%------------------------------------------------------------------------------
% File : Vampire-SAT---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/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 11:59:10 AM UTC 2026
% Result : Theorem 0.06s 0.36s
% Output : Refutation 0.06s
% 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/sandbox2/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(f102,plain,
$false,
inference(forward_subsumption_resolution,[],[f60,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL644+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 16:11:28 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.33 Running first-order model finding
% 0.06/0.33 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
% 0.06/0.36 % (2557680)Will run a generic schedule for satisfiability detection.
% 0.06/0.36 % (2557686)% WARNING: option uhcvi not known.
% 0.06/0.36 % (2557686)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1781654885:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.06/0.36 % (2557685)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2084474892_2999 on theBenchmark for (2999ds/0Mi)
% 0.06/0.36 % (2557691)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2452758351:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.36 % (2557687)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3479262617:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.06/0.36 % (2557688)dis+10_1_sil=32000:sp=arity:random_seed=2107406298:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.06/0.36 % (2557689)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=184694228:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.06/0.36 % (2557690)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2405378009:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.06/0.36 % (2557687) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2557680-2557687"...
% 0.06/0.36 % (2557688) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2557680-2557688"...
% 0.06/0.36 % (2557691) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2557680-2557691"...
% 0.06/0.36 % (2557690) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2557680-2557690"...
% 0.06/0.36 % (2557686) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2557680-2557686"...
% 0.06/0.36 % TRYING [1]
% 0.06/0.36 % TRYING [2]
% 0.06/0.36 % (2557688)...printing done.
% 0.06/0.36 % (2557687)...printing done.
% 0.06/0.36 % (2557691)...printing done.
% 0.06/0.36 % (2557690)...printing done.
% 0.06/0.36 % (2557685) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2557680-2557685"...
% 0.06/0.36 % (2557686)...printing done.
% 0.06/0.36 % (2557688)Refutation found. Thanks to Tanya!
% 0.06/0.36 % SZS status Theorem for theBenchmark
% 0.06/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.36 % (2557688)------------------------------
% 0.06/0.36 % (2557688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.36 % (2557688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.36 % (2557688)CaDiCaL version: 2.1.3
% 0.06/0.36 % (2557688)Termination reason: Refutation
% 0.06/0.36 % (2557688)Time elapsed: 0.001 s
% 0.06/0.36 % (2557688)Peak memory usage: 11 MB
% 0.06/0.36 % (2557688)Instructions burned: 3 (million)
% 0.06/0.36 % (2557680)Success in time 0.026 s
% 0.06/0.36 % Vampire exiting
%------------------------------------------------------------------------------