%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO260^5 : 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 : n002.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 0.28s
% 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 : 13 ( 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_5,type,
sK2: $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,
! [X3: $i > $o,X0: $i,X2: $i,X1: $i] :
? [X5: $i > $o,X4: $i > $o] :
( ( ~ ( X3 @ X2 )
| ( X4 @ X2 ) )
& ( ( X3 @ X1 )
| ( X5 @ X1 ) )
& ( ( X5 @ X0 )
| ( X4 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM125A) ).
thf(f2,negated_conjecture,
~ ! [X3: $i > $o,X0: $i,X2: $i,X1: $i] :
? [X5: $i > $o,X4: $i > $o] :
( ( ~ ( X3 @ X2 )
| ( X4 @ X2 ) )
& ( ( X3 @ X1 )
| ( X5 @ X1 ) )
& ( ( X5 @ X0 )
| ( X4 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i > $o,X1: $i,X2: $i,X3: $i] :
? [X4: $i > $o,X5: $i > $o] :
( ( ~ ( X0 @ X2 )
| ( X5 @ X2 ) )
& ( ( X0 @ X3 )
| ( X4 @ X3 ) )
& ( ( X4 @ X1 )
| ( X5 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: $i > $o,X1: $i,X2: $i,X3: $i] :
? [X4: $i > $o,X5: $i > $o] :
( ( ( ( X0 @ X2 )
!= $true )
| ( ( X5 @ X2 )
= $true ) )
& ( ( $true
= ( X0 @ X3 ) )
| ( ( X4 @ X3 )
= $true ) )
& ( ( ( X5 @ X1 )
= $true )
| ( ( X4 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X1: $i,X3: $i,X2: $i,X0: $i > $o] :
? [X5: $i > $o,X4: $i > $o] :
( ( ( ( X5 @ X1 )
= $true )
| ( ( X4 @ X1 )
= $true ) )
& ( ( $true
= ( X0 @ X3 ) )
| ( ( X4 @ X3 )
= $true ) )
& ( ( ( X5 @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X3: $i,X1: $i,X0: $i > $o,X2: $i] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( ( X4 @ X1 )
!= $true )
& ( ( X5 @ X1 )
!= $true ) )
| ( ( ( X5 @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
| ( ( ( X4 @ X3 )
!= $true )
& ( $true
!= ( X0 @ X3 ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: $i,X1: $i,X2: $i > $o,X3: $i] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( ( X4 @ X1 )
!= $true )
& ( ( X5 @ X1 )
!= $true ) )
| ( ( ( X5 @ X3 )
!= $true )
& ( ( X2 @ X3 )
= $true ) )
| ( ( ( X4 @ X0 )
!= $true )
& ( $true
!= ( X2 @ X0 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
! [X4: $i > $o,X5: $i > $o] :
( ( ( ( X4 @ sK1 )
!= $true )
& ( ( X5 @ sK1 )
!= $true ) )
| ( ( ( X5 @ sK3 )
!= $true )
& ( ( sK2 @ sK3 )
= $true ) )
| ( ( ( X4 @ sK0 )
!= $true )
& ( ( sK2 @ sK0 )
!= $true ) ) ),
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(f16,plain,
! [X4: $i > $o,X5: $i > $o] :
( ( ( X4 @ sK1 )
!= $true )
| ( ( X5 @ sK3 )
!= $true )
| ( ( X4 @ sK0 )
!= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f23,definition,
( spl4_2
<=> ! [X5: $i > $o] :
( ( X5 @ sK3 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f24,plain,
( ! [X5: $i > $o] :
( ( X5 @ sK3 )
!= $true )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f35,definition,
( spl4_5
<=> ! [X4: $i > $o] :
( ( ( X4 @ sK1 )
!= $true )
| ( ( X4 @ sK0 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f36,plain,
( ! [X4: $i > $o] :
( ( ( X4 @ sK1 )
!= $true )
| ( ( X4 @ sK0 )
!= $true ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f48,plain,
( spl4_5
| spl4_2 ),
inference(avatar_split_clause,[],[f16,f23,f35]) ).
thf(f52,plain,
( ! [X6: $i > $o] :
( ( ^ [Y0: $i] :
~ ( X6 @ Y0 )
@ sK3 )
!= $true )
| ~ spl4_2 ),
inference(primitive_instantiation,[],[f24]) ).
thf(f61,plain,
( ! [X6: $i > $o] :
( ( ~ ( X6 @ sK3 ) )
!= $true )
| ~ spl4_2 ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f62,plain,
( ! [X6: $i > $o] :
( ( X6 @ sK3 )
= $true )
| ~ spl4_2 ),
inference(not_proxy_clausification,[],[f61]) ).
thf(f63,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f62,f24]) ).
thf(f64,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f63]) ).
thf(f65,plain,
( ( ( ^ [Y0: $i] : $true
@ sK0 )
!= $true )
| ( ( ^ [Y0: $i] : $true
@ sK1 )
!= $true )
| ~ spl4_5 ),
inference(primitive_instantiation,[],[f36]) ).
thf(f78,plain,
( ( $true != $true )
| ( $true != $true )
| ~ spl4_5 ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f79,plain,
( ( $true != $true )
| ~ spl4_5 ),
inference(duplicate_literal_removal,[],[f78]) ).
thf(f80,plain,
( $false
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f81,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[],[f80]) ).
cnf(s7,plain,
( spl4_2
| spl4_5 ),
inference(sat_conversion,[],[f48]) ).
cnf(s11,plain,
~ spl4_2,
inference(sat_conversion,[],[f64]) ).
cnf(s13,plain,
~ spl4_5,
inference(sat_conversion,[],[f81]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s7,s13,s11]) ).
thf(f82,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO260^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n002.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:44:38 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.21/0.28 % (1530962)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (1530967)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4002384464:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (1530967) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1530962-1530967"...
% 0.21/0.28 % (1530967)...printing done.
% 0.21/0.28 % (1530967)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (1530967)------------------------------
% 0.21/0.28 % (1530967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1530967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1530967)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1530967)Termination reason: Refutation
% 0.21/0.28 % (1530967)Time elapsed: 0.002 s
% 0.21/0.28 % (1530967)Peak memory usage: 13 MB
% 0.21/0.28 % (1530967)Instructions burned: 2 (million)
% 0.21/0.28 % (1530962)Success in time 0.033 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------