%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS111+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 : n001.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 11:41:40 AM UTC 2026
% Result : Unsatisfiable 3.17s 1.32s
% Output : Refutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 8 unt; 0 def)
% Number of atoms : 182 ( 18 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 209 ( 82 ~; 76 |; 42 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 109 ( 88 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rf1(X0,X1)
& cpxcomp(X1) )
& ? [X1] :
( rs(X0,X1)
& cowlThing(X1) )
& ? [X1] :
( rf(X0,X1)
& cp(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f25,axiom,
! [X0] :
( cp(X0)
<=> ~ ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f26,axiom,
! [X0] :
( cpxcomp(X0)
<=> ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f27,axiom,
! [X0,X1,X2] :
( ( rf(X0,X1)
& rf(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f28,axiom,
! [X0,X1,X2] :
( ( rf1(X0,X1)
& rf1(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f33,axiom,
cUnsatisfiable(i2003_11_14_17_21_15425),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
fof(f34,axiom,
! [X0,X1] :
( rs(X0,X1)
=> rf(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
fof(f35,axiom,
! [X0,X1] :
( rs(X0,X1)
=> rf1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
fof(f36,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rf1(X0,X1)
& cpxcomp(X1) )
& ? [X2] :
( rs(X0,X2)
& cowlThing(X2) )
& ? [X3] :
( rf(X0,X3)
& cp(X3) ) ) ),
inference(rectify,[],[f24]) ).
fof(f79,plain,
! [X0] :
( cp(X0)
<=> ! [X1] : ~ ra_Px1(X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f80,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf(X0,X1)
| ~ rf(X0,X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f81,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf(X0,X1)
| ~ rf(X0,X2) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf1(X0,X1)
| ~ rf1(X0,X2) ),
inference(ennf_transformation,[],[f28]) ).
fof(f83,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf1(X0,X1)
| ~ rf1(X0,X2) ),
inference(flattening,[],[f82]) ).
fof(f86,plain,
! [X0,X1] :
( rf(X0,X1)
| ~ rs(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f87,plain,
! [X0,X1] :
( rf1(X0,X1)
| ~ rs(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f89,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf1(X0,X1)
| ~ cpxcomp(X1) )
| ! [X2] :
( ~ rs(X0,X2)
| ~ cowlThing(X2) )
| ! [X3] :
( ~ rf(X0,X3)
| ~ cp(X3) ) )
& ( ( ? [X1] :
( rf1(X0,X1)
& cpxcomp(X1) )
& ? [X2] :
( rs(X0,X2)
& cowlThing(X2) )
& ? [X3] :
( rf(X0,X3)
& cp(X3) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f90,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf1(X0,X1)
| ~ cpxcomp(X1) )
| ! [X2] :
( ~ rs(X0,X2)
| ~ cowlThing(X2) )
| ! [X3] :
( ~ rf(X0,X3)
| ~ cp(X3) ) )
& ( ( ? [X1] :
( rf1(X0,X1)
& cpxcomp(X1) )
& ? [X2] :
( rs(X0,X2)
& cowlThing(X2) )
& ? [X3] :
( rf(X0,X3)
& cp(X3) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf1(X0,X1)
| ~ cpxcomp(X1) )
| ! [X2] :
( ~ rs(X0,X2)
| ~ cowlThing(X2) )
| ! [X3] :
( ~ rf(X0,X3)
| ~ cp(X3) ) )
& ( ( ? [X4] :
( rf1(X0,X4)
& cpxcomp(X4) )
& ? [X5] :
( rs(X0,X5)
& cowlThing(X5) )
& ? [X6] :
( rf(X0,X6)
& cp(X6) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf1(X0,X1)
| ~ cpxcomp(X1) )
| ! [X2] :
( ~ rs(X0,X2)
| ~ cowlThing(X2) )
| ! [X3] :
( ~ rf(X0,X3)
| ~ cp(X3) ) )
& ( ( rf1(X0,sK0(X0))
& cpxcomp(sK0(X0))
& rs(X0,sK1(X0))
& cowlThing(sK1(X0))
& rf(X0,sK2(X0))
& cp(sK2(X0)) )
| ~ cUnsatisfiable(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X4,sK0(X0)),skolemize(X5,sK1(X0)),skolemize(X6,sK2(X0))],[f91]) ).
fof(f93,plain,
! [X0] :
( ( cp(X0)
| ? [X1] : ra_Px1(X0,X1) )
& ( ! [X1] : ~ ra_Px1(X0,X1)
| ~ cp(X0) ) ),
inference(nnf_transformation,[],[f79]) ).
fof(f94,plain,
! [X0] :
( ( cp(X0)
| ? [X1] : ra_Px1(X0,X1) )
& ( ! [X2] : ~ ra_Px1(X0,X2)
| ~ cp(X0) ) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0] :
( ( cp(X0)
| ra_Px1(X0,sK3(X0)) )
& ( ! [X2] : ~ ra_Px1(X0,X2)
| ~ cp(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f94]) ).
fof(f96,plain,
! [X0] :
( ( cpxcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ? [X1] : ra_Px1(X0,X1)
| ~ cpxcomp(X0) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f97,plain,
! [X0] :
( ( cpxcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ? [X2] : ra_Px1(X0,X2)
| ~ cpxcomp(X0) ) ),
inference(rectify,[],[f96]) ).
fof(f98,plain,
! [X0] :
( ( cpxcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ra_Px1(X0,sK4(X0))
| ~ cpxcomp(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0))],[f97]) ).
fof(f127,plain,
! [X0] :
( cp(sK2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f128,plain,
! [X0] :
( rf(X0,sK2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f130,plain,
! [X0] :
( rs(X0,sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f131,plain,
! [X0] :
( cpxcomp(sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f132,plain,
! [X0] :
( rf1(X0,sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f134,plain,
! [X2,X0] :
( ~ ra_Px1(X0,X2)
| ~ cp(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f136,plain,
! [X0] :
( ra_Px1(X0,sK4(X0))
| ~ cpxcomp(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ rf(X0,X1)
| X1 = X2
| ~ rf(X0,X2) ),
inference(cnf_transformation,[],[f81]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ rf1(X0,X1)
| X1 = X2
| ~ rf1(X0,X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f147,plain,
cUnsatisfiable(i2003_11_14_17_21_15425),
inference(cnf_transformation,[],[f33]) ).
fof(f148,plain,
! [X0,X1] :
( rf(X0,X1)
| ~ rs(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f149,plain,
! [X0,X1] :
( rf1(X0,X1)
| ~ rs(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f171,plain,
! [X0] :
( ~ cpxcomp(X0)
| ~ cp(X0) ),
inference(resolution,[],[f136,f134]) ).
fof(f172,plain,
! [X0] :
( ~ cp(sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f171,f131]) ).
fof(f177,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| ~ rf(X0,X1)
| sK2(X0) = X1 ),
inference(resolution,[],[f138,f128]) ).
fof(f181,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| ~ rf1(X0,X1)
| sK0(X0) = X1 ),
inference(resolution,[],[f139,f132]) ).
fof(f188,plain,
! [X0] :
( ~ rf(i2003_11_14_17_21_15425,X0)
| sK2(i2003_11_14_17_21_15425) = X0 ),
inference(resolution,[],[f177,f147]) ).
fof(f191,plain,
! [X0] :
( ~ rs(i2003_11_14_17_21_15425,X0)
| sK2(i2003_11_14_17_21_15425) = X0 ),
inference(resolution,[],[f188,f148]) ).
fof(f194,plain,
( sK2(i2003_11_14_17_21_15425) = sK1(i2003_11_14_17_21_15425)
| ~ cUnsatisfiable(i2003_11_14_17_21_15425) ),
inference(resolution,[],[f191,f130]) ).
fof(f196,plain,
sK2(i2003_11_14_17_21_15425) = sK1(i2003_11_14_17_21_15425),
inference(forward_subsumption_resolution,[],[f194,f147]) ).
fof(f197,plain,
! [X0] :
( ~ rf1(i2003_11_14_17_21_15425,X0)
| sK0(i2003_11_14_17_21_15425) = X0 ),
inference(resolution,[],[f181,f147]) ).
fof(f200,plain,
( cp(sK1(i2003_11_14_17_21_15425))
| ~ cUnsatisfiable(i2003_11_14_17_21_15425) ),
inference(superposition,[],[f127,f196]) ).
fof(f201,plain,
cp(sK1(i2003_11_14_17_21_15425)),
inference(forward_subsumption_resolution,[],[f200,f147]) ).
fof(f211,plain,
! [X0] :
( ~ rs(i2003_11_14_17_21_15425,X0)
| sK0(i2003_11_14_17_21_15425) = X0 ),
inference(resolution,[],[f197,f149]) ).
fof(f214,plain,
( sK1(i2003_11_14_17_21_15425) = sK0(i2003_11_14_17_21_15425)
| ~ cUnsatisfiable(i2003_11_14_17_21_15425) ),
inference(resolution,[],[f211,f130]) ).
fof(f216,plain,
sK1(i2003_11_14_17_21_15425) = sK0(i2003_11_14_17_21_15425),
inference(forward_subsumption_resolution,[],[f214,f147]) ).
fof(f220,plain,
cp(sK0(i2003_11_14_17_21_15425)),
inference(superposition,[],[f201,f216]) ).
fof(f224,plain,
~ cUnsatisfiable(i2003_11_14_17_21_15425),
inference(resolution,[],[f220,f172]) ).
fof(f225,plain,
$false,
inference(forward_subsumption_resolution,[],[f224,f147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS111+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 13:31:00 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.17/1.32 % (3572526)Detected formulas, will run a generic FOF schedule.
% 3.17/1.32 % (3572537)dis-21_1_sil=8000:lcm=predicate:random_seed=2589232246: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)
% 3.17/1.32 % (3572537)Instruction limit reached!
% 3.17/1.32 % (3572537)------------------------------
% 3.17/1.32 % (3572537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.32 % (3572537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.32 % (3572537)CaDiCaL version: 2.1.3
% 3.17/1.32 % (3572537)Termination reason: Instruction limit
% 3.17/1.32 % (3572537)Termination phase: Saturation
% 3.17/1.32 % (3572537)Time elapsed: 0.028 s
% 3.17/1.32 % (3572537)Peak memory usage: 88 MB
% 3.17/1.32 % (3572537)Instructions burned: 131 (million)
% 3.17/1.32 % (3572533)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=1447285092:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.17/1.32 % (3572531)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=1874590410:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.17/1.32 % (3572534)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=815063491:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.17/1.32 % (3572536)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1902265187:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.17/1.32 % (3572535)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=151798836:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.17/1.32 % (3572532)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=1247720529:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.17/1.32 % (3572535)Refutation not found, incomplete strategy
% 3.17/1.32 % (3572535)------------------------------
% 3.17/1.32 % (3572535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.32 % (3572535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.32 % (3572535)CaDiCaL version: 2.1.3
% 3.17/1.32 % (3572535)Termination reason: Refutation not found, incomplete strategy
% 3.17/1.32 % (3572535)Time elapsed: 0.0000 s
% 3.17/1.32 % (3572535)Peak memory usage: 86 MB
% 3.17/1.32 % (3572534)Refutation not found, incomplete strategy
% 3.17/1.32 % (3572534)------------------------------
% 3.17/1.32 % (3572534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.32 % (3572534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.32 % (3572534)CaDiCaL version: 2.1.3
% 3.17/1.32 % (3572534)Termination reason: Refutation not found, incomplete strategy
% 3.17/1.32 % (3572534)Time elapsed: 0.0000 s
% 3.17/1.32 % (3572534)Peak memory usage: 86 MB
% 3.17/1.32 % (3572536)First to succeed.
% 3.17/1.32 % (3572536)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3572526"
% 3.17/1.32 % (3572545)lrs+10_1_sil=8000:sp=occurrence:random_seed=3485414130:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.17/1.32 % (3572545)Refutation not found, incomplete strategy
% 3.17/1.32 % (3572545)------------------------------
% 3.17/1.32 % (3572545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.32 % (3572545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.32 % (3572545)CaDiCaL version: 2.1.3
% 3.17/1.32 % (3572545)Termination reason: Refutation not found, incomplete strategy
% 3.17/1.32 % (3572545)Time elapsed: 0.0000 s
% 3.17/1.32 % (3572545)Peak memory usage: 86 MB
% 3.17/1.32 % (3572535)------------------------------
% 3.17/1.32 % (3572535)------------------------------
% 3.17/1.32 % (3572534)------------------------------
% 3.17/1.32 % (3572534)------------------------------
% 3.17/1.32 % (3572536)Refutation found. Thanks to Tanya!
% 3.17/1.32 % SZS status Unsatisfiable for theBenchmark
% 3.17/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.81/1.52 % (3572536)------------------------------
% 3.81/1.52 % (3572536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.52 % (3572536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.52 % (3572536)CaDiCaL version: 2.1.3
% 3.81/1.52 % (3572536)Termination reason: Refutation
% 3.81/1.52 % (3572536)Time elapsed: 0.005 s
% 3.81/1.52 % (3572536)Peak memory usage: 89 MB
% 3.81/1.52 % (3572536)Instructions burned: 5 (million)
% 3.81/1.52 % (3572536)------------------------------
% 3.81/1.52 % (3572536)------------------------------
% 3.81/1.52 % (3572526)Success in time 0.446 s
% 3.81/1.52 % Vampire exiting
%------------------------------------------------------------------------------