%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO112^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 08:48:59 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 7 unt; 0 typ; 6 def)
% Number of atoms : 361 ( 81 equ; 0 cnn)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 292 ( 76 ~; 87 |; 15 &; 93 @)
% ( 20 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 15 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 42 !; 24 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cP: $i > $o ).
thf(f1,conjecture,
( ! [X0: $i] :
( ( cP @ X0 )
<=> ? [X1: $i] : ( cP @ X1 ) )
<=> ( ! [X0: $i] : ( cP @ X0 )
<=> ? [X1: $i] : ( cP @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM53) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
( ( cP @ X0 )
<=> ? [X1: $i] : ( cP @ X1 ) )
<=> ( ! [X0: $i] : ( cP @ X0 )
<=> ? [X1: $i] : ( cP @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i] :
( ( cP @ X0 )
<=> ? [X1: $i] : ( cP @ X1 ) )
<=> ( ! [X2: $i] : ( cP @ X2 )
<=> ? [X3: $i] : ( cP @ X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ( ( cP @ X0 )
= $true )
<=> ? [X1: $i] :
( ( cP @ X1 )
= $true ) )
<=> ( ! [X2: $i] :
( ( cP @ X2 )
= $true )
<=> ? [X3: $i] :
( ( cP @ X3 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X0: $i] :
( ( ( cP @ X0 )
= $true )
<=> ? [X1: $i] :
( ( cP @ X1 )
= $true ) )
<~> ( ! [X2: $i] :
( ( cP @ X2 )
= $true )
<=> ? [X3: $i] :
( ( cP @ X3 )
= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( ( ! [X3: $i] :
( ( cP @ X3 )
!= $true )
| ? [X2: $i] :
( ( cP @ X2 )
!= $true ) )
& ( ? [X3: $i] :
( ( cP @ X3 )
= $true )
| ! [X2: $i] :
( ( cP @ X2 )
= $true ) ) )
| ? [X0: $i] :
( ( ! [X1: $i] :
( ( cP @ X1 )
!= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ? [X1: $i] :
( ( cP @ X1 )
= $true )
| ( ( cP @ X0 )
= $true ) ) ) )
& ( ( ( ! [X2: $i] :
( ( cP @ X2 )
= $true )
| ! [X3: $i] :
( ( cP @ X3 )
!= $true ) )
& ( ? [X3: $i] :
( ( cP @ X3 )
= $true )
| ? [X2: $i] :
( ( cP @ X2 )
!= $true ) ) )
| ! [X0: $i] :
( ( ( ( cP @ X0 )
= $true )
| ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ? [X1: $i] :
( ( cP @ X1 )
= $true )
| ( ( cP @ X0 )
!= $true ) ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ( ( ! [X0: $i] :
( ( cP @ X0 )
!= $true )
| ? [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ? [X2: $i] :
( ( cP @ X2 )
= $true )
| ! [X3: $i] :
( ( cP @ X3 )
= $true ) ) )
| ? [X4: $i] :
( ( ! [X5: $i] :
( $true
!= ( cP @ X5 ) )
| ( $true
!= ( cP @ X4 ) ) )
& ( ? [X6: $i] :
( $true
= ( cP @ X6 ) )
| ( $true
= ( cP @ X4 ) ) ) ) )
& ( ( ( ! [X7: $i] :
( $true
= ( cP @ X7 ) )
| ! [X8: $i] :
( $true
!= ( cP @ X8 ) ) )
& ( ? [X9: $i] :
( $true
= ( cP @ X9 ) )
| ? [X10: $i] :
( $true
!= ( cP @ X10 ) ) ) )
| ! [X11: $i] :
( ( ( $true
= ( cP @ X11 ) )
| ! [X12: $i] :
( $true
!= ( cP @ X12 ) ) )
& ( ? [X13: $i] :
( $true
= ( cP @ X13 ) )
| ( $true
!= ( cP @ X11 ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( ( ! [X0: $i] :
( ( cP @ X0 )
!= $true )
| ( $true
!= ( cP @ sK0 ) ) )
& ( ( $true
= ( cP @ sK1 ) )
| ! [X3: $i] :
( ( cP @ X3 )
= $true ) ) )
| ( ( ! [X5: $i] :
( $true
!= ( cP @ X5 ) )
| ( $true
!= ( cP @ sK2 ) ) )
& ( ( $true
= ( cP @ sK3 ) )
| ( $true
= ( cP @ sK2 ) ) ) ) )
& ( ( ( ! [X7: $i] :
( $true
= ( cP @ X7 ) )
| ! [X8: $i] :
( $true
!= ( cP @ X8 ) ) )
& ( ( $true
= ( cP @ sK4 ) )
| ( $true
!= ( cP @ sK5 ) ) ) )
| ! [X11: $i] :
( ( ( $true
= ( cP @ X11 ) )
| ! [X12: $i] :
( $true
!= ( cP @ X12 ) ) )
& ( ( $true
= ( cP @ sK6 ) )
| ( $true
!= ( cP @ X11 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X1,sK0),skolemize(X2,sK1),skolemize(X4,sK2),skolemize(X6,sK3),skolemize(X9,sK4),skolemize(X10,sK5),skolemize(X13,sK6)],[f7]) ).
thf(f12,plain,
! [X11: $i,X8: $i,X7: $i,X12: $i] :
( ( $true
= ( cP @ X7 ) )
| ( $true
!= ( cP @ X8 ) )
| ( $true
= ( cP @ X11 ) )
| ( $true
!= ( cP @ X12 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
! [X3: $i] :
( ( $true
= ( cP @ sK1 ) )
| ( ( cP @ X3 )
= $true )
| ( $true
= ( cP @ sK3 ) )
| ( $true
= ( cP @ sK2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
! [X0: $i,X5: $i] :
( ( ( cP @ X0 )
!= $true )
| ( $true
!= ( cP @ sK0 ) )
| ( $true
!= ( cP @ X5 ) )
| ( $true
!= ( cP @ sK2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f20,definition,
( spl7_1
<=> ! [X11: $i] :
( $true
!= ( cP @ X11 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f21,plain,
( ! [X11: $i] :
( $true
!= ( cP @ X11 ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f36,definition,
( spl7_5
<=> ! [X11: $i] :
( $true
= ( cP @ X11 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f37,plain,
( ! [X11: $i] :
( $true
= ( cP @ X11 ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f40,plain,
( spl7_1
| spl7_5
| spl7_1
| spl7_5 ),
inference(avatar_split_clause,[],[f12,f36,f20,f36,f20]) ).
thf(f42,definition,
( spl7_6
<=> ( $true
= ( cP @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f43,plain,
( ( $true
!= ( cP @ sK2 ) )
| spl7_6 ),
inference(avatar_component_clause,[],[f42]) ).
thf(f44,plain,
( ( $true
= ( cP @ sK2 ) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f42]) ).
thf(f46,definition,
( spl7_7
<=> ( $true
= ( cP @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f48,plain,
( ( $true
= ( cP @ sK3 ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f50,definition,
( spl7_8
<=> ( $true
= ( cP @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f52,plain,
( ( $true
= ( cP @ sK1 ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f53,plain,
( spl7_6
| spl7_7
| spl7_5
| spl7_8 ),
inference(avatar_split_clause,[],[f13,f50,f36,f46,f42]) ).
thf(f56,definition,
( spl7_9
<=> ( $true
= ( cP @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
thf(f58,plain,
( ( $true
!= ( cP @ sK0 ) )
| spl7_9 ),
inference(avatar_component_clause,[],[f56]) ).
thf(f60,plain,
( ~ spl7_6
| spl7_1
| ~ spl7_9
| spl7_1 ),
inference(avatar_split_clause,[],[f16,f20,f56,f20,f42]) ).
thf(f64,plain,
( $false
| ~ spl7_5
| spl7_9 ),
inference(forward_subsumption_resolution,[],[f58,f37]) ).
thf(f65,plain,
( ~ spl7_5
| spl7_9 ),
inference(avatar_contradiction_clause,[],[f64]) ).
thf(f66,plain,
( $false
| ~ spl7_5
| spl7_6 ),
inference(forward_subsumption_resolution,[],[f43,f37]) ).
thf(f67,plain,
( ~ spl7_5
| spl7_6 ),
inference(avatar_contradiction_clause,[],[f66]) ).
thf(f72,plain,
( $false
| ~ spl7_1
| ~ spl7_7 ),
inference(forward_subsumption_resolution,[],[f48,f21]) ).
thf(f73,plain,
( ~ spl7_1
| ~ spl7_7 ),
inference(avatar_contradiction_clause,[],[f72]) ).
thf(f74,plain,
( $false
| ~ spl7_1
| ~ spl7_8 ),
inference(forward_subsumption_resolution,[],[f52,f21]) ).
thf(f75,plain,
( ~ spl7_1
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[],[f74]) ).
thf(f76,plain,
( $false
| ~ spl7_1
| ~ spl7_6 ),
inference(forward_subsumption_resolution,[],[f44,f21]) ).
thf(f77,plain,
( ~ spl7_1
| ~ spl7_6 ),
inference(avatar_contradiction_clause,[],[f76]) ).
cnf(s5,plain,
( spl7_1
| spl7_5
| spl7_1
| spl7_5 ),
inference(sat_conversion,[],[f40]) ).
cnf(s6,plain,
( spl7_1
| spl7_5 ),
inference(rat,[],[s5]) ).
cnf(s7,plain,
( spl7_5
| spl7_6
| spl7_7
| spl7_8 ),
inference(sat_conversion,[],[f53]) ).
cnf(s10,plain,
( spl7_1
| spl7_1
| ~ spl7_6
| ~ spl7_9 ),
inference(sat_conversion,[],[f60]) ).
cnf(s11,plain,
( spl7_1
| ~ spl7_6
| ~ spl7_9 ),
inference(rat,[],[s10]) ).
cnf(s13,plain,
( ~ spl7_5
| spl7_9 ),
inference(sat_conversion,[],[f65]) ).
cnf(s14,plain,
( ~ spl7_5
| spl7_6 ),
inference(sat_conversion,[],[f67]) ).
cnf(s17,plain,
( ~ spl7_1
| ~ spl7_7 ),
inference(sat_conversion,[],[f73]) ).
cnf(s18,plain,
( ~ spl7_1
| ~ spl7_8 ),
inference(sat_conversion,[],[f75]) ).
cnf(s19,plain,
( ~ spl7_1
| ~ spl7_6 ),
inference(sat_conversion,[],[f77]) ).
cnf(s20,plain,
spl7_1,
inference(rat,[],[s11,s13,s14,s6]) ).
cnf(s21,plain,
~ spl7_6,
inference(rat,[],[s19,s20]) ).
cnf(s22,plain,
~ spl7_8,
inference(rat,[],[s18,s20]) ).
cnf(s23,plain,
~ spl7_7,
inference(rat,[],[s17,s20]) ).
cnf(s26,plain,
~ spl7_5,
inference(rat,[],[s14,s21]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s7,s22,s26,s23,s21]) ).
thf(f78,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO112^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n003.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 16:35:59 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.26 % (2714015)Will run a generic schedule for satisfiability detection.
% 0.20/0.26 % (2714023)dis+10_1_sil=32000:sp=arity:random_seed=831834030:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.26 % (2714023) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2714015-2714023"...
% 0.20/0.26 % (2714023)...printing done.
% 0.20/0.26 % (2714023)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.26 % (2714023)------------------------------
% 0.20/0.26 % (2714023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (2714023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (2714023)CaDiCaL version: 2.1.3
% 0.20/0.26 % (2714023)Termination reason: Refutation
% 0.20/0.26 % (2714023)Time elapsed: 0.002 s
% 0.20/0.26 % (2714023)Peak memory usage: 12 MB
% 0.20/0.26 % (2714023)Instructions burned: 3 (million)
% 0.20/0.26 % (2714015)Success in time 0.036 s
% 0.20/0.26 % Vampire exiting
%------------------------------------------------------------------------------