%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU354+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 : Tue Sep 29 12:52:59 PM UTC 2026
% Result : Theorem 0.29s 0.46s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 18 unt; 2 def)
% Number of atoms : 104 ( 30 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 94 ( 41 ~; 33 |; 10 &)
% ( 6 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 34 ( 0 sgn 27 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1] :
( element(X1,X0)
=> ( proper_element(X1,X0)
<=> X1 != union(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tex_2) ).
fof(f30,axiom,
! [X0] :
? [X1] :
( element(X1,powerset(X0))
& ~ proper_element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tex_2) ).
fof(f31,axiom,
! [X0] : k1_pcomps_1(X0) = powerset(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
fof(f39,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> ( proper_element(X1,powerset(X0))
<=> X1 != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tex_2) ).
fof(f40,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ( proper_element(X1,powerset(X0))
<=> X1 != X0 ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f44,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f73,plain,
! [X0,X1] :
( ( proper_element(X1,X0)
<=> X1 != union(X0) )
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f84,plain,
? [X0,X1] :
( ( proper_element(X1,powerset(X0))
<~> X1 != X0 )
& element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f88,plain,
! [X0,X1] :
( ( ( proper_element(X1,X0)
| union(X0) = X1 )
& ( X1 != union(X0)
| ~ proper_element(X1,X0) ) )
| ~ element(X1,X0) ),
inference(nnf_transformation,[],[f73]) ).
fof(f93,plain,
! [X0] :
( element(sK4(X0),powerset(X0))
& ~ proper_element(sK4(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f30]) ).
fof(f94,plain,
? [X0,X1] :
( ( X0 = X1
| ~ proper_element(X1,powerset(X0)) )
& ( X1 != X0
| proper_element(X1,powerset(X0)) )
& element(X1,powerset(X0)) ),
inference(nnf_transformation,[],[f84]) ).
fof(f95,plain,
? [X0,X1] :
( ( X0 = X1
| ~ proper_element(X1,powerset(X0)) )
& ( X1 != X0
| proper_element(X1,powerset(X0)) )
& element(X1,powerset(X0)) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
( ( sK5 = sK6
| ~ proper_element(sK6,powerset(sK5)) )
& ( sK5 != sK6
| proper_element(sK6,powerset(sK5)) )
& element(sK6,powerset(sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f95]) ).
fof(f123,plain,
! [X0,X1] :
( ~ element(X1,X0)
| union(X0) = X1
| proper_element(X1,X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f144,plain,
! [X0] : ~ proper_element(sK4(X0),powerset(X0)),
inference(cnf_transformation,[],[f93]) ).
fof(f145,plain,
! [X0] : element(sK4(X0),powerset(X0)),
inference(cnf_transformation,[],[f93]) ).
fof(f146,plain,
! [X0] : powerset(X0) = k1_pcomps_1(X0),
inference(cnf_transformation,[],[f31]) ).
fof(f154,plain,
element(sK6,powerset(sK5)),
inference(cnf_transformation,[],[f96]) ).
fof(f155,plain,
( sK5 != sK6
| proper_element(sK6,powerset(sK5)) ),
inference(cnf_transformation,[],[f96]) ).
fof(f156,plain,
( sK5 = sK6
| ~ proper_element(sK6,powerset(sK5)) ),
inference(cnf_transformation,[],[f96]) ).
fof(f160,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f44]) ).
fof(f181,plain,
! [X0] : element(sK4(X0),k1_pcomps_1(X0)),
inference(definition_unfolding,[],[f145,f146]) ).
fof(f182,plain,
! [X0] : ~ proper_element(sK4(X0),k1_pcomps_1(X0)),
inference(definition_unfolding,[],[f144,f146]) ).
fof(f187,plain,
( sK5 = sK6
| ~ proper_element(sK6,k1_pcomps_1(sK5)) ),
inference(definition_unfolding,[],[f156,f146]) ).
fof(f188,plain,
( sK5 != sK6
| proper_element(sK6,k1_pcomps_1(sK5)) ),
inference(definition_unfolding,[],[f155,f146]) ).
fof(f189,plain,
element(sK6,k1_pcomps_1(sK5)),
inference(definition_unfolding,[],[f154,f146]) ).
fof(f190,plain,
! [X0] : union(k1_pcomps_1(X0)) = X0,
inference(definition_unfolding,[],[f160,f146]) ).
fof(f193,definition,
( spl7_1
<=> proper_element(sK6,k1_pcomps_1(sK5)) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f195,plain,
( proper_element(sK6,k1_pcomps_1(sK5))
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f197,definition,
( spl7_2
<=> sK5 = sK6 ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f198,plain,
( sK5 = sK6
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f200,plain,
( spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f188,f197,f193]) ).
fof(f201,plain,
( ~ spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f187,f197,f193]) ).
fof(f423,plain,
! [X0] :
( sK4(X0) = union(k1_pcomps_1(X0))
| proper_element(sK4(X0),k1_pcomps_1(X0)) ),
inference(resolution,[],[f123,f181]) ).
fof(f424,plain,
( sK6 = union(k1_pcomps_1(sK5))
| proper_element(sK6,k1_pcomps_1(sK5)) ),
inference(resolution,[],[f123,f189]) ).
fof(f426,plain,
! [X0] : sK4(X0) = union(k1_pcomps_1(X0)),
inference(forward_subsumption_resolution,[],[f423,f182]) ).
fof(f431,plain,
! [X0] : sK4(X0) = X0,
inference(forward_demodulation,[],[f426,f190]) ).
fof(f434,plain,
( sK5 = sK6
| proper_element(sK6,k1_pcomps_1(sK5)) ),
inference(forward_demodulation,[],[f424,f190]) ).
fof(f435,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f434,f197,f193]) ).
fof(f439,plain,
( proper_element(sK5,k1_pcomps_1(sK5))
| ~ spl7_1
| ~ spl7_2 ),
inference(forward_demodulation,[],[f195,f198]) ).
fof(f506,plain,
! [X0] : ~ proper_element(X0,k1_pcomps_1(X0)),
inference(superposition,[],[f182,f431]) ).
fof(f545,plain,
( $false
| ~ spl7_1
| ~ spl7_2 ),
inference(resolution,[],[f506,f439]) ).
fof(f546,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(avatar_contradiction_clause,[],[f545]) ).
cnf(s1,plain,
( spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f200]) ).
cnf(s2,plain,
( ~ spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f201]) ).
cnf(s11,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f435]) ).
cnf(s14,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f546]) ).
cnf(s16,plain,
spl7_1,
inference(rat,[],[s1,s11]) ).
cnf(s17,plain,
~ spl7_2,
inference(rat,[],[s14,s16]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s2,s17,s16]) ).
fof(f547,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU354+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 04:53:48 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.29/0.46 % (3667571)Will run a generic schedule for satisfiability detection.
% 0.29/0.46 % (3667579)dis+10_1_sil=32000:sp=arity:random_seed=3715525128:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.29/0.46 % (3667577)% WARNING: option uhcvi not known.
% 0.29/0.46 % (3667579) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3667571-3667579"...
% 0.29/0.46 % (3667579)...printing done.
% 0.29/0.46 % (3667579)Refutation found. Thanks to Tanya!
% 0.29/0.46 % SZS status Theorem for theBenchmark
% 0.29/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.29/0.46 % (3667579)------------------------------
% 0.29/0.46 % (3667579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.46 % (3667579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.46 % (3667579)CaDiCaL version: 2.1.3
% 0.29/0.46 % (3667579)Termination reason: Refutation
% 0.29/0.46 % (3667579)Time elapsed: 0.005 s
% 0.29/0.46 % (3667579)Peak memory usage: 12 MB
% 0.29/0.46 % (3667579)Instructions burned: 10 (million)
% 0.29/0.46 % (3667571)Success in time 0.03 s
% 0.29/0.46 % Vampire exiting
%------------------------------------------------------------------------------