%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET183^5 : 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 : n009.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 08:23:36 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 136 ( 41 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 125 ( 21 ~; 20 |; 14 &; 60 @)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 12 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 27 ( 0 sgn 15 !; 2 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vAND: $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 ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ( ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_42_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ( ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ( ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 ) ) )
= X0 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
=> ( ( X1 @ X2 )
= $true ) )
=> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X0 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= X0 )
& ! [X2: a] :
( ( ( X1 @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
& ! [X2: a] :
( ( $true
= ( sK1 @ X2 ) )
| ( $true
!= ( sK0 @ X2 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5]) ).
thf(f7,plain,
! [X2: a] :
( ( $true
!= ( sK0 @ X2 ) )
| ( $true
= ( sK1 @ X2 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( sK0
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f11,plain,
( ( sK0 @ sK2 )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f12,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f13,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f14,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f15]) ).
thf(f17,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK2 )
& ( sK1 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f19,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(duplicate_literal_removal,[],[f19]) ).
thf(f22,definition,
( spl3_1
<=> ( $false
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f24,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f22]) ).
thf(f26,definition,
( spl3_2
<=> ( $false
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f28,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f29,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f16,f26,f22]) ).
thf(f30,plain,
( ( $true != $true )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(constrained_superposition,[],[f7,f20]) ).
thf(f31,plain,
( $true
= ( sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f33,plain,
( ( $true = $false )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f28,f20]) ).
thf(f38,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f39,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f38]) ).
thf(f40,plain,
( ( $true = $false )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f24,f31]) ).
thf(f44,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f40]) ).
thf(f45,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f44]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f29]) ).
cnf(s3,plain,
~ spl3_2,
inference(sat_conversion,[],[f39]) ).
cnf(s5,plain,
~ spl3_1,
inference(sat_conversion,[],[f45]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f46,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET183^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n009.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 13:37:31 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
% 0.09/0.24 % (3995918)Will run a generic schedule for satisfiability detection.
% 0.09/0.24 % (3995929)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1073964545:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.24 % (3995929) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3995918-3995929"...
% 0.09/0.24 % (3995929)...printing done.
% 0.09/0.24 % (3995929)Refutation found. Thanks to Tanya!
% 0.09/0.24 % SZS status Theorem for theBenchmark
% 0.09/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.24 % (3995929)------------------------------
% 0.09/0.24 % (3995929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.24 % (3995929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.24 % (3995929)CaDiCaL version: 2.1.3
% 0.09/0.24 % (3995929)Termination reason: Refutation
% 0.09/0.24 % (3995929)Time elapsed: 0.001 s
% 0.09/0.24 % (3995929)Peak memory usage: 13 MB
% 0.09/0.24 % (3995929)Instructions burned: 2 (million)
% 0.09/0.24 % (3995918)Success in time 0.024 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------