%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET612^5 : 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 08:23:22 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of formulae : 71 ( 22 unt; 0 typ; 5 def)
% Number of atoms : 421 ( 105 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 501 ( 101 ~; 102 |; 75 &; 218 @)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 8 con; 0-4 aty)
% Number of variables : 40 ( 0 sgn 12 !; 6 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vAND: $o > $o > $o ).
thf(func_def_2,type,
vNOT: $o > $o ).
thf(func_def_3,type,
vOR: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_6,type,
sK0: a > $o ).
thf(func_def_7,type,
sK1: a > $o ).
thf(func_def_8,type,
sK2: a > $o ).
thf(func_def_11,type,
sK3: a ).
thf(f1,conjecture,
! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ^ [X3: a] :
( ( X0 @ X3 )
& ~ ( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) )
= ( ^ [X3: a] :
( ( X0 @ X3 )
& ~ ( X1 @ X3 )
& ( X0 @ X3 )
& ~ ( X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_85_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ( ^ [X3: a] :
( ( X0 @ X3 )
& ~ ( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) )
= ( ^ [X3: a] :
( ( X0 @ X3 )
& ~ ( X1 @ X3 )
& ( X0 @ X3 )
& ~ ( X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( X2 @ X3 )
& ~ ( ( X0 @ X3 )
| ( X1 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ( X2 @ X4 )
& ~ ( X0 @ X4 )
& ( X2 @ X4 )
& ~ ( X1 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X2 @ Y0 )
& ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ~ ( ( X1 @ Y0 )
| ( X0 @ Y0 ) )
& ( X2 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X2 @ Y0 )
& ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ~ ( ( X1 @ Y0 )
| ( X0 @ Y0 ) )
& ( X2 @ Y0 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ~ ( ( X2 @ Y0 )
| ( X1 @ Y0 ) )
& ( X0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ~ ( X2 @ Y0 )
& ( X0 @ Y0 )
& ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ~ ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ~ ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( ^ [Y0: a] :
( ~ ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK0 @ Y0 ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f12,plain,
( ( $true
= ( ^ [Y0: a] :
( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK3 ) )
| ( ( ^ [Y0: a] :
( ~ ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK0 @ Y0 ) )
@ sK3 )
= $true ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f13,plain,
( ( $false
= ( ^ [Y0: a] :
( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK3 ) )
| ( ( ^ [Y0: a] :
( ~ ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK0 @ Y0 ) )
@ sK3 )
= $false ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f14,plain,
( ( $false
= ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) )
| ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
( ( $false
= ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) ) ) )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( $true
= ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $false )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f22]) ).
thf(f24,plain,
( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f26,plain,
( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f24]) ).
thf(f27,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f29,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f31,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f30]) ).
thf(f33,plain,
( ( $true
= ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) ) ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f31]) ).
thf(f34,plain,
( ( $false
= ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f33]) ).
thf(f36,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f34]) ).
thf(f37,plain,
( $false
= ( sK2 @ sK3 ) ),
inference(duplicate_literal_removal,[],[f36]) ).
thf(f38,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f43,plain,
( ( sK0 @ sK3 )
= $true ),
inference(duplicate_literal_removal,[],[f38]) ).
thf(f44,plain,
( ( $true
= ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f27]) ).
thf(f46,plain,
( ( $true
= ( ~ ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f47,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f46]) ).
thf(f48,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f47]) ).
thf(f50,plain,
( $false
= ( sK1 @ sK3 ) ),
inference(duplicate_literal_removal,[],[f48]) ).
thf(f58,definition,
( spl4_1
<=> ( ( sK0 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f60,plain,
( ( ( sK0 @ sK3 )
= $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f62,definition,
( spl4_2
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f64,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f66,definition,
( spl4_3
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f68,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f69,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f23,f66,f62,f58]) ).
thf(f71,definition,
( spl4_4
<=> ( ( sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f73,plain,
( ( ( sK0 @ sK3 )
= $true )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f71]) ).
thf(f75,definition,
( spl4_5
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f77,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f75]) ).
thf(f79,plain,
spl4_4,
inference(avatar_split_clause,[],[f43,f71]) ).
thf(f80,plain,
spl4_5,
inference(avatar_split_clause,[],[f50,f75]) ).
thf(f83,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_5 ),
inference(forward_demodulation,[],[f77,f64]) ).
thf(f84,plain,
( $false
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f85,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f84]) ).
thf(f86,plain,
( ( $false = $true )
| ~ spl4_3 ),
inference(forward_demodulation,[],[f68,f37]) ).
thf(f87,plain,
( $false
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f86]) ).
thf(f88,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f87]) ).
thf(f90,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_4 ),
inference(forward_demodulation,[],[f60,f73]) ).
thf(f91,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f92,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f91]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f69]) ).
cnf(s3,plain,
spl4_4,
inference(sat_conversion,[],[f79]) ).
cnf(s4,plain,
spl4_5,
inference(sat_conversion,[],[f80]) ).
cnf(s8,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f85]) ).
cnf(s9,plain,
~ spl4_3,
inference(sat_conversion,[],[f88]) ).
cnf(s10,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f92]) ).
cnf(s11,plain,
~ spl4_2,
inference(rat,[],[s8,s4]) ).
cnf(s12,plain,
~ spl4_1,
inference(rat,[],[s10,s3]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s9,s11,s12]) ).
thf(f94,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET612^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n015.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:42:33 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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 % (3538201)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (3538208)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3980724757:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.27 % (3538208) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3538201-3538208"...
% 0.20/0.27 % (3538208)...printing done.
% 0.20/0.27 % (3538208)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 % (3538208)------------------------------
% 0.20/0.27 % (3538208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (3538208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (3538208)CaDiCaL version: 2.1.3
% 0.20/0.27 % (3538208)Termination reason: Refutation
% 0.20/0.27 % (3538208)Time elapsed: 0.002 s
% 0.20/0.27 % (3538208)Peak memory usage: 13 MB
% 0.20/0.27 % (3538208)Instructions burned: 5 (million)
% 0.20/0.27 % (3538201)Success in time 0.031 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------