%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL682+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 : n005.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 11:55:50 AM UTC 2026
% Result : Theorem 3.40s 1.23s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 5 unt; 0 def)
% Number of atoms : 223 ( 0 equ)
% Maximal formula atoms : 21 ( 11 avg)
% Number of connectives : 401 ( 197 ~; 174 |; 30 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 12 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 153 ( 126 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,conjecture,
~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| p16(X0) )
| ~ ! [X0] :
( ~ r1(X1,X0)
| p12(X0) )
| ~ ! [X0] :
( ~ r1(X1,X0)
| p14(X0) )
| ~ ! [X0] :
( ~ r1(X1,X0)
| p12(X0) ) ) )
| ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| p15(X0) ) )
| ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| p13(X0) ) )
| ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| p12(X0) ) )
| ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| p11(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f4,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X0] :
( ~ r1(X1,X0)
| p16(X0) )
| ~ ! [X0] :
( ~ r1(X1,X0)
| p12(X0) )
| ~ ! [X0] :
( ~ r1(X1,X0)
| p14(X0) )
| ~ ! [X0] :
( ~ r1(X1,X0)
| p12(X0) ) ) )
| ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| p15(X0) ) )
| ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| p13(X0) ) )
| ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| p12(X0) ) )
| ! [X1] :
( ~ r1(X0,X1)
| ! [X0] :
( ~ r1(X1,X0)
| p11(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| p16(X2) )
| ~ ! [X3] :
( ~ r1(X1,X3)
| p12(X3) )
| ~ ! [X4] :
( ~ r1(X1,X4)
| p14(X4) )
| ~ ! [X5] :
( ~ r1(X1,X5)
| p12(X5) ) ) )
| ! [X6] :
( ~ r1(X0,X6)
| ! [X7] :
( ~ r1(X6,X7)
| p15(X7) ) )
| ! [X8] :
( ~ r1(X0,X8)
| ! [X9] :
( ~ r1(X8,X9)
| p13(X9) ) )
| ! [X10] :
( ~ r1(X0,X10)
| ! [X11] :
( ~ r1(X10,X11)
| p12(X11) ) )
| ! [X12] :
( ~ r1(X0,X12)
| ! [X13] :
( ~ r1(X12,X13)
| p11(X13) ) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| p16(X2) )
| ~ ! [X3] :
( ~ r1(X1,X3)
| p12(X3) )
| ~ ! [X4] :
( ~ r1(X1,X4)
| p14(X4) )
| ~ ! [X5] :
( ~ r1(X1,X5)
| p12(X5) ) ) )
| ! [X6] :
( ~ r1(X0,X6)
| ! [X7] :
( ~ r1(X6,X7)
| p15(X7) ) )
| ! [X8] :
( ~ r1(X0,X8)
| ! [X9] :
( ~ r1(X8,X9)
| p13(X9) ) )
| ! [X10] :
( ~ r1(X0,X10)
| ! [X11] :
( ~ r1(X10,X11)
| p12(X11) ) )
| ! [X12] :
( ~ r1(X0,X12)
| ! [X13] :
( ~ r1(X12,X13)
| p11(X13) ) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| p16(X2) )
| ~ ! [X3] :
( ~ r1(X1,X3)
| p12(X3) )
| ~ ! [X4] :
( ~ r1(X1,X4)
| p14(X4) )
| ~ ! [X5] :
( ~ r1(X1,X5)
| p12(X5) ) ) )
| ! [X6] :
( ~ r1(X0,X6)
| ! [X7] :
( ~ r1(X6,X7)
| p15(X7) ) )
| ! [X8] :
( ~ r1(X0,X8)
| ! [X9] :
( ~ r1(X8,X9)
| p13(X9) ) )
| ! [X10] :
( ~ r1(X0,X10)
| ! [X11] :
( ~ r1(X10,X11)
| p12(X11) ) )
| ! [X12] :
( ~ r1(X0,X12)
| ! [X13] : ~ r1(X12,X13) ) ),
inference(pure_predicate_removal,[],[f6]) ).
fof(f8,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| p16(X2) )
| ~ ! [X3] :
( ~ r1(X1,X3)
| p12(X3) )
| ~ ! [X4] :
( ~ r1(X1,X4)
| p14(X4) )
| ~ ! [X5] :
( ~ r1(X1,X5)
| p12(X5) ) ) )
| ! [X6] :
( ~ r1(X0,X6)
| ! [X7] :
( ~ r1(X6,X7)
| p15(X7) ) )
| ! [X8] :
( ~ r1(X0,X8)
| ! [X9] : ~ r1(X8,X9) )
| ! [X10] :
( ~ r1(X0,X10)
| ! [X11] :
( ~ r1(X10,X11)
| p12(X11) ) )
| ! [X12] :
( ~ r1(X0,X12)
| ! [X13] : ~ r1(X12,X13) ) ),
inference(pure_predicate_removal,[],[f7]) ).
fof(f9,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| p16(X2) )
| ~ ! [X3] :
( ~ r1(X1,X3)
| p12(X3) )
| ~ ! [X4] :
( ~ r1(X1,X4)
| p14(X4) )
| ~ ! [X5] :
( ~ r1(X1,X5)
| p12(X5) ) ) )
| ! [X6] :
( ~ r1(X0,X6)
| ! [X7] : ~ r1(X6,X7) )
| ! [X8] :
( ~ r1(X0,X8)
| ! [X9] : ~ r1(X8,X9) )
| ! [X10] :
( ~ r1(X0,X10)
| ! [X11] :
( ~ r1(X10,X11)
| p12(X11) ) )
| ! [X12] :
( ~ r1(X0,X12)
| ! [X13] : ~ r1(X12,X13) ) ),
inference(pure_predicate_removal,[],[f8]) ).
fof(f10,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| p16(X2) )
| ~ ! [X3] :
( ~ r1(X1,X3)
| p12(X3) )
| ~ ! [X5] :
( ~ r1(X1,X5)
| p12(X5) ) ) )
| ! [X6] :
( ~ r1(X0,X6)
| ! [X7] : ~ r1(X6,X7) )
| ! [X8] :
( ~ r1(X0,X8)
| ! [X9] : ~ r1(X8,X9) )
| ! [X10] :
( ~ r1(X0,X10)
| ! [X11] :
( ~ r1(X10,X11)
| p12(X11) ) )
| ! [X12] :
( ~ r1(X0,X12)
| ! [X13] : ~ r1(X12,X13) ) ),
inference(pure_predicate_removal,[],[f9]) ).
fof(f11,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ~ ! [X3] :
( ~ r1(X1,X3)
| p12(X3) )
| ~ ! [X5] :
( ~ r1(X1,X5)
| p12(X5) ) ) )
| ! [X6] :
( ~ r1(X0,X6)
| ! [X7] : ~ r1(X6,X7) )
| ! [X8] :
( ~ r1(X0,X8)
| ! [X9] : ~ r1(X8,X9) )
| ! [X10] :
( ~ r1(X0,X10)
| ! [X11] :
( ~ r1(X10,X11)
| p12(X11) ) )
| ! [X12] :
( ~ r1(X0,X12)
| ! [X13] : ~ r1(X12,X13) ) ),
inference(pure_predicate_removal,[],[f10]) ).
fof(f14,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ( ! [X3] :
( ~ r1(X1,X3)
| p12(X3) )
& ! [X5] :
( ~ r1(X1,X5)
| p12(X5) ) ) )
& ? [X6] :
( r1(X0,X6)
& ? [X7] : r1(X6,X7) )
& ? [X8] :
( r1(X0,X8)
& ? [X9] : r1(X8,X9) )
& ? [X10] :
( r1(X0,X10)
& ? [X11] :
( r1(X10,X11)
& ~ p12(X11) ) )
& ? [X12] :
( r1(X0,X12)
& ? [X13] : r1(X12,X13) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f15,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| ( ! [X2] :
( ~ r1(X1,X2)
| p12(X2) )
& ! [X3] :
( ~ r1(X1,X3)
| p12(X3) ) ) )
& ? [X4] :
( r1(X0,X4)
& ? [X5] : r1(X4,X5) )
& ? [X6] :
( r1(X0,X6)
& ? [X7] : r1(X6,X7) )
& ? [X8] :
( r1(X0,X8)
& ? [X9] :
( r1(X8,X9)
& ~ p12(X9) ) )
& ? [X10] :
( r1(X0,X10)
& ? [X11] : r1(X10,X11) ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
( ! [X1] :
( ~ r1(sK0,X1)
| ( ! [X2] :
( ~ r1(X1,X2)
| p12(X2) )
& ! [X3] :
( ~ r1(X1,X3)
| p12(X3) ) ) )
& r1(sK0,sK1)
& r1(sK1,sK2)
& r1(sK0,sK3)
& r1(sK3,sK4)
& r1(sK0,sK5)
& r1(sK5,sK6)
& ~ p12(sK6)
& r1(sK0,sK7)
& r1(sK7,sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK0),skolemize(X4,sK1),skolemize(X5,sK2),skolemize(X6,sK3),skolemize(X7,sK4),skolemize(X8,sK5),skolemize(X9,sK6),skolemize(X10,sK7),skolemize(X11,sK8)],[f15]) ).
fof(f21,plain,
~ p12(sK6),
inference(cnf_transformation,[],[f16]) ).
fof(f22,plain,
r1(sK5,sK6),
inference(cnf_transformation,[],[f16]) ).
fof(f23,plain,
r1(sK0,sK5),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X3,X1] :
( p12(X3)
| ~ r1(X1,X3)
| ~ r1(sK0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X0] :
( ~ r1(X0,sK6)
| ~ r1(sK0,X0) ),
inference(resolution,[],[f28,f21]) ).
fof(f31,plain,
~ r1(sK0,sK5),
inference(resolution,[],[f30,f22]) ).
fof(f32,plain,
$false,
inference(resolution,[],[f31,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL682+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
% 0.09/0.38 % Computer : n005.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 16:36:47 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 3.40/1.23 % (4191240)Detected formulas, will run a generic FOF schedule.
% 3.40/1.23 % (4191245)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=2952600403:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.40/1.23 % (4191250)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2294098523:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.40/1.23 % (4191246)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=1016517543:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.40/1.23 % (4191249)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3994672991:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.40/1.23 % (4191247)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=2691848946:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.40/1.23 % (4191248)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=708437602:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.40/1.23 % (4191251)dis-21_1_sil=8000:lcm=predicate:random_seed=3137915882: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)
% 3.40/1.23 % (4191250)Also succeeded, but the first one will report.
% 3.40/1.23 % (4191251)First to succeed.
% 3.40/1.23 % (4191249)Also succeeded, but the first one will report.
% 3.40/1.23 % (4191248)Also succeeded, but the first one will report.
% 3.40/1.23 % (4191251)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4191240"
% 3.40/1.23 % (4191251)Refutation found. Thanks to Tanya!
% 3.40/1.23 % SZS status Theorem for theBenchmark
% 3.40/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.40/1.23 % (4191251)------------------------------
% 3.40/1.23 % (4191251)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.23 % (4191251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.23 % (4191251)CaDiCaL version: 2.1.3
% 3.40/1.23 % (4191251)Termination reason: Refutation
% 3.40/1.23 % (4191251)Time elapsed: 0.002 s
% 3.40/1.23 % (4191251)Peak memory usage: 88 MB
% 3.40/1.23 % (4191251)Instructions burned: 2 (million)
% 3.40/1.23 % (4191251)------------------------------
% 3.40/1.23 % (4191251)------------------------------
% 3.40/1.23 % (4191240)Success in time 0.426 s
% 3.40/1.23 % Vampire exiting
%------------------------------------------------------------------------------