%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL646+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 : n015.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 11:53:48 AM UTC 2026
% Result : Theorem 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 4 unt; 0 def)
% Number of atoms : 159 ( 0 equ)
% Maximal formula atoms : 16 ( 9 avg)
% Number of connectives : 269 ( 127 ~; 124 |; 18 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 10 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 95 ( 76 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p6(X1) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| p4(X1) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ! [X1] :
( ~ r1(X0,X1)
| p5(X1) )
| ! [X1] :
( ~ r1(X0,X1)
| p3(X1) )
| ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f2,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p6(X1) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| p4(X1) )
| ~ ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ! [X1] :
( ~ r1(X0,X1)
| p5(X1) )
| ! [X1] :
( ~ r1(X0,X1)
| p3(X1) )
| ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
| ! [X1] :
( ~ r1(X0,X1)
| p1(X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ~ ? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p6(X1) )
| ~ ! [X2] :
( ~ r1(X0,X2)
| p2(X2) )
| ~ ! [X3] :
( ~ r1(X0,X3)
| p4(X3) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| p2(X4) )
| ! [X5] :
( ~ r1(X0,X5)
| p5(X5) )
| ! [X6] :
( ~ r1(X0,X6)
| p3(X6) )
| ! [X7] :
( ~ r1(X0,X7)
| p2(X7) )
| ! [X8] :
( ~ r1(X0,X8)
| p1(X8) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p6(X1) )
| ~ ! [X2] :
( ~ r1(X0,X2)
| p2(X2) )
| ~ ! [X3] :
( ~ r1(X0,X3)
| p4(X3) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| p2(X4) )
| ! [X5] :
( ~ r1(X0,X5)
| p5(X5) )
| ! [X6] :
( ~ r1(X0,X6)
| p3(X6) )
| ! [X7] :
( ~ r1(X0,X7)
| p2(X7) )
| ! [X8] :
( ~ r1(X0,X8)
| p1(X8) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p6(X1) )
| ~ ! [X2] :
( ~ r1(X0,X2)
| p2(X2) )
| ~ ! [X3] :
( ~ r1(X0,X3)
| p4(X3) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| p2(X4) )
| ! [X5] :
( ~ r1(X0,X5)
| p5(X5) )
| ! [X6] :
( ~ r1(X0,X6)
| p3(X6) )
| ! [X7] :
( ~ r1(X0,X7)
| p2(X7) )
| ! [X8] : ~ r1(X0,X8) ),
inference(pure_predicate_removal,[],[f4]) ).
fof(f6,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p6(X1) )
| ~ ! [X2] :
( ~ r1(X0,X2)
| p2(X2) )
| ~ ! [X3] :
( ~ r1(X0,X3)
| p4(X3) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| p2(X4) )
| ! [X5] :
( ~ r1(X0,X5)
| p5(X5) )
| ! [X6] : ~ r1(X0,X6)
| ! [X7] :
( ~ r1(X0,X7)
| p2(X7) )
| ! [X8] : ~ r1(X0,X8) ),
inference(pure_predicate_removal,[],[f5]) ).
fof(f7,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p6(X1) )
| ~ ! [X2] :
( ~ r1(X0,X2)
| p2(X2) )
| ~ ! [X3] :
( ~ r1(X0,X3)
| p4(X3) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| p2(X4) )
| ! [X5] : ~ r1(X0,X5)
| ! [X6] : ~ r1(X0,X6)
| ! [X7] :
( ~ r1(X0,X7)
| p2(X7) )
| ! [X8] : ~ r1(X0,X8) ),
inference(pure_predicate_removal,[],[f6]) ).
fof(f8,plain,
? [X0] :
~ ( ~ ! [X1] :
( ~ r1(X0,X1)
| p6(X1) )
| ~ ! [X2] :
( ~ r1(X0,X2)
| p2(X2) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| p2(X4) )
| ! [X5] : ~ r1(X0,X5)
| ! [X6] : ~ r1(X0,X6)
| ! [X7] :
( ~ r1(X0,X7)
| p2(X7) )
| ! [X8] : ~ r1(X0,X8) ),
inference(pure_predicate_removal,[],[f7]) ).
fof(f9,plain,
? [X0] :
~ ( ~ ! [X2] :
( ~ r1(X0,X2)
| p2(X2) )
| ~ ! [X4] :
( ~ r1(X0,X4)
| p2(X4) )
| ! [X5] : ~ r1(X0,X5)
| ! [X6] : ~ r1(X0,X6)
| ! [X7] :
( ~ r1(X0,X7)
| p2(X7) )
| ! [X8] : ~ r1(X0,X8) ),
inference(pure_predicate_removal,[],[f8]) ).
fof(f10,plain,
? [X0] :
( ! [X2] :
( ~ r1(X0,X2)
| p2(X2) )
& ! [X4] :
( ~ r1(X0,X4)
| p2(X4) )
& ? [X5] : r1(X0,X5)
& ? [X6] : r1(X0,X6)
& ? [X7] :
( r1(X0,X7)
& ~ p2(X7) )
& ? [X8] : r1(X0,X8) ),
inference(ennf_transformation,[],[f9]) ).
fof(f11,plain,
? [X0] :
( ! [X1] :
( ~ r1(X0,X1)
| p2(X1) )
& ! [X2] :
( ~ r1(X0,X2)
| p2(X2) )
& ? [X3] : r1(X0,X3)
& ? [X4] : r1(X0,X4)
& ? [X5] :
( r1(X0,X5)
& ~ p2(X5) )
& ? [X6] : r1(X0,X6) ),
inference(rectify,[],[f10]) ).
fof(f12,plain,
( ! [X1] :
( ~ r1(sK0,X1)
| p2(X1) )
& ! [X2] :
( ~ r1(sK0,X2)
| p2(X2) )
& r1(sK0,sK1)
& r1(sK0,sK2)
& r1(sK0,sK3)
& ~ p2(sK3)
& r1(sK0,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X3,sK1),skolemize(X4,sK2),skolemize(X5,sK3),skolemize(X6,sK4)],[f11]) ).
fof(f14,plain,
~ p2(sK3),
inference(cnf_transformation,[],[f12]) ).
fof(f15,plain,
r1(sK0,sK3),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X2] :
( ~ r1(sK0,X2)
| p2(X2) ),
inference(cnf_transformation,[],[f12]) ).
fof(f22,plain,
p2(sK3),
inference(resolution,[],[f18,f15]) ).
fof(f24,plain,
$false,
inference(forward_subsumption_resolution,[],[f22,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL646+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
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 16:15:45 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.17/1.50 % (1832283)Detected formulas, will run a generic FOF schedule.
% 0.17/1.50 % (1832288)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=3793258414:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.50 % (1832293)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1082790620:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.50 % (1832294)dis-21_1_sil=8000:lcm=predicate:random_seed=3884853991: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)
% 0.17/1.50 % (1832289)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=4093082794:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.50 % (1832291)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3310406827:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.50 % (1832290)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=1615578211:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.50 % (1832292)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=639530607:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.50 % (1832291)Also succeeded, but the first one will report.
% 0.17/1.50 % (1832294)Also succeeded, but the first one will report.
% 0.17/1.50 % (1832292)First to succeed.
% 0.17/1.50 % (1832293)Also succeeded, but the first one will report.
% 0.17/1.50 % (1832292)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1832283"
% 0.17/1.50 % (1832292)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Theorem for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (1832292)------------------------------
% 0.17/1.50 % (1832292)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (1832292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (1832292)CaDiCaL version: 2.1.3
% 0.17/1.50 % (1832292)Termination reason: Refutation
% 0.17/1.50 % (1832292)Time elapsed: 0.002 s
% 0.17/1.50 % (1832292)Peak memory usage: 88 MB
% 0.17/1.50 % (1832292)Instructions burned: 1 (million)
% 0.17/1.50 % (1832292)------------------------------
% 0.17/1.50 % (1832292)------------------------------
% 0.17/1.50 % (1832283)Success in time 0.441 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------