( X5 @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i,X3: $i,X2: $i > $o] :
? [X4: $i > $o,X5: $i > $o] :
( ( ( $true
= ( X2 @ X3 ) )
| ( $true
= ( X4 @ X3 ) ) )
& ( ( $true
= ( X4 @ X1 ) )
| ( ( X5 @ X1 )
= $true ) )
& ( ( ( X5 @ X0 )
= $true )
| ( $true
!= ( X2 @ X0 ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X3: $i,X2: $i > $o,X0: $i,X1: $i] :
! [X5: $i > $o,X4: $i > $o] :
( ( ( ( X5 @ X1 )
!= $true )
& ( $true
!= ( X4 @ X1 ) ) )
| ( ( $true
= ( X2 @ X0 ) )
& ( ( X5 @ X0 )
!= $true ) )
| ( ( $true
!= ( X4 @ X3 ) )
& ( $true
!= ( X2 @ X3 ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: $i,X1: $i > $o,X2: $i,X3: $i] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( $true
!= ( X4 @ X3 ) )
& ( $true
!= ( X5 @ X3 ) ) )
| ( ( $true
= ( X1 @ X2 ) )
& ( ( X4 @ X2 )
!= $true ) )
| ( ( ( X5 @ X0 )
!= $true )
& ( $true
!= ( X1 @ X0 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
! [X4: $i > $o,X5: $i > $o] :
( ( ( $true
!= ( X4 @ sK3 ) )
& ( $true
!= ( X5 @ sK3 ) ) )
| ( ( $true
= ( sK1 @ sK2 ) )
& ( $true
!= ( X4 @ sK2 ) ) )
| ( ( $true
!= ( X5 @ sK0 ) )
& ( $true
!= ( sK1 @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f7]) ).
thf(f14,plain,
! [X4: $i > $o,X5: $i > $o] :
( ( $true
!= ( X5 @ sK0 ) )
| ( $true
!= ( X4 @ sK3 ) )
| ( $true
!= ( X4 @ sK2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f35,definition,
( spl4_5
<=> ! [X4: $i > $o] :
( ( $true
!= ( X4 @ sK2 ) )
| ( $true
!= ( X4 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f36,plain,
( ! [X4: $i > $o] :
( ( $true
!= ( X4 @ sK3 ) )
| ( $true
!= ( X4 @ sK2 ) ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f39,definition,
( spl4_6
<=> ! [X5: $i > $o] :
( $true
!= ( X5 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f40,plain,
( ! [X5: $i > $o] :
( $true
!= ( X5 @ sK0 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f42,plain,
( spl4_6
| spl4_5 ),
inference(avatar_split_clause,[],[f14,f35,f39]) ).
thf(f63,plain,
( ! [X6: $i > $o] :
( $true
!= ( ^ [Y0: $i] :
~ ( X6 @ Y0 )
@ sK0 ) )
| ~ spl4_6 ),
inference(primitive_instantiation,[],[f40]) ).
thf(f69,plain,
( ! [X6: $i > $o] :
( $true
!= ( ~ ( X6 @ sK0 ) ) )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f70,plain,
( ! [X6: $i > $o] :
( $true
= ( X6 @ sK0 ) )
| ~ spl4_6 ),
inference(not_proxy_clausification,[],[f69]) ).
thf(f72,plain,
( $false
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f70,f40]) ).
thf(f73,plain,
~ spl4_6,
inference(avatar_contradiction_clause,[],[f72]) ).
thf(f74,plain,
( ( $true
!= ( ^ [Y0: $i] : $true
@ sK2 ) )
| ( $true
!= ( ^ [Y0: $i] : $true
@ sK3 ) )
| ~ spl4_5 ),
inference(primitive_instantiation,[],[f36]) ).
thf(f89,plain,
( ( $true != $true )
| ( $true != $true )
| ~ spl4_5 ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f90,plain,
( ( $true != $true )
| ~ spl4_5 ),
inference(duplicate_literal_removal,[],[f89]) ).
thf(f91,plain,
( $false
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f92,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[],[f91]) ).
cnf(s6,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f42]) ).
cnf(s14,plain,
~ spl4_6,
inference(sat_conversion,[],[f73]) ).
cnf(s16,plain,
~ spl4_5,
inference(sat_conversion,[],[f92]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s6,s14,s16]) ).
thf(f95,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO259^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n010.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 16:42:03 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 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
% 0.21/0.29 % (3114830)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (3114840)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2931207733:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (3114841)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (3114841)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.29 % (3114840) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3114830-3114840"...
% 0.21/0.29 % (3114840)...printing done.
% 0.21/0.29 % (3114840)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (3114840)------------------------------
% 0.21/0.29 % (3114840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3114840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3114840)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3114840)Termination reason: Refutation
% 0.21/0.29 % (3114840)Time elapsed: 0.003 s
% 0.21/0.29 % (3114840)Peak memory usage: 13 MB
% 0.21/0.29 % (3114840)Instructions burned: 3 (million)
% 0.21/0.29 % (3114830)Success in time 0.033 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------