%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO259^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 08:49:37 AM UTC 2026
% Result : Theorem 0.09s 0.23s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 133 ( 41 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 163 ( 51 ~; 37 |; 16 &; 57 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 50 ( 2 sgn 33 !; 14 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_6,type,
sK3: $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,
! [X0: $i,X1: $i,X2: $i,X3: $i > $o] :
? [X4: $i > $o,X5: $i > $o] :
( ( ~ ( X3 @ X2 )
| ( X4 @ X2 ) )
& ( ( X5 @ X1 )
| ( X3 @ X1 ) )
& ( ( X4 @ X0 )
| ( X5 @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM125B) ).
thf(f2,negated_conjecture,
~ ! [X0: $i,X1: $i,X2: $i,X3: $i > $o] :
? [X4: $i > $o,X5: $i > $o] :
( ( ~ ( X3 @ X2 )
| ( X4 @ X2 ) )
& ( ( X5 @ X1 )
| ( X3 @ X1 ) )
& ( ( X4 @ X0 )
| ( X5 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i,X1: $i,X2: $i,X3: $i > $o] :
? [X4: $i > $o,X5: $i > $o] :
( ( ~ ( X3 @ X2 )
| ( X4 @ X2 ) )
& ( ( X5 @ X1 )
| ( X3 @ X1 ) )
& ( ( X4 @ X0 )
| ( X5 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i,X2: $i,X3: $i > $o] :
? [X4: $i > $o,X5: $i > $o] :
( ( ( ( X3 @ X2 )
!= $true )
| ( ( X4 @ X2 )
= $true ) )
& ( ( ( X5 @ X1 )
= $true )
| ( ( X3 @ X1 )
= $true ) )
& ( ( ( X4 @ X0 )
= $true )
| ( ( X5 @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i,X2: $i,X3: $i > $o] :
? [X4: $i > $o,X5: $i > $o] :
( ( ( ( X3 @ X2 )
!= $true )
| ( ( X4 @ X2 )
= $true ) )
& ( ( ( X5 @ X1 )
= $true )
| ( ( X3 @ X1 )
= $true ) )
& ( ( ( X4 @ X0 )
= $true )
| ( ( X5 @ X0 )
= $true ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X0: $i,X1: $i,X2: $i,X3: $i > $o] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( ( X3 @ X2 )
= $true )
& ( ( X4 @ X2 )
!= $true ) )
| ( ( ( X5 @ X1 )
!= $true )
& ( ( X3 @ X1 )
!= $true ) )
| ( ( ( X4 @ X0 )
!= $true )
& ( ( X5 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
! [X4: $i > $o,X5: $i > $o] :
( ( ( $true
= ( sK3 @ sK2 ) )
& ( $true
!= ( X4 @ sK2 ) ) )
| ( ( $true
!= ( X5 @ sK1 ) )
& ( $true
!= ( sK3 @ sK1 ) ) )
| ( ( $true
!= ( X4 @ sK0 ) )
& ( $true
!= ( X5 @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f6]) ).
thf(f11,plain,
! [X4: $i > $o,X5: $i > $o] :
( ( $true
!= ( X4 @ sK2 ) )
| ( $true
!= ( X5 @ sK1 ) )
| ( $true
!= ( X4 @ sK0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f30,definition,
( spl4_4
<=> ! [X4: $i > $o] :
( ( $true
!= ( X4 @ sK2 ) )
| ( $true
!= ( X4 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f31,plain,
( ! [X4: $i > $o] :
( ( $true
!= ( X4 @ sK2 ) )
| ( $true
!= ( X4 @ sK0 ) ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f38,definition,
( spl4_6
<=> ! [X5: $i > $o] :
( $true
!= ( X5 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f39,plain,
( ! [X5: $i > $o] :
( $true
!= ( X5 @ sK1 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f38]) ).
thf(f40,plain,
( spl4_6
| spl4_4 ),
inference(avatar_split_clause,[],[f11,f30,f38]) ).
thf(f51,plain,
( ! [X6: $i > $o] :
( $true
!= ( ^ [Y0: $i] :
~ ( X6 @ Y0 )
@ sK1 ) )
| ~ spl4_6 ),
inference(primitive_instantiation,[],[f39]) ).
thf(f54,plain,
( ! [X6: $i > $o] :
( $true
!= ( ~ ( X6 @ sK1 ) ) )
| ~ spl4_6 ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f55,plain,
( ! [X6: $i > $o] :
( $true
= ( X6 @ sK1 ) )
| ~ spl4_6 ),
inference(not_proxy_clausification,[],[f54]) ).
thf(f60,plain,
( $false
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f55,f39]) ).
thf(f61,plain,
~ spl4_6,
inference(avatar_contradiction_clause,[],[f60]) ).
thf(f62,plain,
( ( $true
!= ( ^ [Y0: $i] : $true
@ sK2 ) )
| ( $true
!= ( ^ [Y0: $i] : $true
@ sK0 ) )
| ~ spl4_4 ),
inference(primitive_instantiation,[],[f31]) ).
thf(f80,plain,
( ( $true != $true )
| ( $true != $true )
| ~ spl4_4 ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f81,plain,
( ( $true != $true )
| ~ spl4_4 ),
inference(duplicate_literal_removal,[],[f80]) ).
thf(f82,plain,
( $false
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f81]) ).
thf(f83,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[],[f82]) ).
cnf(s4,plain,
( spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f40]) ).
cnf(s11,plain,
~ spl4_6,
inference(sat_conversion,[],[f61]) ).
cnf(s13,plain,
~ spl4_4,
inference(sat_conversion,[],[f83]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s4,s11,s13]) ).
thf(f86,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO259^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.16 % Computer : n007.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 16:39:56 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 Running first-order model finding
% 0.09/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.23 % (3619411)Will run a generic schedule for satisfiability detection.
% 0.09/0.23 % (3619419)dis+10_1_sil=32000:sp=arity:random_seed=559940765:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.23 % (3619419) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3619411-3619419"...
% 0.09/0.23 % (3619417)% WARNING: option uhcvi not known.
% 0.09/0.23 % (3619419)...printing done.
% 0.09/0.23 % (3619419)Refutation found. Thanks to Tanya!
% 0.09/0.23 % SZS status Theorem for theBenchmark
% 0.09/0.23 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.23 % (3619419)------------------------------
% 0.09/0.24 % (3619419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.24 % (3619419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.24 % (3619419)CaDiCaL version: 2.1.3
% 0.09/0.24 % (3619419)Termination reason: Refutation
% 0.09/0.24 % (3619419)Time elapsed: 0.002 s
% 0.09/0.24 % (3619419)Peak memory usage: 12 MB
% 0.09/0.24 % (3619419)Instructions burned: 3 (million)
% 0.09/0.24 % (3619411)Success in time 0.025 s
% 0.09/0.24 % Vampire exiting
%------------------------------------------------------------------------------