%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN377^5 : 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 : n018.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 08:41:52 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 6 unt; 0 typ; 6 def)
% Number of atoms : 377 ( 83 equ; 0 cnn)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 308 ( 84 ~; 95 |; 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 47 !; 19 ?; 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',cX2128) ).
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,
( ( ( ( ( $true
!= ( cP @ sK0 ) )
| ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ! [X2: $i] :
( ( cP @ X2 )
= $true )
| ( $true
= ( cP @ sK1 ) ) ) )
| ( ( ( $true
!= ( cP @ sK3 ) )
| ( $true
!= ( cP @ sK2 ) ) )
& ( ! [X6: $i] :
( $true
= ( cP @ X6 ) )
| ( $true
= ( cP @ sK2 ) ) ) ) )
& ( ( ( ( $true
= ( cP @ sK4 ) )
| ( $true
!= ( cP @ sK5 ) ) )
& ( ! [X9: $i] :
( $true
= ( cP @ X9 ) )
| ! [X10: $i] :
( $true
!= ( cP @ X10 ) ) ) )
| ! [X11: $i] :
( ( ( $true
= ( cP @ X11 ) )
| ( $true
!= ( cP @ sK6 ) ) )
& ( ! [X13: $i] :
( $true
= ( cP @ X13 ) )
| ( $true
!= ( cP @ X11 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X3,sK1),skolemize(X4,sK2),skolemize(X5,sK3),skolemize(X7,sK4),skolemize(X8,sK5),skolemize(X12,sK6)],[f7]) ).
thf(f9,plain,
! [X10: $i,X11: $i,X9: $i,X13: $i] :
( ( $true
= ( cP @ X9 ) )
| ( $true
!= ( cP @ X10 ) )
| ( $true
= ( cP @ X13 ) )
| ( $true
!= ( cP @ X11 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
! [X2: $i,X6: $i] :
( ( ( cP @ X2 )
= $true )
| ( $true
= ( cP @ sK1 ) )
| ( $true
= ( cP @ X6 ) )
| ( $true
= ( cP @ sK2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
! [X1: $i] :
( ( $true
!= ( cP @ sK0 ) )
| ( ( cP @ X1 )
!= $true )
| ( $true
!= ( cP @ sK3 ) )
| ( $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(f23,definition,
( spl7_2
<=> ! [X13: $i] :
( $true
= ( cP @ X13 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f24,plain,
( ! [X13: $i] :
( $true
= ( cP @ X13 ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f25,plain,
( spl7_1
| spl7_2
| spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f9,f23,f20,f23,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 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f48,plain,
( ( $true
= ( cP @ sK1 ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f49,plain,
( spl7_6
| spl7_2
| spl7_7
| spl7_2 ),
inference(avatar_split_clause,[],[f13,f23,f46,f23,f42]) ).
thf(f51,definition,
( spl7_8
<=> ( $true
= ( cP @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f53,plain,
( ( $true
!= ( cP @ sK3 ) )
| spl7_8 ),
inference(avatar_component_clause,[],[f51]) ).
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_8
| spl7_1
| ~ spl7_9 ),
inference(avatar_split_clause,[],[f16,f56,f20,f51,f42]) ).
thf(f61,plain,
( $false
| ~ spl7_2
| spl7_9 ),
inference(forward_subsumption_resolution,[],[f58,f24]) ).
thf(f62,plain,
( ~ spl7_2
| spl7_9 ),
inference(avatar_contradiction_clause,[],[f61]) ).
thf(f63,plain,
( $false
| ~ spl7_2
| spl7_6 ),
inference(forward_subsumption_resolution,[],[f43,f24]) ).
thf(f64,plain,
( ~ spl7_2
| spl7_6 ),
inference(avatar_contradiction_clause,[],[f63]) ).
thf(f65,plain,
( $false
| ~ spl7_2
| spl7_8 ),
inference(forward_subsumption_resolution,[],[f53,f24]) ).
thf(f66,plain,
( ~ spl7_2
| spl7_8 ),
inference(avatar_contradiction_clause,[],[f65]) ).
thf(f67,plain,
( $false
| ~ spl7_1
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f21,f24]) ).
thf(f68,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(avatar_contradiction_clause,[],[f67]) ).
thf(f71,plain,
( ( $true != $true )
| ~ spl7_1
| ~ spl7_6 ),
inference(constrained_superposition,[],[f21,f44]) ).
thf(f72,plain,
( $false
| ~ spl7_1
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f73,plain,
( ~ spl7_1
| ~ spl7_6 ),
inference(avatar_contradiction_clause,[],[f72]) ).
thf(f74,plain,
( ( $true != $true )
| ~ spl7_1
| ~ spl7_7 ),
inference(constrained_superposition,[],[f21,f48]) ).
thf(f75,plain,
( $false
| ~ spl7_1
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f76,plain,
( ~ spl7_1
| ~ spl7_7 ),
inference(avatar_contradiction_clause,[],[f75]) ).
cnf(s1,plain,
( spl7_1
| spl7_2
| spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s2,plain,
( spl7_1
| spl7_2 ),
inference(rat,[],[s1]) ).
cnf(s7,plain,
( spl7_2
| spl7_2
| spl7_6
| spl7_7 ),
inference(sat_conversion,[],[f49]) ).
cnf(s8,plain,
( spl7_2
| spl7_6
| spl7_7 ),
inference(rat,[],[s7]) ).
cnf(s11,plain,
( spl7_1
| ~ spl7_6
| ~ spl7_8
| ~ spl7_9 ),
inference(sat_conversion,[],[f60]) ).
cnf(s12,plain,
( ~ spl7_2
| spl7_9 ),
inference(sat_conversion,[],[f62]) ).
cnf(s13,plain,
( ~ spl7_2
| spl7_6 ),
inference(sat_conversion,[],[f64]) ).
cnf(s14,plain,
( ~ spl7_2
| spl7_8 ),
inference(sat_conversion,[],[f66]) ).
cnf(s15,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f68]) ).
cnf(s17,plain,
( ~ spl7_1
| ~ spl7_6 ),
inference(sat_conversion,[],[f73]) ).
cnf(s18,plain,
( ~ spl7_1
| ~ spl7_7 ),
inference(sat_conversion,[],[f76]) ).
cnf(s19,plain,
spl7_1,
inference(rat,[],[s11,s12,s13,s14,s2]) ).
cnf(s20,plain,
~ spl7_7,
inference(rat,[],[s18,s19]) ).
cnf(s21,plain,
~ spl7_6,
inference(rat,[],[s17,s19]) ).
cnf(s23,plain,
~ spl7_2,
inference(rat,[],[s15,s19]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s8,s23,s20,s21]) ).
thf(f77,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN377^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:17:41 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 0.20/0.28 % (283885)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (283894)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1131029505:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (283894)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (283894) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-283885-283894"...
% 0.20/0.28 % (283891)% WARNING: option uhcvi not known.
% 0.20/0.28 % (283894)...printing done.
% 0.20/0.28 % (283894)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (283894)------------------------------
% 0.20/0.28 % (283894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (283894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (283894)CaDiCaL version: 2.1.3
% 0.20/0.28 % (283894)Termination reason: Refutation
% 0.20/0.28 % (283894)Time elapsed: 0.002 s
% 0.20/0.28 % (283894)Peak memory usage: 12 MB
% 0.20/0.28 % (283894)Instructions burned: 3 (million)
% 0.20/0.28 % (283885)Success in time 0.033 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------