%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU890^5 : 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 : n015.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 08:31:53 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 60 ( 8 unt; 0 typ; 6 def)
% Number of atoms : 244 ( 90 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 306 ( 74 ~; 78 |; 27 &; 116 @)
% ( 10 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 20 !; 24 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
c: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_7,type,
a: $tType ).
thf(type_def_8,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cG: c > b ).
thf(func_def_1,type,
cF: b > a ).
thf(func_def_2,type,
cS: c > $o ).
thf(func_def_6,type,
sK0: a ).
thf(func_def_7,type,
sK1: b ).
thf(func_def_8,type,
sK2: c ).
thf(func_def_9,type,
sK3: c ).
thf(func_def_10,type,
vNOT: $o > $o ).
thf(f1,conjecture,
! [X0: a] :
( ? [X1: c] :
( ( X0
= ( cF @ ( cG @ X1 ) ) )
& ( cS @ X1 ) )
<=> ? [X1: b] :
( ( X0
= ( cF @ X1 ) )
& ? [X2: c] :
( ( cS @ X2 )
& ( X1
= ( cG @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM29_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ? [X1: c] :
( ( X0
= ( cF @ ( cG @ X1 ) ) )
& ( cS @ X1 ) )
<=> ? [X1: b] :
( ( X0
= ( cF @ X1 ) )
& ? [X2: c] :
( ( cS @ X2 )
& ( X1
= ( cG @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a] :
( ? [X1: c] :
( ( X0
= ( cF @ ( cG @ X1 ) ) )
& ( cS @ X1 ) )
<=> ? [X2: b] :
( ( ( cF @ X2 )
= X0 )
& ? [X3: c] :
( ( cS @ X3 )
& ( ( cG @ X3 )
= X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a] :
( ? [X1: c] :
( ( ( cS @ X1 )
= $true )
& ( ( cF @ ( cG @ X1 ) )
= X0 ) )
<=> ? [X2: b] :
( ? [X3: c] :
( ( ( cG @ X3 )
= X2 )
& ( ( cS @ X3 )
= $true ) )
& ( ( cF @ X2 )
= X0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a] :
( ? [X1: c] :
( ( ( cS @ X1 )
= $true )
& ( ( cF @ ( cG @ X1 ) )
= X0 ) )
<~> ? [X2: b] :
( ? [X3: c] :
( ( ( cG @ X3 )
= X2 )
& ( ( cS @ X3 )
= $true ) )
& ( ( cF @ X2 )
= X0 ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a] :
( ( ! [X2: b] :
( ! [X3: c] :
( ( ( cG @ X3 )
!= X2 )
| ( ( cS @ X3 )
!= $true ) )
| ( ( cF @ X2 )
!= X0 ) )
| ! [X1: c] :
( ( ( cS @ X1 )
!= $true )
| ( ( cF @ ( cG @ X1 ) )
!= X0 ) ) )
& ( ? [X2: b] :
( ? [X3: c] :
( ( ( cG @ X3 )
= X2 )
& ( ( cS @ X3 )
= $true ) )
& ( ( cF @ X2 )
= X0 ) )
| ? [X1: c] :
( ( ( cS @ X1 )
= $true )
& ( ( cF @ ( cG @ X1 ) )
= X0 ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a] :
( ( ! [X1: b] :
( ! [X2: c] :
( ( ( cG @ X2 )
!= X1 )
| ( ( cS @ X2 )
!= $true ) )
| ( ( cF @ X1 )
!= X0 ) )
| ! [X3: c] :
( ( ( cS @ X3 )
!= $true )
| ( ( cF @ ( cG @ X3 ) )
!= X0 ) ) )
& ( ? [X4: b] :
( ? [X5: c] :
( ( ( cG @ X5 )
= X4 )
& ( ( cS @ X5 )
= $true ) )
& ( ( cF @ X4 )
= X0 ) )
| ? [X6: c] :
( ( ( cS @ X6 )
= $true )
& ( ( cF @ ( cG @ X6 ) )
= X0 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ! [X1: b] :
( ! [X2: c] :
( ( ( cG @ X2 )
!= X1 )
| ( ( cS @ X2 )
!= $true ) )
| ( ( cF @ X1 )
!= sK0 ) )
| ! [X3: c] :
( ( ( cS @ X3 )
!= $true )
| ( ( cF @ ( cG @ X3 ) )
!= sK0 ) ) )
& ( ( ( ( cG @ sK2 )
= sK1 )
& ( $true
= ( cS @ sK2 ) )
& ( ( cF @ sK1 )
= sK0 ) )
| ( ( ( cS @ sK3 )
= $true )
& ( sK0
= ( cF @ ( cG @ sK3 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X4,sK1),skolemize(X5,sK2),skolemize(X6,sK3)],[f7]) ).
thf(f9,plain,
( ( ( cF @ sK1 )
= sK0 )
| ( sK0
= ( cF @ ( cG @ sK3 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( ( cF @ sK1 )
= sK0 )
| ( ( cS @ sK3 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( sK0
= ( cF @ ( cG @ sK3 ) ) )
| ( $true
= ( cS @ sK2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( ( ( cS @ sK3 )
= $true )
| ( $true
= ( cS @ sK2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
( ( ( cG @ sK2 )
= sK1 )
| ( sK0
= ( cF @ ( cG @ sK3 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( ( ( cS @ sK3 )
= $true )
| ( ( cG @ sK2 )
= sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
! [X2: c,X3: c,X1: b] :
( ( ( cG @ X2 )
!= X1 )
| ( ( cS @ X2 )
!= $true )
| ( ( cF @ X1 )
!= sK0 )
| ( ( cS @ X3 )
!= $true )
| ( ( cF @ ( cG @ X3 ) )
!= sK0 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f18,plain,
! [X2: c,X3: c] :
( ( sK0
!= ( cF @ ( cG @ X2 ) ) )
| ( ( cF @ ( cG @ X3 ) )
!= sK0 )
| ( ( cS @ X3 )
!= $true )
| ( ( cS @ X2 )
!= $true ) ),
inference(equality_resolution,[],[f15]) ).
thf(f20,definition,
( spl4_1
<=> ( $true
= ( cS @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f21,plain,
( ( $true
= ( cS @ sK2 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f23,definition,
( spl4_2
<=> ( sK0
= ( cF @ ( cG @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f24,plain,
( ( sK0
= ( cF @ ( cG @ sK3 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f25,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f11,f23,f20]) ).
thf(f27,definition,
( spl4_3
<=> ( ( cF @ sK1 )
= sK0 ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f28,plain,
( ( ( cF @ sK1 )
= sK0 )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f30,definition,
( spl4_4
<=> ( ( cS @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f31,plain,
( ( ( cS @ sK3 )
= $true )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f32,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f10,f30,f27]) ).
thf(f33,plain,
( spl4_1
| spl4_4 ),
inference(avatar_split_clause,[],[f12,f30,f20]) ).
thf(f35,definition,
( spl4_5
<=> ( ( cG @ sK2 )
= sK1 ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f36,plain,
( ( ( cG @ sK2 )
= sK1 )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f37,plain,
( spl4_5
| spl4_2 ),
inference(avatar_split_clause,[],[f13,f23,f35]) ).
thf(f39,definition,
( spl4_6
<=> ! [X3: c] :
( ( ( cF @ ( cG @ X3 ) )
!= sK0 )
| ( ( cS @ X3 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f40,plain,
( ! [X3: c] :
( ( ( cF @ ( cG @ X3 ) )
!= sK0 )
| ( ( cS @ X3 )
!= $true ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f41,plain,
( spl4_6
| spl4_6 ),
inference(avatar_split_clause,[],[f18,f39,f39]) ).
thf(f42,plain,
( spl4_5
| spl4_4 ),
inference(avatar_split_clause,[],[f14,f30,f35]) ).
thf(f43,plain,
( spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f9,f27,f23]) ).
thf(f44,plain,
( ( sK0 != sK0 )
| ( ( cS @ sK3 )
!= $true )
| ~ spl4_2
| ~ spl4_6 ),
inference(constrained_superposition,[],[f40,f24]) ).
thf(f45,plain,
( ( ( cS @ sK3 )
!= $true )
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f44]) ).
thf(f46,plain,
( $false
| ~ spl4_2
| ~ spl4_4
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f45,f31]) ).
thf(f47,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f46]) ).
thf(f48,plain,
( ( $true
!= ( cS @ sK2 ) )
| ( ( cF @ sK1 )
!= sK0 )
| ~ spl4_5
| ~ spl4_6 ),
inference(constrained_superposition,[],[f40,f36]) ).
thf(f49,plain,
( ( ( cF @ sK1 )
!= sK0 )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f48,f21]) ).
thf(f50,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f49,f28]) ).
thf(f51,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f50]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s2,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f32]) ).
cnf(s3,plain,
( spl4_1
| spl4_4 ),
inference(sat_conversion,[],[f33]) ).
cnf(s4,plain,
( spl4_2
| spl4_5 ),
inference(sat_conversion,[],[f37]) ).
cnf(s5,plain,
( spl4_6
| spl4_6 ),
inference(sat_conversion,[],[f41]) ).
cnf(s6,plain,
spl4_6,
inference(rat,[],[s5]) ).
cnf(s7,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f42]) ).
cnf(s8,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f43]) ).
cnf(s9,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_6 ),
inference(sat_conversion,[],[f47]) ).
cnf(s10,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f51]) ).
cnf(s11,plain,
spl4_1,
inference(rat,[],[s9,s1,s3,s6]) ).
cnf(s12,plain,
spl4_2,
inference(rat,[],[s10,s4,s8,s11,s6]) ).
cnf(s13,plain,
~ spl4_4,
inference(rat,[],[s9,s6,s12]) ).
cnf(s14,plain,
spl4_5,
inference(rat,[],[s7,s13]) ).
cnf(s15,plain,
spl4_3,
inference(rat,[],[s2,s13]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s10,s6,s11,s14,s15]) ).
thf(f52,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU890^5 : 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 : n015.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 14:47:33 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 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
% 0.20/0.27 % (3618409)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (3618419)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2315494471:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.27 % (3618419) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3618409-3618419"...
% 0.20/0.27 % (3618419)...printing done.
% 0.20/0.27 % (3618419)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (3618419)------------------------------
% 0.20/0.27 % (3618419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (3618419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (3618419)CaDiCaL version: 2.1.3
% 0.20/0.27 % (3618419)Termination reason: Refutation
% 0.20/0.27 % (3618419)Time elapsed: 0.002 s
% 0.20/0.27 % (3618419)Peak memory usage: 13 MB
% 0.20/0.27 % (3618419)Instructions burned: 3 (million)
% 0.20/0.27 % (3618409)Success in time 0.033 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------