%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS128+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 11:41:43 AM UTC 2026
% Result : Unsatisfiable 3.37s 1.35s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 7 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 125 ( 48 ~; 40 |; 23 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 56 ( 46 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rr(X0,X1)
& cexcomp(X1) )
& ! [X1] :
( rr(X0,X1)
=> cd(X1) )
& ! [X1] :
( rr(X0,X1)
=> ca_Cx4(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f9,axiom,
! [X0] :
( ca_Cx4(X0)
<=> ? [X1] : ra_Px4(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f10,axiom,
! [X0] :
( ca_Cx4xcomp(X0)
<=> ~ ? [X1] : ra_Px4(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
fof(f11,axiom,
! [X0] :
( ca_Cx4xcomp(X0)
<=> ( cd(X0)
& cexcomp(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
fof(f12,axiom,
cUnsatisfiable(i2003_11_14_17_22_31584),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
fof(f13,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rr(X0,X1)
& cexcomp(X1) )
& ! [X2] :
( rr(X0,X2)
=> cd(X2) )
& ! [X3] :
( rr(X0,X3)
=> ca_Cx4(X3) ) ) ),
inference(rectify,[],[f3]) ).
fof(f15,plain,
! [X0] :
( cUnsatisfiable(X0)
=> ( ? [X1] :
( rr(X0,X1)
& cexcomp(X1) )
& ! [X2] :
( rr(X0,X2)
=> cd(X2) )
& ! [X3] :
( rr(X0,X3)
=> ca_Cx4(X3) ) ) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f16,plain,
! [X0] :
( ca_Cx4(X0)
=> ? [X1] : ra_Px4(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f21,plain,
! [X0] :
( ( ? [X1] :
( rr(X0,X1)
& cexcomp(X1) )
& ! [X2] :
( cd(X2)
| ~ rr(X0,X2) )
& ! [X3] :
( ca_Cx4(X3)
| ~ rr(X0,X3) ) )
| ~ cUnsatisfiable(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0] :
( ? [X1] : ra_Px4(X0,X1)
| ~ ca_Cx4(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f23,plain,
! [X0] :
( ca_Cx4xcomp(X0)
<=> ! [X1] : ~ ra_Px4(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f24,plain,
! [X0] :
( ( rr(X0,sK0(X0))
& cexcomp(sK0(X0))
& ! [X2] :
( cd(X2)
| ~ rr(X0,X2) )
& ! [X3] :
( ca_Cx4(X3)
| ~ rr(X0,X3) ) )
| ~ cUnsatisfiable(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f21]) ).
fof(f31,plain,
! [X0] :
( ra_Px4(X0,sK3(X0))
| ~ ca_Cx4(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f22]) ).
fof(f32,plain,
! [X0] :
( ( ca_Cx4xcomp(X0)
| ? [X1] : ra_Px4(X0,X1) )
& ( ! [X1] : ~ ra_Px4(X0,X1)
| ~ ca_Cx4xcomp(X0) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f33,plain,
! [X0] :
( ( ca_Cx4xcomp(X0)
| ? [X1] : ra_Px4(X0,X1) )
& ( ! [X2] : ~ ra_Px4(X0,X2)
| ~ ca_Cx4xcomp(X0) ) ),
inference(rectify,[],[f32]) ).
fof(f34,plain,
! [X0] :
( ( ca_Cx4xcomp(X0)
| ra_Px4(X0,sK4(X0)) )
& ( ! [X2] : ~ ra_Px4(X0,X2)
| ~ ca_Cx4xcomp(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f33]) ).
fof(f35,plain,
! [X0] :
( ( ca_Cx4xcomp(X0)
| ~ cd(X0)
| ~ cexcomp(X0) )
& ( ( cd(X0)
& cexcomp(X0) )
| ~ ca_Cx4xcomp(X0) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f36,plain,
! [X0] :
( ( ca_Cx4xcomp(X0)
| ~ cd(X0)
| ~ cexcomp(X0) )
& ( ( cd(X0)
& cexcomp(X0) )
| ~ ca_Cx4xcomp(X0) ) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X3,X0] :
( ca_Cx4(X3)
| ~ rr(X0,X3)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f38,plain,
! [X2,X0] :
( cd(X2)
| ~ rr(X0,X2)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
! [X0] :
( cexcomp(sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f40,plain,
! [X0] :
( rr(X0,sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
! [X0] :
( ra_Px4(X0,sK3(X0))
| ~ ca_Cx4(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f46,plain,
! [X2,X0] :
( ~ ca_Cx4xcomp(X0)
| ~ ra_Px4(X0,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
! [X0] :
( ~ cd(X0)
| ca_Cx4xcomp(X0)
| ~ cexcomp(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f51,plain,
cUnsatisfiable(i2003_11_14_17_22_31584),
inference(cnf_transformation,[],[f12]) ).
fof(f53,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| ~ rr(X0,X1)
| ca_Cx4xcomp(X1)
| ~ cexcomp(X1) ),
inference(resolution,[],[f38,f50]) ).
fof(f55,plain,
! [X0] :
( ~ rr(i2003_11_14_17_22_31584,X0)
| ca_Cx4xcomp(X0)
| ~ cexcomp(X0) ),
inference(resolution,[],[f53,f51]) ).
fof(f56,plain,
( ca_Cx4xcomp(sK0(i2003_11_14_17_22_31584))
| ~ cexcomp(sK0(i2003_11_14_17_22_31584))
| ~ cUnsatisfiable(i2003_11_14_17_22_31584) ),
inference(resolution,[],[f55,f40]) ).
fof(f57,plain,
( ca_Cx4xcomp(sK0(i2003_11_14_17_22_31584))
| ~ cUnsatisfiable(i2003_11_14_17_22_31584) ),
inference(forward_subsumption_resolution,[],[f56,f39]) ).
fof(f58,plain,
ca_Cx4xcomp(sK0(i2003_11_14_17_22_31584)),
inference(forward_subsumption_resolution,[],[f57,f51]) ).
fof(f59,plain,
! [X0] : ~ ra_Px4(sK0(i2003_11_14_17_22_31584),X0),
inference(resolution,[],[f58,f46]) ).
fof(f63,plain,
~ ca_Cx4(sK0(i2003_11_14_17_22_31584)),
inference(resolution,[],[f59,f45]) ).
fof(f65,plain,
! [X0] :
( ~ rr(X0,sK0(i2003_11_14_17_22_31584))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f63,f37]) ).
fof(f66,plain,
( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ cUnsatisfiable(i2003_11_14_17_22_31584) ),
inference(resolution,[],[f65,f40]) ).
fof(f67,plain,
~ cUnsatisfiable(i2003_11_14_17_22_31584),
inference(duplicate_literal_removal,[],[f66]) ).
fof(f68,plain,
$false,
inference(forward_subsumption_resolution,[],[f67,f51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS128+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 13:28:50 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 3.37/1.35 % (3383634)Detected formulas, will run a generic FOF schedule.
% 3.37/1.35 % (3383641)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=3744760544:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.37/1.35 % (3383640)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=3564292042:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.37/1.35 % (3383644)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3491768399:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.37/1.35 % (3383639)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=1086393777:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.37/1.35 % (3383644)First to succeed.
% 3.37/1.35 % (3383644)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3383634"
% 3.37/1.35 % (3383643)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=311428293:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.37/1.35 % (3383642)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2960178641:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.37/1.35 % (3383645)dis-21_1_sil=8000:lcm=predicate:random_seed=2352136636: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)
% 3.37/1.35 % (3383643)Refutation not found, incomplete strategy
% 3.37/1.35 % (3383643)------------------------------
% 3.37/1.35 % (3383643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.35 % (3383643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.35 % (3383642)Refutation not found, incomplete strategy
% 3.37/1.35 % (3383642)------------------------------
% 3.37/1.35 % (3383642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.35 % (3383643)CaDiCaL version: 2.1.3
% 3.37/1.35 % (3383642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.35 % (3383643)Termination reason: Refutation not found, incomplete strategy
% 3.37/1.35 % (3383643)Time elapsed: 0.0000 s
% 3.37/1.35 % (3383643)Peak memory usage: 86 MB
% 3.37/1.35 % (3383642)CaDiCaL version: 2.1.3
% 3.37/1.35 % (3383642)Termination reason: Refutation not found, incomplete strategy
% 3.37/1.35 % (3383642)Time elapsed: 0.0000 s
% 3.37/1.35 % (3383642)Peak memory usage: 86 MB
% 3.37/1.35 % (3383645)Also succeeded, but the first one will report.
% 3.37/1.35 % (3383643)------------------------------
% 3.37/1.35 % (3383643)------------------------------
% 3.37/1.35 % (3383642)------------------------------
% 3.37/1.35 % (3383642)------------------------------
% 3.37/1.35 % (3383644)Refutation found. Thanks to Tanya!
% 3.37/1.35 % SZS status Unsatisfiable for theBenchmark
% 3.37/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.37/1.35 % (3383644)------------------------------
% 3.37/1.35 % (3383644)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.35 % (3383644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.35 % (3383644)CaDiCaL version: 2.1.3
% 3.37/1.35 % (3383644)Termination reason: Refutation
% 3.37/1.35 % (3383644)Time elapsed: 0.003 s
% 3.37/1.35 % (3383644)Peak memory usage: 88 MB
% 3.37/1.35 % (3383644)Instructions burned: 2 (million)
% 3.37/1.35 % (3383644)------------------------------
% 3.37/1.35 % (3383644)------------------------------
% 3.37/1.35 % (3383634)Success in time 0.409 s
% 3.37/1.35 % Vampire exiting
%------------------------------------------------------------------------------