%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL686+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 11:56:15 AM UTC 2026
% Result : Theorem 2.70s 1.32s
% Output : Refutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 4 unt; 0 def)
% Number of atoms : 195 ( 0 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 334 ( 164 ~; 126 |; 44 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 10 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 85 ( 73 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f3,conjecture,
~ ? [X0] :
~ ( ! [X1] :
( ~ r1(X0,X1)
| ~ p3(X1)
| ! [X0] :
( ~ r1(X1,X0)
| ~ p1(X0) ) )
| ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( ! [X1] :
( ~ r1(X0,X1)
| $false )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ( p2(X1)
& ~ p1(X1) )
| ( ~ p2(X1)
& p1(X1) ) ) )
| ! [X1] :
( ~ r1(X0,X1)
| p3(X1) )
| ! [X1] :
( ~ r1(X0,X1)
| ( ~ p1(X1)
& ~ p2(X1) )
| ( p2(X1)
& p1(X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f4,negated_conjecture,
~ ~ ? [X0] :
~ ( ! [X1] :
( ~ r1(X0,X1)
| ~ p3(X1)
| ! [X0] :
( ~ r1(X1,X0)
| ~ p1(X0) ) )
| ! [X1] :
( ~ r1(X0,X1)
| ~ ! [X0] :
( ~ r1(X1,X0)
| ~ ( ! [X1] :
( ~ r1(X0,X1)
| $false )
| ~ ! [X1] :
( ~ r1(X0,X1)
| ~ ( ( p2(X1)
& ~ p1(X1) )
| ( ~ p2(X1)
& p1(X1) ) ) )
| ! [X1] :
( ~ r1(X0,X1)
| p3(X1) )
| ! [X1] :
( ~ r1(X0,X1)
| ( ~ p1(X1)
& ~ p2(X1) )
| ( p2(X1)
& p1(X1) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
~ ~ ? [X0] :
~ ( ! [X1] :
( ~ r1(X0,X1)
| ~ p3(X1)
| ! [X2] :
( ~ r1(X1,X2)
| ~ p1(X2) ) )
| ! [X3] :
( ~ r1(X0,X3)
| ~ ! [X4] :
( ~ r1(X3,X4)
| ~ ( ! [X5] :
( ~ r1(X4,X5)
| $false )
| ~ ! [X6] :
( ~ r1(X4,X6)
| ~ ( ( p2(X6)
& ~ p1(X6) )
| ( ~ p2(X6)
& p1(X6) ) ) )
| ! [X7] :
( ~ r1(X4,X7)
| p3(X7) )
| ! [X8] :
( ~ r1(X4,X8)
| ( ~ p1(X8)
& ~ p2(X8) )
| ( p2(X8)
& p1(X8) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
~ ~ ? [X0] :
~ ( ! [X1] :
( ~ r1(X0,X1)
| ~ p3(X1)
| ! [X2] :
( ~ r1(X1,X2)
| ~ p1(X2) ) )
| ! [X3] :
( ~ r1(X0,X3)
| ~ ! [X4] :
( ~ r1(X3,X4)
| ~ ( ! [X5] : ~ r1(X4,X5)
| ~ ! [X6] :
( ~ r1(X4,X6)
| ~ ( ( p2(X6)
& ~ p1(X6) )
| ( ~ p2(X6)
& p1(X6) ) ) )
| ! [X7] :
( ~ r1(X4,X7)
| p3(X7) )
| ! [X8] :
( ~ r1(X4,X8)
| ( ~ p1(X8)
& ~ p2(X8) )
| ( p2(X8)
& p1(X8) ) ) ) ) ) ),
inference(true_and_false_elimination,[],[f5]) ).
fof(f7,plain,
? [X0] :
~ ( ! [X1] :
( ~ r1(X0,X1)
| ~ p3(X1)
| ! [X2] :
( ~ r1(X1,X2)
| ~ p1(X2) ) )
| ! [X3] :
( ~ r1(X0,X3)
| ~ ! [X4] :
( ~ r1(X3,X4)
| ~ ( ! [X5] : ~ r1(X4,X5)
| ~ ! [X6] :
( ~ r1(X4,X6)
| ~ ( ( p2(X6)
& ~ p1(X6) )
| ( ~ p2(X6)
& p1(X6) ) ) )
| ! [X7] :
( ~ r1(X4,X7)
| p3(X7) )
| ! [X8] :
( ~ r1(X4,X8)
| ( ~ p1(X8)
& ~ p2(X8) )
| ( p2(X8)
& p1(X8) ) ) ) ) ) ),
inference(flattening,[],[f6]) ).
fof(f10,plain,
? [X0] :
( ? [X1] :
( r1(X0,X1)
& p3(X1)
& ? [X2] :
( r1(X1,X2)
& p1(X2) ) )
& ? [X3] :
( r1(X0,X3)
& ! [X4] :
( ~ r1(X3,X4)
| ( ? [X5] : r1(X4,X5)
& ! [X6] :
( ~ r1(X4,X6)
| ( ( ~ p2(X6)
| p1(X6) )
& ( p2(X6)
| ~ p1(X6) ) ) )
& ? [X7] :
( r1(X4,X7)
& ~ p3(X7) )
& ? [X8] :
( r1(X4,X8)
& ( p1(X8)
| p2(X8) )
& ( ~ p2(X8)
| ~ p1(X8) ) ) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f11,plain,
( r1(sK0,sK1)
& p3(sK1)
& r1(sK1,sK2)
& p1(sK2)
& r1(sK0,sK3)
& ! [X4] :
( ~ r1(sK3,X4)
| ( r1(X4,sK4(X4))
& ! [X6] :
( ~ r1(X4,X6)
| ( ( ~ p2(X6)
| p1(X6) )
& ( p2(X6)
| ~ p1(X6) ) ) )
& r1(X4,sK5(X4))
& ~ p3(sK5(X4))
& r1(X4,sK6(X4))
& ( p1(sK6(X4))
| p2(sK6(X4)) )
& ( ~ p2(sK6(X4))
| ~ p1(sK6(X4)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X5,sK4(X4)),skolemize(X7,sK5(X4)),skolemize(X8,sK6(X4))],[f10]) ).
fof(f12,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X4] :
( ~ p2(sK6(X4))
| ~ r1(sK3,X4)
| ~ p1(sK6(X4)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f15,plain,
! [X4] :
( p2(sK6(X4))
| p1(sK6(X4))
| ~ r1(sK3,X4) ),
inference(cnf_transformation,[],[f11]) ).
fof(f16,plain,
! [X4] :
( r1(X4,sK6(X4))
| ~ r1(sK3,X4) ),
inference(cnf_transformation,[],[f11]) ).
fof(f19,plain,
! [X6,X4] :
( p2(X6)
| ~ r1(X4,X6)
| ~ r1(sK3,X4)
| ~ p1(X6) ),
inference(cnf_transformation,[],[f11]) ).
fof(f20,plain,
! [X6,X4] :
( ~ p2(X6)
| ~ r1(X4,X6)
| ~ r1(sK3,X4)
| p1(X6) ),
inference(cnf_transformation,[],[f11]) ).
fof(f29,plain,
! [X0,X1] :
( ~ r1(X0,sK6(X1))
| ~ r1(sK3,X0)
| ~ p1(sK6(X1))
| ~ r1(sK3,X1)
| ~ p1(sK6(X1)) ),
inference(resolution,[],[f19,f14]) ).
fof(f30,plain,
! [X0,X1] :
( ~ p1(sK6(X1))
| ~ r1(sK3,X0)
| ~ r1(X0,sK6(X1))
| ~ r1(sK3,X1) ),
inference(duplicate_literal_removal,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ~ r1(X0,sK6(X1))
| ~ r1(sK3,X0)
| p1(sK6(X1))
| p1(sK6(X1))
| ~ r1(sK3,X1) ),
inference(resolution,[],[f20,f15]) ).
fof(f33,plain,
! [X0,X1] :
( p1(sK6(X1))
| ~ r1(sK3,X0)
| ~ r1(X0,sK6(X1))
| ~ r1(sK3,X1) ),
inference(duplicate_literal_removal,[],[f31]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ r1(sK3,X0)
| ~ r1(X0,sK6(X1))
| ~ r1(sK3,X1)
| ~ r1(sK3,X2)
| ~ r1(X2,sK6(X1))
| ~ r1(sK3,X1) ),
inference(resolution,[],[f33,f30]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ r1(X0,sK6(X1))
| ~ r1(X2,sK6(X1))
| ~ r1(sK3,X1)
| ~ r1(sK3,X2)
| ~ r1(sK3,X0) ),
inference(duplicate_literal_removal,[],[f34]) ).
fof(f42,plain,
! [X0,X1] :
( ~ r1(X0,sK6(X1))
| ~ r1(sK3,X1)
| ~ r1(sK3,X0)
| ~ r1(sK3,X0) ),
inference(factoring,[],[f35]) ).
fof(f43,plain,
! [X0,X1] :
( ~ r1(X0,sK6(X1))
| ~ r1(sK3,X1)
| ~ r1(sK3,X0) ),
inference(duplicate_literal_removal,[],[f42]) ).
fof(f46,plain,
! [X0] :
( ~ r1(sK3,X0)
| ~ r1(sK3,X0)
| ~ r1(sK3,X0) ),
inference(resolution,[],[f43,f16]) ).
fof(f49,plain,
! [X0] : ~ r1(sK3,X0),
inference(duplicate_literal_removal,[],[f46]) ).
fof(f50,plain,
$false,
inference(resolution,[],[f49,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL686+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
% 0.11/0.35 % Computer : n014.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sun Sep 27 16:38:16 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.38 Running first-order theorem proving
% 0.14/0.38 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
% 2.70/1.32 % (993320)Detected formulas, will run a generic FOF schedule.
% 2.70/1.32 % (993331)dis-21_1_sil=8000:lcm=predicate:random_seed=2869644580: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)
% 2.70/1.32 % (993331)First to succeed.
% 2.70/1.32 % (993331)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-993320"
% 2.70/1.32 % (993325)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=4286141656:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.70/1.32 % (993330)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1735661717:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.70/1.32 % (993328)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1551343470:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.70/1.32 % (993326)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=10896021:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.70/1.32 % (993327)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=1934465884:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.70/1.32 % (993329)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3970789534:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.70/1.32 % (993329)Also succeeded, but the first one will report.
% 2.70/1.32 % (993330)Also succeeded, but the first one will report.
% 2.70/1.32 % (993328)Also succeeded, but the first one will report.
% 2.70/1.32 % (993331)Refutation found. Thanks to Tanya!
% 2.70/1.32 % SZS status Theorem for theBenchmark
% 2.70/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.70/1.32 % (993331)------------------------------
% 2.70/1.32 % (993331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.32 % (993331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.32 % (993331)CaDiCaL version: 2.1.3
% 2.70/1.32 % (993331)Termination reason: Refutation
% 2.70/1.32 % (993331)Time elapsed: 0.002 s
% 2.70/1.32 % (993331)Peak memory usage: 88 MB
% 2.70/1.32 % (993331)Instructions burned: 2 (million)
% 2.70/1.32 % (993331)------------------------------
% 2.70/1.32 % (993331)------------------------------
% 2.70/1.32 % (993320)Success in time 0.294 s
% 2.70/1.32 % Vampire exiting
%------------------------------------------------------------------------------