%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL644+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 : n014.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 11:53:46 AM UTC 2026
% Result : Theorem 0.15s 11.60s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 3 unt; 5 def)
% Number of atoms : 432 ( 0 equ)
% Maximal formula atoms : 53 ( 25 avg)
% Number of connectives : 645 ( 230 ~; 232 |; 183 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 14 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 158 ( 119 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X0] :
~ ( ~ ( ! [X1] :
( ~ r1(X0,X1)
| ~ ( p2(X1)
& ! [X0] :
( ~ r1(X1,X0)
| p2(X0) ) )
| p1(X1) )
| ! [X1] :
( ~ r1(X0,X1)
| p2(X1)
| ~ ( p1(X1)
& ! [X0] :
( ~ r1(X1,X0)
| p1(X0) )
& p1(X1) ) )
| ~ ( ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| ~ ( p2(X0)
& ! [X1] :
( ~ r1(X0,X1)
| p2(X1) ) )
| p1(X0) )
| p2(X1)
| ~ ( p1(X1)
& ! [X0] :
( ~ r1(X1,X0)
| p1(X0) )
& p1(X1) ) )
& ! [X1] :
( ~ r1(X0,X1)
| ~ ( p2(X1)
& ! [X0] :
( ~ r1(X1,X0)
| p2(X0) ) )
| p1(X1)
| ! [X0] :
( ~ r1(X1,X0)
| p2(X0)
| ~ ( p1(X0)
& ! [X1] :
( ~ r1(X0,X1)
| p1(X1) )
& p1(X0) ) ) )
& ! [X1] :
( ~ r1(X0,X1)
| ~ ( p2(X1)
& ! [X0] :
( ~ r1(X1,X0)
| p2(X0) ) )
| p1(X1)
| p2(X1)
| ~ ( p1(X1)
& ! [X0] :
( ~ r1(X1,X0)
| p1(X0) )
& p1(X1) ) ) ) )
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1)
| ~ ( ! [X0] :
( ~ r1(X1,X0)
| p1(X0) )
& p1(X1) ) )
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1)
| ~ ( ! [X0] :
( ~ r1(X1,X0)
| p1(X0) )
& p1(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f2,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ( ! [X1] :
( ~ r1(X0,X1)
| ~ ( p2(X1)
& ! [X0] :
( ~ r1(X1,X0)
| p2(X0) ) )
| p1(X1) )
| ! [X1] :
( ~ r1(X0,X1)
| p2(X1)
| ~ ( p1(X1)
& ! [X0] :
( ~ r1(X1,X0)
| p1(X0) )
& p1(X1) ) )
| ~ ( ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| ~ ( p2(X0)
& ! [X1] :
( ~ r1(X0,X1)
| p2(X1) ) )
| p1(X0) )
| p2(X1)
| ~ ( p1(X1)
& ! [X0] :
( ~ r1(X1,X0)
| p1(X0) )
& p1(X1) ) )
& ! [X1] :
( ~ r1(X0,X1)
| ~ ( p2(X1)
& ! [X0] :
( ~ r1(X1,X0)
| p2(X0) ) )
| p1(X1)
| ! [X0] :
( ~ r1(X1,X0)
| p2(X0)
| ~ ( p1(X0)
& ! [X1] :
( ~ r1(X0,X1)
| p1(X1) )
& p1(X0) ) ) )
& ! [X1] :
( ~ r1(X0,X1)
| ~ ( p2(X1)
& ! [X0] :
( ~ r1(X1,X0)
| p2(X0) ) )
| p1(X1)
| p2(X1)
| ~ ( p1(X1)
& ! [X0] :
( ~ r1(X1,X0)
| p1(X0) )
& p1(X1) ) ) ) )
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1)
| ~ ( ! [X0] :
( ~ r1(X1,X0)
| p1(X0) )
& p1(X1) ) )
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1)
| ~ ( ! [X0] :
( ~ r1(X1,X0)
| p1(X0) )
& p1(X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ~ ? [X0] :
~ ( ~ ( ! [X1] :
( ~ r1(X0,X1)
| ~ ( p2(X1)
& ! [X2] :
( ~ r1(X1,X2)
| p2(X2) ) )
| p1(X1) )
| ! [X3] :
( ~ r1(X0,X3)
| p2(X3)
| ~ ( p1(X3)
& ! [X4] :
( ~ r1(X3,X4)
| p1(X4) )
& p1(X3) ) )
| ~ ( ! [X5] :
( ~ r1(X0,X5)
| ! [X6] :
( ~ r1(X5,X6)
| ~ ( p2(X6)
& ! [X7] :
( ~ r1(X6,X7)
| p2(X7) ) )
| p1(X6) )
| p2(X5)
| ~ ( p1(X5)
& ! [X8] :
( ~ r1(X5,X8)
| p1(X8) )
& p1(X5) ) )
& ! [X9] :
( ~ r1(X0,X9)
| ~ ( p2(X9)
& ! [X10] :
( ~ r1(X9,X10)
| p2(X10) ) )
| p1(X9)
| ! [X11] :
( ~ r1(X9,X11)
| p2(X11)
| ~ ( p1(X11)
& ! [X12] :
( ~ r1(X11,X12)
| p1(X12) )
& p1(X11) ) ) )
& ! [X13] :
( ~ r1(X0,X13)
| ~ ( p2(X13)
& ! [X14] :
( ~ r1(X13,X14)
| p2(X14) ) )
| p1(X13)
| p2(X13)
| ~ ( p1(X13)
& ! [X15] :
( ~ r1(X13,X15)
| p1(X15) )
& p1(X13) ) ) ) )
| ! [X16] :
( ~ r1(X0,X16)
| p1(X16)
| ~ ( ! [X17] :
( ~ r1(X16,X17)
| p1(X17) )
& p1(X16) ) )
| ! [X18] :
( ~ r1(X0,X18)
| p1(X18)
| ~ ( ! [X19] :
( ~ r1(X18,X19)
| p1(X19) )
& p1(X18) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
? [X0] :
~ ( ~ ( ! [X1] :
( ~ r1(X0,X1)
| ~ ( p2(X1)
& ! [X2] :
( ~ r1(X1,X2)
| p2(X2) ) )
| p1(X1) )
| ! [X3] :
( ~ r1(X0,X3)
| p2(X3)
| ~ ( p1(X3)
& ! [X4] :
( ~ r1(X3,X4)
| p1(X4) )
& p1(X3) ) )
| ~ ( ! [X5] :
( ~ r1(X0,X5)
| ! [X6] :
( ~ r1(X5,X6)
| ~ ( p2(X6)
& ! [X7] :
( ~ r1(X6,X7)
| p2(X7) ) )
| p1(X6) )
| p2(X5)
| ~ ( p1(X5)
& ! [X8] :
( ~ r1(X5,X8)
| p1(X8) )
& p1(X5) ) )
& ! [X9] :
( ~ r1(X0,X9)
| ~ ( p2(X9)
& ! [X10] :
( ~ r1(X9,X10)
| p2(X10) ) )
| p1(X9)
| ! [X11] :
( ~ r1(X9,X11)
| p2(X11)
| ~ ( p1(X11)
& ! [X12] :
( ~ r1(X11,X12)
| p1(X12) )
& p1(X11) ) ) )
& ! [X13] :
( ~ r1(X0,X13)
| ~ ( p2(X13)
& ! [X14] :
( ~ r1(X13,X14)
| p2(X14) ) )
| p1(X13)
| p2(X13)
| ~ ( p1(X13)
& ! [X15] :
( ~ r1(X13,X15)
| p1(X15) )
& p1(X13) ) ) ) )
| ! [X16] :
( ~ r1(X0,X16)
| p1(X16)
| ~ ( ! [X17] :
( ~ r1(X16,X17)
| p1(X17) )
& p1(X16) ) )
| ! [X18] :
( ~ r1(X0,X18)
| p1(X18)
| ~ ( ! [X19] :
( ~ r1(X18,X19)
| p1(X19) )
& p1(X18) ) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
? [X0] :
( ( ! [X1] :
( ~ r1(X0,X1)
| ~ p2(X1)
| ? [X2] :
( r1(X1,X2)
& ~ p2(X2) )
| p1(X1) )
| ! [X3] :
( ~ r1(X0,X3)
| p2(X3)
| ~ p1(X3)
| ? [X4] :
( r1(X3,X4)
& ~ p1(X4) )
| ~ p1(X3) )
| ? [X5] :
( r1(X0,X5)
& ? [X6] :
( r1(X5,X6)
& p2(X6)
& ! [X7] :
( ~ r1(X6,X7)
| p2(X7) )
& ~ p1(X6) )
& ~ p2(X5)
& p1(X5)
& ! [X8] :
( ~ r1(X5,X8)
| p1(X8) )
& p1(X5) )
| ? [X9] :
( r1(X0,X9)
& p2(X9)
& ! [X10] :
( ~ r1(X9,X10)
| p2(X10) )
& ~ p1(X9)
& ? [X11] :
( r1(X9,X11)
& ~ p2(X11)
& p1(X11)
& ! [X12] :
( ~ r1(X11,X12)
| p1(X12) )
& p1(X11) ) )
| ? [X13] :
( r1(X0,X13)
& p2(X13)
& ! [X14] :
( ~ r1(X13,X14)
| p2(X14) )
& ~ p1(X13)
& ~ p2(X13)
& p1(X13)
& ! [X15] :
( ~ r1(X13,X15)
| p1(X15) )
& p1(X13) ) )
& ? [X16] :
( r1(X0,X16)
& ~ p1(X16)
& ! [X17] :
( ~ r1(X16,X17)
| p1(X17) )
& p1(X16) )
& ? [X18] :
( r1(X0,X18)
& ~ p1(X18)
& ! [X19] :
( ~ r1(X18,X19)
| p1(X19) )
& p1(X18) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f6,plain,
? [X0] :
( ( ! [X1] :
( ~ r1(X0,X1)
| ~ p2(X1)
| ? [X2] :
( r1(X1,X2)
& ~ p2(X2) )
| p1(X1) )
| ! [X3] :
( ~ r1(X0,X3)
| p2(X3)
| ~ p1(X3)
| ? [X4] :
( r1(X3,X4)
& ~ p1(X4) )
| ~ p1(X3) )
| ? [X5] :
( r1(X0,X5)
& ? [X6] :
( r1(X5,X6)
& p2(X6)
& ! [X7] :
( ~ r1(X6,X7)
| p2(X7) )
& ~ p1(X6) )
& ~ p2(X5)
& p1(X5)
& ! [X8] :
( ~ r1(X5,X8)
| p1(X8) )
& p1(X5) )
| ? [X9] :
( r1(X0,X9)
& p2(X9)
& ! [X10] :
( ~ r1(X9,X10)
| p2(X10) )
& ~ p1(X9)
& ? [X11] :
( r1(X9,X11)
& ~ p2(X11)
& p1(X11)
& ! [X12] :
( ~ r1(X11,X12)
| p1(X12) )
& p1(X11) ) )
| ? [X13] :
( r1(X0,X13)
& p2(X13)
& ! [X14] :
( ~ r1(X13,X14)
| p2(X14) )
& ~ p1(X13)
& ~ p2(X13)
& p1(X13)
& ! [X15] :
( ~ r1(X13,X15)
| p1(X15) )
& p1(X13) ) )
& ? [X16] :
( r1(X0,X16)
& ~ p1(X16)
& ! [X17] :
( ~ r1(X16,X17)
| p1(X17) )
& p1(X16) )
& ? [X18] :
( r1(X0,X18)
& ~ p1(X18)
& ! [X19] :
( ~ r1(X18,X19)
| p1(X19) )
& p1(X18) ) ),
inference(flattening,[],[f5]) ).
fof(f7,definition,
! [X9] :
( ? [X11] :
( r1(X9,X11)
& ~ p2(X11)
& p1(X11)
& ! [X12] :
( ~ r1(X11,X12)
| p1(X12) )
& p1(X11) )
| ~ sP0(X9) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f8,definition,
! [X5] :
( ? [X6] :
( r1(X5,X6)
& p2(X6)
& ! [X7] :
( ~ r1(X6,X7)
| p2(X7) )
& ~ p1(X6) )
| ~ sP1(X5) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f9,definition,
! [X0] :
( ? [X13] :
( r1(X0,X13)
& p2(X13)
& ! [X14] :
( ~ r1(X13,X14)
| p2(X14) )
& ~ p1(X13)
& ~ p2(X13)
& p1(X13)
& ! [X15] :
( ~ r1(X13,X15)
| p1(X15) )
& p1(X13) )
| ~ sP2(X0) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f10,definition,
! [X0] :
( ? [X5] :
( r1(X0,X5)
& sP1(X5)
& ~ p2(X5)
& p1(X5)
& ! [X8] :
( ~ r1(X5,X8)
| p1(X8) )
& p1(X5) )
| ~ sP3(X0) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f11,definition,
! [X0] :
( ? [X9] :
( r1(X0,X9)
& p2(X9)
& ! [X10] :
( ~ r1(X9,X10)
| p2(X10) )
& ~ p1(X9)
& sP0(X9) )
| ~ sP4(X0) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f12,plain,
? [X0] :
( ( ! [X1] :
( ~ r1(X0,X1)
| ~ p2(X1)
| ? [X2] :
( r1(X1,X2)
& ~ p2(X2) )
| p1(X1) )
| ! [X3] :
( ~ r1(X0,X3)
| p2(X3)
| ~ p1(X3)
| ? [X4] :
( r1(X3,X4)
& ~ p1(X4) )
| ~ p1(X3) )
| sP3(X0)
| sP4(X0)
| sP2(X0) )
& ? [X16] :
( r1(X0,X16)
& ~ p1(X16)
& ! [X17] :
( ~ r1(X16,X17)
| p1(X17) )
& p1(X16) )
& ? [X18] :
( r1(X0,X18)
& ~ p1(X18)
& ! [X19] :
( ~ r1(X18,X19)
| p1(X19) )
& p1(X18) ) ),
inference(definition_folding,[],[f6,f11,f10,f9,f8,f7]) ).
fof(f28,plain,
? [X0] :
( ( ! [X1] :
( ~ r1(X0,X1)
| ~ p2(X1)
| ? [X2] :
( r1(X1,X2)
& ~ p2(X2) )
| p1(X1) )
| ! [X3] :
( ~ r1(X0,X3)
| p2(X3)
| ~ p1(X3)
| ? [X4] :
( r1(X3,X4)
& ~ p1(X4) )
| ~ p1(X3) )
| sP3(X0)
| sP4(X0)
| sP2(X0) )
& ? [X5] :
( r1(X0,X5)
& ~ p1(X5)
& ! [X6] :
( ~ r1(X5,X6)
| p1(X6) )
& p1(X5) )
& ? [X7] :
( r1(X0,X7)
& ~ p1(X7)
& ! [X8] :
( ~ r1(X7,X8)
| p1(X8) )
& p1(X7) ) ),
inference(rectify,[],[f12]) ).
fof(f29,plain,
( ( ! [X1] :
( ~ r1(sK10,X1)
| ~ p2(X1)
| ( r1(X1,sK11(X1))
& ~ p2(sK11(X1)) )
| p1(X1) )
| ! [X3] :
( ~ r1(sK10,X3)
| p2(X3)
| ~ p1(X3)
| ( r1(X3,sK12(X3))
& ~ p1(sK12(X3)) )
| ~ p1(X3) )
| sP3(sK10)
| sP4(sK10)
| sP2(sK10) )
& r1(sK10,sK13)
& ~ p1(sK13)
& ! [X6] :
( ~ r1(sK13,X6)
| p1(X6) )
& p1(sK13)
& r1(sK10,sK14)
& ~ p1(sK14)
& ! [X8] :
( ~ r1(sK14,X8)
| p1(X8) )
& p1(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14]),skolemize(X0,sK10),skolemize(X2,sK11(X1)),skolemize(X4,sK12(X3)),skolemize(X5,sK13),skolemize(X7,sK14)],[f28]) ).
fof(f58,plain,
p1(sK14),
inference(cnf_transformation,[],[f29]) ).
fof(f60,plain,
~ p1(sK14),
inference(cnf_transformation,[],[f29]) ).
fof(f74,plain,
$false,
inference(forward_subsumption_resolution,[],[f60,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL644+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/10.60 % Computer : n014.cluster.edu
% 0.09/10.60 % Model : x86_64 x86_64
% 0.09/10.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.60 % Memory : 8046.5625MB
% 0.09/10.60 % OS : Linux 6.8.0-71-generic
% 0.03/10.60 % CPULimit : 300
% 0.03/10.60 % WCLimit : 300
% 0.03/10.60 % DateTime : Sun Sep 27 16:11:30 UTC 2026
% 0.03/10.60 % CPUTime :
% 0.03/10.60 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/10.63 Running first-order theorem proving
% 0.03/10.63 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
% 0.15/11.60 % (978726)Detected formulas, will run a generic FOF schedule.
% 0.15/11.60 % (978732)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=2124252725:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.15/11.60 % (978737)dis-21_1_sil=8000:lcm=predicate:random_seed=1184039014: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)
% 0.15/11.60 % (978736)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=965146768:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.15/11.60 % (978735)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3838288121:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.15/11.60 % (978731)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=1101564083:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.15/11.60 % (978733)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=2489744535:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.15/11.60 % (978734)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3879793199:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.15/11.60 % (978735)First to succeed.
% 0.15/11.60 % (978736)Also succeeded, but the first one will report.
% 0.15/11.60 % (978737)Also succeeded, but the first one will report.
% 0.15/11.60 % (978735)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-978726"
% 0.15/11.60 % (978734)Also succeeded, but the first one will report.
% 0.15/11.60 % (978735)Refutation found. Thanks to Tanya!
% 0.15/11.60 % SZS status Theorem for theBenchmark
% 0.15/11.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/11.60 % (978735)------------------------------
% 0.15/11.60 % (978735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/11.60 % (978735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/11.60 % (978735)CaDiCaL version: 2.1.3
% 0.15/11.60 % (978735)Termination reason: Refutation
% 0.15/11.60 % (978735)Time elapsed: 0.003 s
% 0.15/11.60 % (978735)Peak memory usage: 88 MB
% 0.15/11.60 % (978735)Instructions burned: 3 (million)
% 0.15/11.60 % (978735)------------------------------
% 0.15/11.60 % (978735)------------------------------
% 0.15/11.60 % (978726)Success in time 0.434 s
% 0.15/11.60 % Vampire exiting
%------------------------------------------------------------------------------