%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL656+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 11:54:21 AM UTC 2026
% Result : Theorem 2.56s 1.35s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 7 unt; 1 def)
% Number of atoms : 389 ( 0 equ)
% Maximal formula atoms : 37 ( 13 avg)
% Number of connectives : 649 ( 288 ~; 224 |; 137 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 10 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 99 ( 80 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f2,conjecture,
~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ ( ! [X1] :
( ~ r1(X0,X1)
| ( ( ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ p2(X0)
& ~ p102(X0)
& p101(X0) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( p2(X0)
& ~ p102(X0)
& p101(X0) ) ) )
| ~ ( ~ p101(X1)
& p100(X1) ) )
& ( ( ( ! [X0] :
( ~ r1(X1,X0)
| ~ p2(X0)
| ~ p101(X0) )
| p2(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p2(X0)
| ~ p101(X0) )
| ~ p2(X1) ) )
| ~ p101(X1) )
& ( ( ( ! [X0] :
( ~ r1(X1,X0)
| ~ p1(X0)
| ~ p100(X0) )
| p1(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p1(X0)
| ~ p100(X0) )
| ~ p1(X1) ) )
| ~ p100(X1) )
& ( p101(X1)
| ~ p102(X1) )
& ( p100(X1)
| ~ p101(X1) ) ) )
& ~ p101(X0)
& p100(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f3,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ ( ! [X1] :
( ~ r1(X0,X1)
| ( ( ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( ~ p2(X0)
& ~ p102(X0)
& p101(X0) ) )
& ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( p2(X0)
& ~ p102(X0)
& p101(X0) ) ) )
| ~ ( ~ p101(X1)
& p100(X1) ) )
& ( ( ( ! [X0] :
( ~ r1(X1,X0)
| ~ p2(X0)
| ~ p101(X0) )
| p2(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p2(X0)
| ~ p101(X0) )
| ~ p2(X1) ) )
| ~ p101(X1) )
& ( ( ( ! [X0] :
( ~ r1(X1,X0)
| ~ p1(X0)
| ~ p100(X0) )
| p1(X1) )
& ( ! [X0] :
( ~ r1(X1,X0)
| p1(X0)
| ~ p100(X0) )
| ~ p1(X1) ) )
| ~ p100(X1) )
& ( p101(X1)
| ~ p102(X1) )
& ( p100(X1)
| ~ p101(X1) ) ) )
& ~ p101(X0)
& p100(X0) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ ( ! [X2] :
( ~ r1(X0,X2)
| ( ( ( ~ ! [X3] :
( ~ r1(X2,X3)
| ~ ( ~ p2(X3)
& ~ p102(X3)
& p101(X3) ) )
& ~ ! [X4] :
( ~ r1(X2,X4)
| ~ ( p2(X4)
& ~ p102(X4)
& p101(X4) ) ) )
| ~ ( ~ p101(X2)
& p100(X2) ) )
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p2(X5)
| ~ p101(X5) )
| p2(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p2(X6)
| ~ p101(X6) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X7] :
( ~ r1(X2,X7)
| ~ p1(X7)
| ~ p100(X7) )
| p1(X2) )
& ( ! [X8] :
( ~ r1(X2,X8)
| p1(X8)
| ~ p100(X8) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p101(X2)
| ~ p102(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X0)
& p100(X0) ) ),
inference(rectify,[],[f3]) ).
fof(f5,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ ( ! [X2] :
( ~ r1(X0,X2)
| ( ( ( ~ ! [X3] :
( ~ r1(X2,X3)
| ~ ( ~ p2(X3)
& ~ p102(X3)
& p101(X3) ) )
& ~ ! [X4] :
( ~ r1(X2,X4)
| ~ ( p2(X4)
& ~ p102(X4)
& p101(X4) ) ) )
| ~ ( ~ p101(X2)
& p100(X2) ) )
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p2(X5)
| ~ p101(X5) )
| p2(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p2(X6)
| ~ p101(X6) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X7] :
( ~ r1(X2,X7)
| ~ p1(X7)
| ~ p100(X7) )
| p1(X2) )
& ( ! [X8] :
( ~ r1(X2,X8)
| p1(X8)
| ~ p100(X8) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p101(X2)
| ~ p102(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X0)
& p100(X0) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ ( ! [X2] :
( ~ r1(X0,X2)
| ( ( ( ~ ! [X3] :
( ~ r1(X2,X3)
| ~ ( ~ p2(X3)
& p101(X3) ) )
& ~ ! [X4] :
( ~ r1(X2,X4)
| ~ ( p2(X4)
& p101(X4) ) ) )
| ~ ( ~ p101(X2)
& p100(X2) ) )
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p2(X5)
| ~ p101(X5) )
| p2(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p2(X6)
| ~ p101(X6) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X7] :
( ~ r1(X2,X7)
| ~ p1(X7)
| ~ p100(X7) )
| p1(X2) )
& ( ! [X8] :
( ~ r1(X2,X8)
| p1(X8)
| ~ p100(X8) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X0)
& p100(X0) ) ),
inference(pure_predicate_removal,[],[f5]) ).
fof(f7,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ! [X2] :
( ~ r1(X0,X2)
| ( ( ( ? [X3] :
( r1(X2,X3)
& ~ p2(X3)
& p101(X3) )
& ? [X4] :
( r1(X2,X4)
& p2(X4)
& p101(X4) ) )
| p101(X2)
| ~ p100(X2) )
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p2(X5)
| ~ p101(X5) )
| p2(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p2(X6)
| ~ p101(X6) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X7] :
( ~ r1(X2,X7)
| ~ p1(X7)
| ~ p100(X7) )
| p1(X2) )
& ( ! [X8] :
( ~ r1(X2,X8)
| p1(X8)
| ~ p100(X8) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X0)
& p100(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f8,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ! [X2] :
( ~ r1(X0,X2)
| ( ( ( ? [X3] :
( r1(X2,X3)
& ~ p2(X3)
& p101(X3) )
& ? [X4] :
( r1(X2,X4)
& p2(X4)
& p101(X4) ) )
| p101(X2)
| ~ p100(X2) )
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p2(X5)
| ~ p101(X5) )
| p2(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p2(X6)
| ~ p101(X6) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X7] :
( ~ r1(X2,X7)
| ~ p1(X7)
| ~ p100(X7) )
| p1(X2) )
& ( ! [X8] :
( ~ r1(X2,X8)
| p1(X8)
| ~ p100(X8) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X0)
& p100(X0) ),
inference(flattening,[],[f7]) ).
fof(f9,definition,
! [X2] :
( ( ? [X3] :
( r1(X2,X3)
& ~ p2(X3)
& p101(X3) )
& ? [X4] :
( r1(X2,X4)
& p2(X4)
& p101(X4) ) )
| p101(X2)
| ~ p100(X2)
| ~ sP0(X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f10,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ! [X2] :
( ~ r1(X0,X2)
| ( sP0(X2)
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p2(X5)
| ~ p101(X5) )
| p2(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p2(X6)
| ~ p101(X6) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X7] :
( ~ r1(X2,X7)
| ~ p1(X7)
| ~ p100(X7) )
| p1(X2) )
& ( ! [X8] :
( ~ r1(X2,X8)
| p1(X8)
| ~ p100(X8) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X0)
& p100(X0) ),
inference(definition_folding,[],[f8,f9]) ).
fof(f11,plain,
! [X2] :
( ( ? [X3] :
( r1(X2,X3)
& ~ p2(X3)
& p101(X3) )
& ? [X4] :
( r1(X2,X4)
& p2(X4)
& p101(X4) ) )
| p101(X2)
| ~ p100(X2)
| ~ sP0(X2) ),
inference(nnf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0] :
( ( ? [X1] :
( r1(X0,X1)
& ~ p2(X1)
& p101(X1) )
& ? [X2] :
( r1(X0,X2)
& p2(X2)
& p101(X2) ) )
| p101(X0)
| ~ p100(X0)
| ~ sP0(X0) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
! [X0] :
( ( r1(X0,sK1(X0))
& ~ p2(sK1(X0))
& p101(sK1(X0))
& r1(X0,sK2(X0))
& p2(sK2(X0))
& p101(sK2(X0)) )
| p101(X0)
| ~ p100(X0)
| ~ sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f12]) ).
fof(f14,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ! [X2] :
( ~ r1(X0,X2)
| ( sP0(X2)
& ( ( ( ! [X3] :
( ~ r1(X2,X3)
| ~ p2(X3)
| ~ p101(X3) )
| p2(X2) )
& ( ! [X4] :
( ~ r1(X2,X4)
| p2(X4)
| ~ p101(X4) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p1(X5)
| ~ p100(X5) )
| p1(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p1(X6)
| ~ p100(X6) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X0)
& p100(X0) ),
inference(rectify,[],[f10]) ).
fof(f15,plain,
( ! [X1] :
( ~ r1(sK3,X1)
| p2(X1) )
& ! [X2] :
( ~ r1(sK3,X2)
| ( sP0(X2)
& ( ( ( ! [X3] :
( ~ r1(X2,X3)
| ~ p2(X3)
| ~ p101(X3) )
| p2(X2) )
& ( ! [X4] :
( ~ r1(X2,X4)
| p2(X4)
| ~ p101(X4) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X5] :
( ~ r1(X2,X5)
| ~ p1(X5)
| ~ p100(X5) )
| p1(X2) )
& ( ! [X6] :
( ~ r1(X2,X6)
| p1(X6)
| ~ p100(X6) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(sK3)
& p100(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f14]) ).
fof(f20,plain,
! [X0] :
( ~ p2(sK1(X0))
| p101(X0)
| ~ p100(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X0] :
( r1(X0,sK1(X0))
| p101(X0)
| ~ p100(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
p100(sK3),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
~ p101(sK3),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2] :
( ~ r1(sK3,X2)
| sP0(X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X1] :
( ~ r1(sK3,X1)
| p2(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f45,plain,
sP0(sK3),
inference(resolution,[],[f31,f29]) ).
fof(f83,plain,
( p101(sK3)
| ~ p100(sK3)
| ~ sP0(sK3)
| p2(sK1(sK3)) ),
inference(resolution,[],[f21,f30]) ).
fof(f90,plain,
( p101(sK3)
| ~ p100(sK3)
| ~ sP0(sK3) ),
inference(forward_subsumption_resolution,[],[f83,f20]) ).
fof(f98,plain,
( ~ p100(sK3)
| ~ sP0(sK3) ),
inference(forward_subsumption_resolution,[],[f90,f23]) ).
fof(f106,plain,
~ sP0(sK3),
inference(forward_subsumption_resolution,[],[f98,f22]) ).
fof(f111,plain,
$false,
inference(forward_subsumption_resolution,[],[f106,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL656+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n019.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 16:20:04 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 2.56/1.35 % (3245159)Detected formulas, will run a generic FOF schedule.
% 2.56/1.35 % (3245168)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1918309268:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.56/1.35 % (3245168)First to succeed.
% 2.56/1.35 % (3245168)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3245159"
% 2.56/1.35 % (3245169)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=293779016:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.56/1.35 % (3245169)Also succeeded, but the first one will report.
% 2.56/1.35 % (3245164)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=2417873995:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.56/1.35 % (3245165)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=1249992666:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.56/1.35 % (3245166)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=3372319113:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.56/1.35 % (3245167)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=288376407:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.56/1.35 % (3245167)Also succeeded, but the first one will report.
% 2.56/1.35 % (3245170)dis-21_1_sil=8000:lcm=predicate:random_seed=1417186309: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)
% 2.56/1.35 % (3245170)Also succeeded, but the first one will report.
% 2.56/1.35 % (3245168)Refutation found. Thanks to Tanya!
% 2.56/1.35 % SZS status Theorem for theBenchmark
% 2.56/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.35 % (3245168)------------------------------
% 2.56/1.35 % (3245168)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.35 % (3245168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.35 % (3245168)CaDiCaL version: 2.1.3
% 2.56/1.35 % (3245168)Termination reason: Refutation
% 2.56/1.35 % (3245168)Time elapsed: 0.002 s
% 2.56/1.35 % (3245168)Peak memory usage: 88 MB
% 2.56/1.35 % (3245168)Instructions burned: 3 (million)
% 2.56/1.35 % (3245168)------------------------------
% 2.56/1.35 % (3245168)------------------------------
% 2.56/1.35 % (3245159)Success in time 0.278 s
% 2.56/1.35 % Vampire exiting
%------------------------------------------------------------------------------