%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET614^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:23:43 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 58 ( 19 unt; 0 typ; 3 def)
% Number of atoms : 339 ( 88 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 389 ( 79 ~; 82 |; 50 &; 175 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 35 ( 0 sgn 12 !; 3 ?; 35 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vNOT: $o > $o ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_5,type,
vOR: $o > $o > $o ).
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,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( X2 @ X3 )
& ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) )
= ( ^ [X3: a] :
( ~ ( ( X2 @ X3 )
| ( X1 @ X3 ) )
& ( X0 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_88_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( X2 @ X3 )
& ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) )
= ( ^ [X3: a] :
( ~ ( ( X2 @ X3 )
| ( X1 @ X3 ) )
& ( X0 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( X2 @ X3 )
& ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) )
= ( ^ [X4: a] :
( ~ ( ( X2 @ X4 )
| ( X1 @ X4 ) )
& ( X0 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( ( X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( ( X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f18,plain,
( ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f24]) ).
thf(f26,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f27]) ).
thf(f29,plain,
( ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f30,plain,
( ( $true
= ( ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f32,plain,
( ( $true
= ( ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f31]) ).
thf(f33,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f31]) ).
thf(f35,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f33]) ).
thf(f36,plain,
( $true
= ( sK0 @ sK3 ) ),
inference(duplicate_literal_removal,[],[f35]) ).
thf(f40,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f32]) ).
thf(f41,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f40]) ).
thf(f43,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f41]) ).
thf(f45,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f43]) ).
thf(f46,plain,
( $false
= ( sK1 @ sK3 ) ),
inference(duplicate_literal_removal,[],[f45]) ).
thf(f47,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f30]) ).
thf(f48,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f50,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
| ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f48]) ).
thf(f51,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f50]) ).
thf(f53,plain,
( $false
= ( sK2 @ sK3 ) ),
inference(duplicate_literal_removal,[],[f51]) ).
thf(f55,definition,
( spl4_1
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f57,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f59,definition,
( spl4_2
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f61,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f63,definition,
( spl4_3
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f65,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f66,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f28,f63,f59,f55]) ).
thf(f67,plain,
( ( $true = $false )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f61,f46]) ).
thf(f68,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f69,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f68]) ).
thf(f71,plain,
( ( $true = $false )
| ~ spl4_3 ),
inference(forward_demodulation,[],[f65,f53]) ).
thf(f72,plain,
( $false
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f73,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f72]) ).
thf(f77,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f36,f57]) ).
thf(f81,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f82,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f81]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f66]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f69]) ).
cnf(s3,plain,
~ spl4_3,
inference(sat_conversion,[],[f73]) ).
cnf(s5,plain,
~ spl4_1,
inference(sat_conversion,[],[f82]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s2,s5]) ).
thf(f83,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET614^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n014.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 13:39:16 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.24 % (2668866)Will run a generic schedule for satisfiability detection.
% 0.08/0.24 % (2668875)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3827835167:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.08/0.24 % (2668875)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.24 % (2668875) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2668866-2668875"...
% 0.08/0.24 % (2668875)...printing done.
% 0.08/0.24 % (2668875)Refutation found. Thanks to Tanya!
% 0.08/0.24 % SZS status Theorem for theBenchmark
% 0.08/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.24 % (2668875)------------------------------
% 0.08/0.24 % (2668875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.24 % (2668875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.24 % (2668875)CaDiCaL version: 2.1.3
% 0.08/0.24 % (2668875)Termination reason: Refutation
% 0.08/0.24 % (2668875)Time elapsed: 0.002 s
% 0.08/0.24 % (2668875)Peak memory usage: 12 MB
% 0.08/0.24 % (2668875)Instructions burned: 4 (million)
% 0.08/0.24 % (2668866)Success in time 0.017 s
% 0.08/0.24 % Vampire exiting
%------------------------------------------------------------------------------