%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL463+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 : Tue Sep 29 11:52:31 AM UTC 2026
% Result : Theorem 7.75s 1.83s
% Output : Refutation 8.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 15
% Syntax : Number of formulae : 97 ( 31 unt; 1 def)
% Number of atoms : 203 ( 9 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 201 ( 95 ~; 89 |; 2 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 189 ( 0 sgn 187 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_1) ).
fof(f19,axiom,
( cn1
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn1) ).
fof(f20,axiom,
( cn2
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn2) ).
fof(f21,axiom,
( cn3
<=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_modus_ponens) ).
fof(f36,axiom,
cn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn1) ).
fof(f37,axiom,
cn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn2) ).
fof(f38,axiom,
cn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn3) ).
fof(f40,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f43,conjecture,
implies_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f44,negated_conjecture,
~ implies_1,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ implies_1,
inference(flattening,[],[f44]) ).
fof(f46,plain,
( cn3
=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f21]) ).
fof(f47,plain,
( cn2
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f48,plain,
( cn1
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f49,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
=> implies_1 ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f51,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f55,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f51]) ).
fof(f56,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f55]) ).
fof(f58,plain,
( implies_1
| ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f59,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ),
inference(ennf_transformation,[],[f48]) ).
fof(f60,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ),
inference(ennf_transformation,[],[f47]) ).
fof(f61,plain,
( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ),
inference(ennf_transformation,[],[f46]) ).
fof(f62,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f63,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f65,plain,
( implies_1
| ~ is_a_theorem(implies(sK0,implies(sK1,sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f58]) ).
fof(f66,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f56]) ).
fof(f68,plain,
( implies_1
| ~ is_a_theorem(implies(sK0,implies(sK1,sK0))) ),
inference(cnf_transformation,[],[f65]) ).
fof(f69,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ),
inference(cnf_transformation,[],[f59]) ).
fof(f70,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ),
inference(cnf_transformation,[],[f60]) ).
fof(f71,plain,
! [X0] :
( is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ),
inference(cnf_transformation,[],[f61]) ).
fof(f72,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f62]) ).
fof(f73,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f63]) ).
fof(f77,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f78,plain,
cn1,
inference(cnf_transformation,[],[f36]) ).
fof(f79,plain,
cn2,
inference(cnf_transformation,[],[f37]) ).
fof(f80,plain,
cn3,
inference(cnf_transformation,[],[f38]) ).
fof(f82,plain,
op_or,
inference(cnf_transformation,[],[f40]) ).
fof(f83,plain,
op_implies_and,
inference(cnf_transformation,[],[f41]) ).
fof(f85,plain,
~ implies_1,
inference(cnf_transformation,[],[f45]) ).
fof(f87,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f73,f83]) ).
fof(f88,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f72,f82]) ).
fof(f89,plain,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(forward_subsumption_resolution,[],[f71,f80]) ).
fof(f90,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(forward_subsumption_resolution,[],[f70,f79]) ).
fof(f91,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(forward_subsumption_resolution,[],[f69,f78]) ).
fof(f92,plain,
~ is_a_theorem(implies(sK0,implies(sK1,sK0))),
inference(forward_subsumption_resolution,[],[f68,f85]) ).
fof(f94,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f66,f77]) ).
fof(f95,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f88,f87]) ).
fof(f100,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(superposition,[],[f90,f95]) ).
fof(f101,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),X0)),
inference(superposition,[],[f89,f95]) ).
fof(f110,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f94,f91]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f110,f94]) ).
fof(f120,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X1),or(X0,X1)))
| ~ is_a_theorem(implies(not(X0),X2)) ),
inference(superposition,[],[f110,f95]) ).
fof(f121,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X1),or(X0,X1)))
| ~ is_a_theorem(or(X0,X2)) ),
inference(forward_demodulation,[],[f120,f95]) ).
fof(f122,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(implies(X0,implies(implies(X2,X3),implies(X1,X3))))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f118,f91]) ).
fof(f123,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| is_a_theorem(implies(X0,implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(resolution,[],[f118,f110]) ).
fof(f126,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f118,f101]) ).
fof(f132,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(X2,X3),implies(X1,X3))) ),
inference(resolution,[],[f122,f94]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(X1,X2),implies(not(X0),X2))) ),
inference(resolution,[],[f132,f90]) ).
fof(f166,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),or(X0,X2)))
| ~ is_a_theorem(X0) ),
inference(forward_demodulation,[],[f157,f95]) ).
fof(f167,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,or(X0,X3))) ),
inference(resolution,[],[f166,f118]) ).
fof(f254,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X1,or(X0,X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f167,f90]) ).
fof(f274,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(or(X1,X0)) ),
inference(resolution,[],[f126,f121]) ).
fof(f276,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f126,f254]) ).
fof(f290,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X3,X0))
| is_a_theorem(implies(X2,implies(X3,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f276,f123]) ).
fof(f304,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f274,f94]) ).
fof(f321,plain,
! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(implies(implies(X2,X4),implies(X1,X4)),X3))
| is_a_theorem(implies(X0,implies(implies(X1,X2),X3))) ),
inference(resolution,[],[f290,f91]) ).
fof(f340,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(implies(X0,implies(implies(X1,X2),X3)))
| ~ is_a_theorem(X3) ),
inference(resolution,[],[f321,f276]) ).
fof(f360,plain,
! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(X2,implies(X3,X4)))
| is_a_theorem(implies(X1,implies(X2,X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f340,f123]) ).
fof(f377,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(X2) ),
inference(resolution,[],[f360,f90]) ).
fof(f396,definition,
( spl2_4
<=> ! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(X2) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f397,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(X2) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f396]) ).
fof(f400,plain,
spl2_4,
inference(avatar_split_clause,[],[f377,f396]) ).
fof(f413,plain,
( ! [X2,X0,X1] :
( is_a_theorem(or(X0,implies(X1,X2)))
| ~ is_a_theorem(X2) )
| ~ spl2_4 ),
inference(superposition,[],[f397,f95]) ).
fof(f641,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X1,X0),X2))
| ~ is_a_theorem(X0)
| is_a_theorem(X2) )
| ~ spl2_4 ),
inference(resolution,[],[f413,f304]) ).
fof(f657,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(implies(X4,X0),implies(X3,X1)))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(X0) )
| ~ spl2_4 ),
inference(resolution,[],[f641,f122]) ).
fof(f706,plain,
( ! [X2,X3,X0,X1] :
( is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(X3,X1),X2)))
| ~ is_a_theorem(X3) )
| ~ spl2_4 ),
inference(resolution,[],[f657,f91]) ).
fof(f741,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(implies(X1,X2),X3))
| ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(X0,X2),X3)) )
| ~ spl2_4 ),
inference(resolution,[],[f706,f94]) ).
fof(f744,plain,
( ! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) )
| ~ spl2_4 ),
inference(resolution,[],[f741,f89]) ).
fof(f776,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,implies(X0,X2)))
| ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,X2)) )
| ~ spl2_4 ),
inference(resolution,[],[f744,f118]) ).
fof(f791,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X2,implies(X3,X0)))
| is_a_theorem(implies(X2,implies(X3,X1)))
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl2_4 ),
inference(resolution,[],[f776,f122]) ).
fof(f994,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ is_a_theorem(implies(implies(X4,X2),X3))
| is_a_theorem(implies(X0,implies(implies(X1,X2),X3)))
| ~ is_a_theorem(implies(X0,implies(X4,X1))) )
| ~ spl2_4 ),
inference(resolution,[],[f791,f122]) ).
fof(f1066,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(implies(X1,X2),X2)))
| ~ is_a_theorem(implies(X0,implies(not(X2),X1))) )
| ~ spl2_4 ),
inference(resolution,[],[f994,f89]) ).
fof(f1097,plain,
( ! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(implies(X1,X2),X2)))
| ~ is_a_theorem(implies(X0,or(X2,X1))) )
| ~ spl2_4 ),
inference(forward_demodulation,[],[f1066,f95]) ).
fof(f1098,plain,
( ! [X2,X3,X0,X1] :
( ~ is_a_theorem(implies(X3,implies(X2,X1)))
| is_a_theorem(implies(X0,implies(X3,X1)))
| ~ is_a_theorem(implies(X0,or(X1,X2))) )
| ~ spl2_4 ),
inference(resolution,[],[f1097,f123]) ).
fof(f1122,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X2,not(X1))))
| is_a_theorem(implies(X0,implies(X1,X2))) )
| ~ spl2_4 ),
inference(resolution,[],[f1098,f90]) ).
fof(f1157,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ spl2_4 ),
inference(resolution,[],[f1122,f100]) ).
fof(f1199,plain,
( $false
| ~ spl2_4 ),
inference(resolution,[],[f1157,f92]) ).
fof(f1202,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[],[f1199]) ).
cnf(s4,plain,
spl2_4,
inference(sat_conversion,[],[f400]) ).
cnf(s23,plain,
~ spl2_4,
inference(sat_conversion,[],[f1202]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s4,s23]) ).
fof(f1203,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL463+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 15:49:09 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.75/1.83 % (2539975)Detected formulas, will run a generic FOF schedule.
% 7.75/1.83 % (2539986)dis-21_1_sil=8000:lcm=predicate:random_seed=2796990168:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 7.75/1.83 % (2539986)Refutation not found, incomplete strategy
% 7.75/1.83 % (2539986)------------------------------
% 7.75/1.83 % (2539986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.83 % (2539986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.83 % (2539986)CaDiCaL version: 2.1.3
% 7.75/1.83 % (2539986)Termination reason: Refutation not found, incomplete strategy
% 7.75/1.83 % (2539986)Time elapsed: 0.001 s
% 7.75/1.83 % (2539986)Peak memory usage: 88 MB
% 7.75/1.83 % (2539986)Instructions burned: 1 (million)
% 7.75/1.83 % (2539983)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2134362161:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.75/1.83 % (2539985)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3654842625:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.75/1.83 % (2539980)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1382985793:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.75/1.83 % (2539984)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3549996950:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.75/1.83 % (2539981)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3373846226:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.75/1.83 % (2539982)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2370340219:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.75/1.83 % (2539983)Refutation not found, incomplete strategy
% 7.75/1.83 % (2539983)------------------------------
% 7.75/1.83 % (2539983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.83 % (2539983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.83 % (2539983)CaDiCaL version: 2.1.3
% 7.75/1.83 % (2539983)Termination reason: Refutation not found, incomplete strategy
% 7.75/1.83 % (2539983)Time elapsed: 0.0000 s
% 7.75/1.83 % (2539983)Peak memory usage: 87 MB
% 7.75/1.83 % (2539984)Refutation not found, incomplete strategy
% 7.75/1.83 % (2539984)------------------------------
% 7.75/1.83 % (2539984)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.83 % (2539984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.83 % (2539984)CaDiCaL version: 2.1.3
% 7.75/1.83 % (2539984)Termination reason: Refutation not found, incomplete strategy
% 7.75/1.83 % (2539984)Time elapsed: 0.0000 s
% 7.75/1.83 % (2539984)Peak memory usage: 87 MB
% 7.75/1.83 % (2539985)Instruction limit reached!
% 7.75/1.83 % (2539985)------------------------------
% 7.75/1.83 % (2539985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.83 % (2539985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.83 % (2539985)CaDiCaL version: 2.1.3
% 7.75/1.83 % (2539985)Termination reason: Instruction limit
% 7.75/1.83 % (2539985)Termination phase: Saturation
% 7.75/1.83 % (2539985)Time elapsed: 0.097 s
% 7.75/1.83 % (2539985)Peak memory usage: 90 MB
% 7.75/1.83 % (2539985)Instructions burned: 139 (million)
% 7.75/1.83 % (2539986)------------------------------
% 7.75/1.83 % (2539986)------------------------------
% 7.75/1.83 % (2539984)------------------------------
% 7.75/1.83 % (2539984)------------------------------
% 7.75/1.83 % (2539983)------------------------------
% 7.75/1.83 % (2539983)------------------------------
% 7.75/1.83 % (2539994)lrs+10_1_sil=8000:sp=occurrence:random_seed=3462991569:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 7.75/1.83 % (2539994)Refutation not found, incomplete strategy
% 7.75/1.83 % (2539994)------------------------------
% 7.75/1.83 % (2539994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.83 % (2539994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.83 % (2539994)CaDiCaL version: 2.1.3
% 7.75/1.83 % (2539994)Termination reason: Refutation not found, incomplete strategy
% 7.75/1.83 % (2539994)Time elapsed: 0.001 s
% 7.75/1.83 % (2539994)Peak memory usage: 87 MB
% 7.75/1.83 % (2539995)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1860375444:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 7.75/1.83 % (2539995)Refutation not found, incomplete strategy
% 7.75/1.83 % (2539995)------------------------------
% 7.75/1.83 % (2539995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.83 % (2539995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.83 % (2539995)CaDiCaL version: 2.1.3
% 7.75/1.83 % (2539995)Termination reason: Refutation not found, incomplete strategy
% 7.75/1.83 % (2539995)Time elapsed: 0.001 s
% 7.75/1.83 % (2539995)Peak memory usage: 87 MB
% 7.75/1.83 % (2539998)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=710439197:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 7.75/1.83 % (2539997)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2056176071:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 7.75/1.83 % (2539997)Refutation not found, incomplete strategy
% 7.75/1.83 % (2539997)------------------------------
% 7.75/1.83 % (2539997)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.83 % (2539997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.83 % (2539997)CaDiCaL version: 2.1.3
% 7.75/1.83 % (2539997)Termination reason: Refutation not found, incomplete strategy
% 7.75/1.83 % (2539997)Time elapsed: 0.001 s
% 7.75/1.83 % (2539997)Peak memory usage: 87 MB
% 7.75/1.83 % (2539995)------------------------------
% 7.75/1.83 % (2539995)------------------------------
% 7.75/1.83 % (2539994)------------------------------
% 7.75/1.83 % (2539994)------------------------------
% 7.75/1.83 % (2539982)Refutation not found, incomplete strategy
% 7.75/1.83 % (2539982)------------------------------
% 7.75/1.83 % (2539982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.83 % (2539982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.83 % (2539982)CaDiCaL version: 2.1.3
% 7.75/1.83 % (2539982)Termination reason: Refutation not found, incomplete strategy
% 7.75/1.83 % (2539982)Time elapsed: 0.557 s
% 7.75/1.83 % (2539982)Peak memory usage: 126 MB
% 7.75/1.83 % (2539982)Instructions burned: 825 (million)
% 7.75/1.83 % (2539998)Instruction limit reached!
% 7.75/1.83 % (2539998)------------------------------
% 7.75/1.83 % (2539998)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.83 % (2539998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.83 % (2539998)CaDiCaL version: 2.1.3
% 7.75/1.83 % (2539998)Termination reason: Instruction limit
% 7.75/1.83 % (2539998)Termination phase: Saturation
% 7.75/1.83 % (2539998)Time elapsed: 0.160 s
% 7.75/1.83 % (2539998)Peak memory usage: 92 MB
% 7.75/1.83 % (2539998)Instructions burned: 248 (million)
% 7.75/1.83 % (2540002)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4003627761:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 7.75/1.83 % (2540002)Refutation not found, incomplete strategy
% 7.75/1.83 % (2540002)------------------------------
% 7.75/1.83 % (2540002)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.83 % (2540002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.83 % (2540002)CaDiCaL version: 2.1.3
% 7.75/1.83 % (2540002)Termination reason: Refutation not found, incomplete strategy
% 7.75/1.83 % (2540002)Time elapsed: 0.0000 s
% 7.75/1.83 % (2540002)Peak memory usage: 87 MB
% 7.75/1.83 % (2539997)------------------------------
% 7.75/1.83 % (2539997)------------------------------
% 7.75/1.83 % (2540003)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1909223122:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 7.75/1.83 % (2540002)------------------------------
% 7.75/1.83 % (2540002)------------------------------
% 7.75/1.83 % (2540005)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1204754528:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 7.75/1.83 % (2540005)Refutation not found, incomplete strategy
% 7.75/1.83 % (2540005)------------------------------
% 7.75/1.83 % (2540005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.83 % (2540005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.83 % (2540005)CaDiCaL version: 2.1.3
% 7.75/1.83 % (2540005)Termination reason: Refutation not found, incomplete strategy
% 7.75/1.83 % (2540005)Time elapsed: 0.001 s
% 7.75/1.83 % (2540005)Peak memory usage: 88 MB
% 7.75/1.83 % (2539980)First to succeed.
% 7.75/1.83 % (2539980)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2539975"
% 7.75/1.83 % (2539982)------------------------------
% 7.75/1.83 % (2539982)------------------------------
% 7.75/1.83 % (2540006)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=849805145:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 7.75/1.83 % (2540008)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=543027281:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 7.75/1.83 % (2540008)Refutation not found, incomplete strategy
% 7.75/1.83 % (2540008)------------------------------
% 7.75/1.83 % (2540008)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.83 % (2540008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.83 % (2540008)CaDiCaL version: 2.1.3
% 7.75/1.83 % (2540008)Termination reason: Refutation not found, incomplete strategy
% 7.75/1.83 % (2540008)Time elapsed: 0.0000 s
% 7.75/1.83 % (2540008)Peak memory usage: 87 MB
% 7.75/1.83 % (2540006)Instruction limit reached!
% 7.75/1.83 % (2540006)------------------------------
% 7.75/1.83 % (2540006)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.83 % (2540006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.83 % (2540006)CaDiCaL version: 2.1.3
% 7.75/1.83 % (2540006)Termination reason: Instruction limit
% 7.75/1.83 % (2540006)Termination phase: Saturation
% 7.75/1.83 % (2540006)Time elapsed: 0.075 s
% 7.75/1.83 % (2540006)Peak memory usage: 89 MB
% 7.75/1.83 % (2540006)Instructions burned: 128 (million)
% 7.75/1.83 % (2540010)lrs+10_1_sil=8000:sp=occurrence:random_seed=4148195000:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 7.75/1.83 % (2540010)Refutation not found, incomplete strategy
% 7.75/1.83 % (2540010)------------------------------
% 7.75/1.83 % (2540010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.75/1.83 % (2540010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.83 % (2540010)CaDiCaL version: 2.1.3
% 7.75/1.83 % (2540010)Termination reason: Refutation not found, incomplete strategy
% 7.75/1.83 % (2540010)Time elapsed: 0.001 s
% 7.75/1.83 % (2540010)Peak memory usage: 87 MB
% 7.75/1.83 % (2540005)------------------------------
% 7.75/1.83 % (2540005)------------------------------
% 7.75/1.83 % (2540008)------------------------------
% 7.75/1.83 % (2540008)------------------------------
% 7.75/1.83 % (2539980)Refutation found. Thanks to Tanya!
% 7.75/1.83 % SZS status Theorem for theBenchmark
% 7.75/1.83 % SZS output start Proof for theBenchmark
% See solution above
% 8.90/1.93 % (2539980)------------------------------
% 8.90/1.93 % (2539980)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.90/1.93 % (2539980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.90/1.93 % (2539980)CaDiCaL version: 2.1.3
% 8.90/1.93 % (2539980)Termination reason: Refutation
% 8.90/1.93 % (2539980)Time elapsed: 0.792 s
% 8.90/1.93 % (2539980)Peak memory usage: 130 MB
% 8.90/1.93 % (2539980)Instructions burned: 1178 (million)
% 8.90/1.93 % (2539980)------------------------------
% 8.90/1.93 % (2539980)------------------------------
% 8.90/1.93 % (2539975)Success in time 1.218 s
% 8.90/1.93 % Vampire exiting
%------------------------------------------------------------------------------