%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL638+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 THM
% Computer : n003.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 11:53:41 AM UTC 2026
% Result : Theorem 5.71s 1.87s
% Output : Refutation 5.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 27 ( 4 unt; 0 def)
% Number of atoms : 298 ( 0 equ)
% Maximal formula atoms : 31 ( 11 avg)
% Number of connectives : 585 ( 314 ~; 215 |; 56 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-1 aty)
% Number of variables : 182 ( 161 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
& ~ p1(X1) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p1(X1) ) )
& p1(X1) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| ~ p1(X0) ) ) )
& ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p1(X1) ) ) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
& ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| $false ) )
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
fof(f2,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
& ~ p1(X1) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p1(X1) ) )
& p1(X1) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| ~ p1(X0) ) ) )
& ! [X0] :
( ~ r1(X1,X0)
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ p1(X1) ) ) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) )
& ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| $false ) )
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| p1(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X3] :
( ~ r1(X2,X3)
| p1(X3) ) )
& ~ p1(X1) ) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| ~ ( ~ ! [X5] :
( ~ r1(X4,X5)
| ~ ! [X6] :
( ~ r1(X5,X6)
| ~ p1(X6) ) )
& p1(X4) ) )
| ~ ! [X7] :
( ~ r1(X0,X7)
| ~ ( ~ ! [X8] :
( ~ r1(X7,X8)
| ! [X9] :
( ~ r1(X8,X9)
| ~ ! [X10] :
( ~ r1(X9,X10)
| ~ p1(X10) ) ) )
& ! [X11] :
( ~ r1(X7,X11)
| ~ ! [X12] :
( ~ r1(X11,X12)
| ~ p1(X12) ) ) ) )
| ~ ! [X13] :
( ~ r1(X0,X13)
| ~ ( ~ ! [X14] :
( ~ r1(X13,X14)
| ! [X15] :
( ~ r1(X14,X15)
| p1(X15) ) )
& ! [X16] :
( ~ r1(X13,X16)
| p1(X16) ) ) )
| ~ ! [X17] :
( ~ r1(X0,X17)
| ~ ! [X18] :
( ~ r1(X17,X18)
| $false ) )
| ! [X19] :
( ~ r1(X0,X19)
| p1(X19)
| ~ ! [X20] :
( ~ r1(X19,X20)
| p1(X20) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X3] :
( ~ r1(X2,X3)
| p1(X3) ) )
& ~ p1(X1) ) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| ~ ( ~ ! [X5] :
( ~ r1(X4,X5)
| ~ ! [X6] :
( ~ r1(X5,X6)
| ~ p1(X6) ) )
& p1(X4) ) )
| ~ ! [X7] :
( ~ r1(X0,X7)
| ~ ( ~ ! [X8] :
( ~ r1(X7,X8)
| ! [X9] :
( ~ r1(X8,X9)
| ~ ! [X10] :
( ~ r1(X9,X10)
| ~ p1(X10) ) ) )
& ! [X11] :
( ~ r1(X7,X11)
| ~ ! [X12] :
( ~ r1(X11,X12)
| ~ p1(X12) ) ) ) )
| ~ ! [X13] :
( ~ r1(X0,X13)
| ~ ( ~ ! [X14] :
( ~ r1(X13,X14)
| ! [X15] :
( ~ r1(X14,X15)
| p1(X15) ) )
& ! [X16] :
( ~ r1(X13,X16)
| p1(X16) ) ) )
| ~ ! [X17] :
( ~ r1(X0,X17)
| ~ ! [X18] : ~ r1(X17,X18) )
| ! [X19] :
( ~ r1(X0,X19)
| p1(X19)
| ~ ! [X20] :
( ~ r1(X19,X20)
| p1(X20) ) ) ),
inference(true_and_false_elimination,[],[f3]) ).
fof(f5,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X3] :
( ~ r1(X2,X3)
| p1(X3) ) )
& ~ p1(X1) ) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| ~ ( ~ ! [X5] :
( ~ r1(X4,X5)
| ~ ! [X6] :
( ~ r1(X5,X6)
| ~ p1(X6) ) )
& p1(X4) ) )
| ~ ! [X7] :
( ~ r1(X0,X7)
| ~ ( ~ ! [X8] :
( ~ r1(X7,X8)
| ! [X9] :
( ~ r1(X8,X9)
| ~ ! [X10] :
( ~ r1(X9,X10)
| ~ p1(X10) ) ) )
& ! [X11] :
( ~ r1(X7,X11)
| ~ ! [X12] :
( ~ r1(X11,X12)
| ~ p1(X12) ) ) ) )
| ~ ! [X13] :
( ~ r1(X0,X13)
| ~ ( ~ ! [X14] :
( ~ r1(X13,X14)
| ! [X15] :
( ~ r1(X14,X15)
| p1(X15) ) )
& ! [X16] :
( ~ r1(X13,X16)
| p1(X16) ) ) )
| ~ ! [X17] :
( ~ r1(X0,X17)
| ~ ! [X18] : ~ r1(X17,X18) )
| ! [X19] :
( ~ r1(X0,X19)
| p1(X19)
| ~ ! [X20] :
( ~ r1(X19,X20)
| p1(X20) ) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ! [X2] :
( ~ r1(X1,X2)
| ? [X3] :
( r1(X2,X3)
& ~ p1(X3) ) )
| p1(X1) )
& ! [X4] :
( ~ r1(X0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ? [X6] :
( r1(X5,X6)
& p1(X6) ) )
| ~ p1(X4) )
& ! [X7] :
( ~ r1(X0,X7)
| ! [X8] :
( ~ r1(X7,X8)
| ! [X9] :
( ~ r1(X8,X9)
| ? [X10] :
( r1(X9,X10)
& p1(X10) ) ) )
| ? [X11] :
( r1(X7,X11)
& ! [X12] :
( ~ r1(X11,X12)
| ~ p1(X12) ) ) )
& ! [X13] :
( ~ r1(X0,X13)
| ! [X14] :
( ~ r1(X13,X14)
| ! [X15] :
( ~ r1(X14,X15)
| p1(X15) ) )
| ? [X16] :
( r1(X13,X16)
& ~ p1(X16) ) )
& ! [X17] :
( ~ r1(X0,X17)
| ? [X18] : r1(X17,X18) )
& ? [X19] :
( r1(X0,X19)
& ~ p1(X19)
& ! [X20] :
( ~ r1(X19,X20)
| p1(X20) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f7,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ! [X2] :
( ~ r1(X1,X2)
| ? [X3] :
( r1(X2,X3)
& ~ p1(X3) ) )
| p1(X1) )
& ! [X4] :
( ~ r1(X0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ? [X6] :
( r1(X5,X6)
& p1(X6) ) )
| ~ p1(X4) )
& ! [X7] :
( ~ r1(X0,X7)
| ! [X8] :
( ~ r1(X7,X8)
| ! [X9] :
( ~ r1(X8,X9)
| ? [X10] :
( r1(X9,X10)
& p1(X10) ) ) )
| ? [X11] :
( r1(X7,X11)
& ! [X12] :
( ~ r1(X11,X12)
| ~ p1(X12) ) ) )
& ! [X13] :
( ~ r1(X0,X13)
| ! [X14] :
( ~ r1(X13,X14)
| ! [X15] :
( ~ r1(X14,X15)
| p1(X15) ) )
| ? [X16] :
( r1(X13,X16)
& ~ p1(X16) ) )
& ! [X17] :
( ~ r1(X0,X17)
| ? [X18] : r1(X17,X18) )
& ? [X19] :
( r1(X0,X19)
& ~ p1(X19)
& ! [X20] :
( ~ r1(X19,X20)
| p1(X20) ) ) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
( ! [X1] :
( ~ r1(sK0,X1)
| ! [X2] :
( ~ r1(X1,X2)
| ( r1(X2,sK1(X2))
& ~ p1(sK1(X2)) ) )
| p1(X1) )
& ! [X4] :
( ~ r1(sK0,X4)
| ! [X5] :
( ~ r1(X4,X5)
| ( r1(X5,sK2(X5))
& p1(sK2(X5)) ) )
| ~ p1(X4) )
& ! [X7] :
( ~ r1(sK0,X7)
| ! [X8] :
( ~ r1(X7,X8)
| ! [X9] :
( ~ r1(X8,X9)
| ( r1(X9,sK3(X9))
& p1(sK3(X9)) ) ) )
| ( r1(X7,sK4(X7))
& ! [X12] :
( ~ r1(sK4(X7),X12)
| ~ p1(X12) ) ) )
& ! [X13] :
( ~ r1(sK0,X13)
| ! [X14] :
( ~ r1(X13,X14)
| ! [X15] :
( ~ r1(X14,X15)
| p1(X15) ) )
| ( r1(X13,sK5(X13))
& ~ p1(sK5(X13)) ) )
& ! [X17] :
( ~ r1(sK0,X17)
| r1(X17,sK6(X17)) )
& r1(sK0,sK7)
& ~ p1(sK7)
& ! [X20] :
( ~ r1(sK7,X20)
| p1(X20) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X3,sK1(X2)),skolemize(X6,sK2(X5)),skolemize(X10,sK3(X9)),skolemize(X11,sK4(X7)),skolemize(X16,sK5(X13)),skolemize(X18,sK6(X17)),skolemize(X19,sK7)],[f7]) ).
fof(f9,plain,
! [X20] :
( ~ r1(sK7,X20)
| p1(X20) ),
inference(cnf_transformation,[],[f8]) ).
fof(f10,plain,
~ p1(sK7),
inference(cnf_transformation,[],[f8]) ).
fof(f11,plain,
r1(sK0,sK7),
inference(cnf_transformation,[],[f8]) ).
fof(f12,plain,
! [X17] :
( r1(X17,sK6(X17))
| ~ r1(sK0,X17) ),
inference(cnf_transformation,[],[f8]) ).
fof(f13,plain,
! [X14,X15,X13] :
( ~ p1(sK5(X13))
| ~ r1(X13,X14)
| ~ r1(X14,X15)
| p1(X15)
| ~ r1(sK0,X13) ),
inference(cnf_transformation,[],[f8]) ).
fof(f14,plain,
! [X14,X15,X13] :
( r1(X13,sK5(X13))
| ~ r1(X13,X14)
| ~ r1(X14,X15)
| p1(X15)
| ~ r1(sK0,X13) ),
inference(cnf_transformation,[],[f8]) ).
fof(f21,plain,
! [X2,X1] :
( ~ p1(sK1(X2))
| ~ r1(X1,X2)
| ~ r1(sK0,X1)
| p1(X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f22,plain,
! [X2,X1] :
( r1(X2,sK1(X2))
| ~ r1(X1,X2)
| ~ r1(sK0,X1)
| p1(X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f33,plain,
! [X0,X1] :
( ~ r1(sK7,X0)
| ~ r1(X0,X1)
| p1(X1)
| ~ r1(sK0,sK7)
| p1(sK5(sK7)) ),
inference(resolution,[],[f14,f9]) ).
fof(f36,plain,
! [X0,X1] :
( ~ r1(sK7,X0)
| ~ r1(X0,X1)
| p1(X1)
| ~ r1(sK0,sK7) ),
inference(forward_subsumption_resolution,[],[f33,f13]) ).
fof(f37,plain,
! [X0,X1] :
( ~ r1(sK7,X0)
| ~ r1(X0,X1)
| p1(X1) ),
inference(forward_subsumption_resolution,[],[f36,f11]) ).
fof(f41,plain,
! [X0] :
( ~ r1(sK6(sK7),X0)
| p1(X0)
| ~ r1(sK0,sK7) ),
inference(resolution,[],[f37,f12]) ).
fof(f43,plain,
! [X0] :
( ~ r1(sK6(sK7),X0)
| p1(X0) ),
inference(forward_subsumption_resolution,[],[f41,f11]) ).
fof(f45,plain,
! [X0] :
( p1(sK1(sK6(sK7)))
| ~ r1(X0,sK6(sK7))
| ~ r1(sK0,X0)
| p1(X0) ),
inference(resolution,[],[f43,f22]) ).
fof(f50,plain,
! [X0] :
( ~ r1(X0,sK6(sK7))
| ~ r1(sK0,X0)
| p1(X0) ),
inference(forward_subsumption_resolution,[],[f45,f21]) ).
fof(f61,plain,
( ~ r1(sK0,sK7)
| p1(sK7)
| ~ r1(sK0,sK7) ),
inference(resolution,[],[f50,f12]) ).
fof(f62,plain,
( ~ r1(sK0,sK7)
| p1(sK7) ),
inference(duplicate_literal_removal,[],[f61]) ).
fof(f63,plain,
p1(sK7),
inference(forward_subsumption_resolution,[],[f62,f11]) ).
fof(f64,plain,
$false,
inference(forward_subsumption_resolution,[],[f63,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.35 % Computer : n003.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8046.5625MB
% 0.12/0.35 % OS : Linux 6.8.0-71-generic
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sun Sep 27 16:10:41 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.71/1.87 % (749562)Detected formulas, will run a generic FOF schedule.
% 5.71/1.87 % (749571)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=3148304933:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.71/1.87 % (749569)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=2470740703:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.71/1.87 % (749575)dis-21_1_sil=8000:lcm=predicate:random_seed=3125395127: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)
% 5.71/1.87 % (749573)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1931374225:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.71/1.87 % (749572)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1365595862:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.71/1.87 % (749573)First to succeed.
% 5.71/1.87 % (749573)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-749562"
% 5.71/1.87 % (749572)Also succeeded, but the first one will report.
% 5.71/1.87 % (749570)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=973124528:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.71/1.87 % (749574)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1955787636:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.71/1.87 % (749574)Also succeeded, but the first one will report.
% 5.71/1.87 % (749575)Also succeeded, but the first one will report.
% 5.71/1.87 % (749573)Refutation found. Thanks to Tanya!
% 5.71/1.87 % SZS status Theorem for theBenchmark
% 5.71/1.87 % SZS output start Proof for theBenchmark
% See solution above
% 5.71/1.87 % (749573)------------------------------
% 5.71/1.87 % (749573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.87 % (749573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.87 % (749573)CaDiCaL version: 2.1.3
% 5.71/1.87 % (749573)Termination reason: Refutation
% 5.71/1.87 % (749573)Time elapsed: 0.005 s
% 5.71/1.87 % (749573)Peak memory usage: 88 MB
% 5.71/1.87 % (749573)Instructions burned: 3 (million)
% 5.71/1.87 % (749573)------------------------------
% 5.71/1.87 % (749573)------------------------------
% 5.71/1.87 % (749562)Success in time 0.711 s
% 5.71/1.87 % Vampire exiting
%------------------------------------------------------------------------------