%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET619^5 : 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 : n007.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 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 64 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 381 ( 89 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 459 ( 73 ~; 115 |; 60 &; 207 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 30 ( 0 sgn 8 !; 2 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vOR: $o > $o > $o ).
thf(func_def_2,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_4,type,
vAND: $o > $o > $o ).
thf(func_def_5,type,
vNOT: $o > $o ).
thf(func_def_6,type,
sK0: a > $o ).
thf(func_def_7,type,
sK1: a > $o ).
thf(func_def_10,type,
sK2: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= ( ^ [X2: a] :
( ( ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_95_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= ( ^ [X2: a] :
( ( ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
| ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= ( ^ [X3: a] :
( ( ( X1 @ X3 )
& ( X0 @ X3 ) )
| ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
@ sK2 )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f18,plain,
( ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( $false
= ( ( sK0 @ sK2 )
| ( sK1 @ sK2 ) ) )
| ( $false
= ( ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) )
| ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) )
| ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) )
| ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f20]) ).
thf(f24,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f22]) ).
thf(f26,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f24]) ).
thf(f27,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( ~ ( sK1 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f28]) ).
thf(f34,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f21]) ).
thf(f35,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f21]) ).
thf(f36,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f35]) ).
thf(f40,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ~ ( sK0 @ sK2 ) ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f36]) ).
thf(f41,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f40]) ).
thf(f42,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f41]) ).
thf(f43,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f44,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f43]) ).
thf(f45,plain,
( ( $true
= ( ( sK0 @ sK2 )
| ( sK1 @ sK2 ) ) )
| ( $true
= ( ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) )
| ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f46,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) )
| ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f46]) ).
thf(f48,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) ) ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f64,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) )
| ( $true
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f48]) ).
thf(f66,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK2 )
& ~ ( sK1 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f64]) ).
thf(f68,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f66]) ).
thf(f69,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f68]) ).
thf(f79,definition,
( spl3_1
<=> ( $true
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f81,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f83,definition,
( spl3_2
<=> ( $false
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f85,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f86,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f29,f83,f79]) ).
thf(f88,definition,
( spl3_3
<=> ( $false
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f90,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f88]) ).
thf(f93,definition,
( spl3_4
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f95,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f93]) ).
thf(f96,plain,
( spl3_4
| spl3_3 ),
inference(avatar_split_clause,[],[f42,f88,f93]) ).
thf(f97,plain,
( spl3_2
| spl3_3 ),
inference(avatar_split_clause,[],[f44,f88,f83]) ).
thf(f99,plain,
( spl3_4
| spl3_1 ),
inference(avatar_split_clause,[],[f69,f79,f93]) ).
thf(f100,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_demodulation,[],[f95,f85]) ).
thf(f101,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f102,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f101]) ).
thf(f105,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_3 ),
inference(constrained_superposition,[],[f81,f90]) ).
thf(f109,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f105]) ).
thf(f110,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f109]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f86]) ).
cnf(s3,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f96]) ).
cnf(s4,plain,
( spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f97]) ).
cnf(s6,plain,
( spl3_1
| spl3_4 ),
inference(sat_conversion,[],[f99]) ).
cnf(s7,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(sat_conversion,[],[f102]) ).
cnf(s9,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(sat_conversion,[],[f110]) ).
cnf(s10,plain,
spl3_1,
inference(rat,[],[s7,s1,s6]) ).
cnf(s11,plain,
~ spl3_3,
inference(rat,[],[s9,s10]) ).
cnf(s12,plain,
spl3_2,
inference(rat,[],[s4,s11]) ).
cnf(s13,plain,
spl3_4,
inference(rat,[],[s3,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s7,s13,s12]) ).
thf(f111,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET619^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n007.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % 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 13:37:41 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.09/0.26 % (3369252)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (3369262)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2375296335:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.26 % (3369262) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3369252-3369262"...
% 0.09/0.26 % (3369262)...printing done.
% 0.09/0.26 % (3369258)% WARNING: option uhcvi not known.
% 0.09/0.26 % (3369262)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.26 % (3369262)------------------------------
% 0.09/0.26 % (3369262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (3369262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (3369262)CaDiCaL version: 2.1.3
% 0.09/0.26 % (3369262)Termination reason: Refutation
% 0.09/0.26 % (3369262)Time elapsed: 0.002 s
% 0.09/0.26 % (3369262)Peak memory usage: 13 MB
% 0.09/0.26 % (3369262)Instructions burned: 5 (million)
% 0.09/0.26 % (3369252)Success in time 0.039 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------