%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET144^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:23:14 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 71 ( 15 unt; 0 typ; 6 def)
% Number of atoms : 357 ( 90 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 376 ( 45 ~; 102 |; 38 &; 177 @)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 9 con; 0-4 aty)
% Number of variables : 48 ( 0 sgn 20 !; 6 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vOR: $o > $o > $o ).
thf(func_def_4,type,
vAND: $o > $o > $o ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
sK0: a > $o ).
thf(func_def_8,type,
sK1: a > $o ).
thf(func_def_9,type,
sK2: a > $o ).
thf(func_def_10,type,
sK3: a ).
thf(f1,conjecture,
! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
=> ( ( ^ [X4: a] :
( ( X0 @ X4 )
| ( ( X2 @ X4 )
& ( X1 @ X4 ) ) ) )
= ( ^ [X3: a] :
( ( ( X1 @ X3 )
| ( X0 @ X3 ) )
& ( X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_44_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
=> ( ( ^ [X4: a] :
( ( X0 @ X4 )
| ( ( X2 @ X4 )
& ( X1 @ X4 ) ) ) )
= ( ^ [X3: a] :
( ( ( 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] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
=> ( ( ^ [X4: a] :
( ( X0 @ X4 )
| ( ( X1 @ X4 )
& ( X2 @ X4 ) ) ) )
= ( ^ [X5: a] :
( ( ( X2 @ X5 )
| ( X0 @ X5 ) )
& ( X1 @ X5 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ( ( X1 @ X3 )
= $true ) )
=> ( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
& ( X1 @ Y0 ) )
| ( X0 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( ( X0 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X2: a > $o,X1: a > $o,X0: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) )
& ( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
& ( X1 @ Y0 ) )
| ( X0 @ 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] :
( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) )
& ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( X2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( ( X2 @ Y0 )
| ( X0 @ Y0 ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ! [X3: a] :
( ( $true
= ( sK1 @ X3 ) )
| ( $true
!= ( sK2 @ X3 ) ) )
& ( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( ( sK2 @ 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] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X3: a] :
( ( $true
!= ( sK2 @ X3 ) )
| ( $true
= ( sK1 @ X3 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( sK2 @ Y0 ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f13,plain,
( ( $true
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( sK2 @ Y0 ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f12]) ).
thf(f14,plain,
( ( ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( sK2 @ Y0 ) )
@ sK3 )
= $false )
| ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) ) )
@ sK3 )
= $false ) ),
inference(xor_proxy_clausification,[],[f12]) ).
thf(f15,plain,
( ( ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( sK2 @ sK3 ) )
= $false )
| ( ( ( sK1 @ sK3 )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f16,plain,
( ( ( ( sK1 @ sK3 )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( ( ( ( sK1 @ sK3 )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
= $false )
| ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f15]) ).
thf(f18,plain,
( ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $false )
| ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f18]) ).
thf(f23,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f19]) ).
thf(f24,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f23]) ).
thf(f25,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f16]) ).
thf(f27,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f25]) ).
thf(f28,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(duplicate_literal_removal,[],[f27]) ).
thf(f29,plain,
( ( $true
= ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
| ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f30,plain,
( ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f32,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f33,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f32]) ).
thf(f35,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f33]) ).
thf(f36,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f35]) ).
thf(f38,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f31]) ).
thf(f39,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f38]) ).
thf(f43,definition,
( spl4_1
<=> ( ( sK2 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f45,plain,
( ( ( sK2 @ sK3 )
= $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f47,definition,
( spl4_2
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f49,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f47]) ).
thf(f51,definition,
( spl4_3
<=> ( ( sK1 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f53,plain,
( ( ( sK1 @ sK3 )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f55,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f24,f47,f51]) ).
thf(f56,plain,
( spl4_3
| spl4_1 ),
inference(avatar_split_clause,[],[f28,f43,f51]) ).
thf(f60,definition,
( spl4_4
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f62,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f64,definition,
( spl4_5
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f66,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f67,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f36,f64,f60]) ).
thf(f68,plain,
( $true
= ( sK1 @ sK3 ) ),
inference(forward_subsumption_resolution,[],[f39,f9]) ).
thf(f71,definition,
( spl4_6
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f73,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f71]) ).
thf(f75,plain,
spl4_6,
inference(avatar_split_clause,[],[f68,f71]) ).
thf(f77,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_demodulation,[],[f73,f53]) ).
thf(f78,plain,
( $false
| ~ spl4_3
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f79,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f78]) ).
thf(f80,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_4 ),
inference(forward_demodulation,[],[f45,f62]) ).
thf(f81,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f82,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f81]) ).
thf(f84,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_5 ),
inference(forward_demodulation,[],[f66,f49]) ).
thf(f85,plain,
( $false
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f86,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f85]) ).
cnf(s2,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f55]) ).
cnf(s3,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f56]) ).
cnf(s5,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f67]) ).
cnf(s7,plain,
spl4_6,
inference(sat_conversion,[],[f75]) ).
cnf(s9,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(sat_conversion,[],[f79]) ).
cnf(s10,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f82]) ).
cnf(s11,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f86]) ).
cnf(s12,plain,
~ spl4_3,
inference(rat,[],[s9,s7]) ).
cnf(s14,plain,
spl4_1,
inference(rat,[],[s3,s12]) ).
cnf(s15,plain,
~ spl4_4,
inference(rat,[],[s10,s14]) ).
cnf(s16,plain,
spl4_5,
inference(rat,[],[s5,s15]) ).
cnf(s17,plain,
~ spl4_2,
inference(rat,[],[s11,s16]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s2,s12,s17]) ).
thf(f87,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET144^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n013.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 13:36:21 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.26 % (2115281)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.26 % (2115286)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3154622829:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.10/0.26 % (2115286) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2115281-2115286"...
% 0.10/0.26 % (2115286)...printing done.
% 0.10/0.26 % (2115286)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.26 % (2115286)------------------------------
% 0.10/0.26 % (2115286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (2115286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (2115286)CaDiCaL version: 2.1.3
% 0.10/0.26 % (2115286)Termination reason: Refutation
% 0.10/0.26 % (2115286)Time elapsed: 0.002 s
% 0.10/0.26 % (2115286)Peak memory usage: 13 MB
% 0.10/0.26 % (2115286)Instructions burned: 4 (million)
% 0.10/0.26 % (2115281)Success in time 0.029 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------