%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET607^5 : 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 08:23:41 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 16 unt; 0 typ; 4 def)
% Number of atoms : 228 ( 56 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 246 ( 44 ~; 72 |; 14 &; 112 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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,
vAND: $o > $o > $o ).
thf(func_def_4,type,
vNOT: $o > $o ).
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_10,type,
sK2: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
| ( X0 @ X2 ) ) )
= ( ^ [X2: a] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_79_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
| ( X0 @ X2 ) ) )
= ( ^ [X2: a] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) )
| ( X0 @ X2 ) ) )
= ( ^ [X3: a] :
( ( X1 @ X3 )
| ( X0 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 @ Y0 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( 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 )
& ~ ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
@ sK2 )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f18,plain,
( ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( $false
= ( ( sK0 @ sK2 )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) ) )
| ( $false
= ( ( sK0 @ sK2 )
| ( sK1 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( ( $false
= ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) )
| ( $false
= ( ( sK0 @ sK2 )
| ( sK1 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK2 )
| ( sK1 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f20]) ).
thf(f24,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f22]) ).
thf(f25,plain,
( $false
= ( sK0 @ sK2 ) ),
inference(duplicate_literal_removal,[],[f24]) ).
thf(f26,plain,
( ( $false
= ( ~ ( sK0 @ sK2 ) ) )
| ( $false
= ( ( sK0 @ sK2 )
| ( sK1 @ sK2 ) ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f27,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK2 )
| ( sK1 @ sK2 ) ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f27]) ).
thf(f30,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f28]) ).
thf(f31,plain,
( ( $true
= ( ( sK0 @ sK2 )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) ) )
| ( $true
= ( ( sK0 @ sK2 )
| ( sK1 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f32,plain,
( ( $true
= ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) )
| ( $true
= ( ( sK0 @ sK2 )
| ( sK1 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f31]) ).
thf(f34,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK2 )
| ( sK1 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f32]) ).
thf(f35,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f34]) ).
thf(f36,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f35]) ).
thf(f41,definition,
( spl3_1
<=> ( $false
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f43,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f45,definition,
( spl3_2
<=> ( $false
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f47,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f50,definition,
( spl3_3
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f52,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f53,plain,
( spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f30,f50,f41]) ).
thf(f55,definition,
( spl3_4
<=> ( $true
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f57,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f58,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f36,f55,f50]) ).
thf(f59,plain,
spl3_2,
inference(avatar_split_clause,[],[f25,f45]) ).
thf(f62,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f52,f47]) ).
thf(f63,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f64,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f63]) ).
thf(f67,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_4 ),
inference(constrained_superposition,[],[f43,f57]) ).
thf(f71,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f72,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f71]) ).
cnf(s2,plain,
( spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f53]) ).
cnf(s3,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f58]) ).
cnf(s4,plain,
spl3_2,
inference(sat_conversion,[],[f59]) ).
cnf(s5,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f64]) ).
cnf(s7,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(sat_conversion,[],[f72]) ).
cnf(s8,plain,
~ spl3_3,
inference(rat,[],[s5,s4]) ).
cnf(s9,plain,
spl3_4,
inference(rat,[],[s3,s8]) ).
cnf(s10,plain,
~ spl3_1,
inference(rat,[],[s7,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s2,s8,s10]) ).
thf(f74,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET607^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n009.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:39:00 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 0.07/0.25 % (4000196)Will run a generic schedule for satisfiability detection.
% 0.07/0.25 % (4000207)dis+10_1_sil=32000:sp=arity:random_seed=2928083249:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.25 % (4000207) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4000196-4000207"...
% 0.07/0.25 % (4000207)...printing done.
% 0.07/0.25 % (4000207)Refutation found. Thanks to Tanya!
% 0.07/0.25 % SZS status Theorem for theBenchmark
% 0.07/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.25 % (4000207)------------------------------
% 0.07/0.25 % (4000207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (4000207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (4000207)CaDiCaL version: 2.1.3
% 0.07/0.25 % (4000207)Termination reason: Refutation
% 0.07/0.25 % (4000207)Time elapsed: 0.002 s
% 0.07/0.25 % (4000207)Peak memory usage: 12 MB
% 0.07/0.25 % (4000207)Instructions burned: 3 (million)
% 0.07/0.25 % (4000196)Success in time 0.025 s
% 0.07/0.25 % Vampire exiting
%------------------------------------------------------------------------------