%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS069+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 : n008.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 11:41:35 AM UTC 2026
% Result : Unsatisfiable 3.62s 1.47s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 7 unt; 0 def)
% Number of atoms : 143 ( 19 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 167 ( 65 ~; 60 |; 36 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 82 ( 67 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rf1(X0,X1)
& cp1(X1) )
& ? [X1] :
( rf2(X0,X1)
& ~ cp1(X1) )
& ? [X1] :
( rf3(X0,X1)
& cp2(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f17,axiom,
! [X0,X1,X2] :
( ( rf1(X0,X1)
& rf1(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f18,axiom,
! [X0,X1,X2] :
( ( rf2(X0,X1)
& rf2(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f20,axiom,
cUnsatisfiable(i2003_11_14_17_18_2750),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f21,axiom,
! [X0,X1] :
( rf3(X0,X1)
=> rf1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f22,axiom,
! [X0,X1] :
( rf3(X0,X1)
=> rf2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f23,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rf1(X0,X1)
& cp1(X1) )
& ? [X2] :
( rf2(X0,X2)
& ~ cp1(X2) )
& ? [X3] :
( rf3(X0,X3)
& cp2(X3) ) ) ),
inference(rectify,[],[f16]) ).
fof(f50,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf1(X0,X1)
| ~ rf1(X0,X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f51,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf1(X0,X1)
| ~ rf1(X0,X2) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf2(X0,X1)
| ~ rf2(X0,X2) ),
inference(ennf_transformation,[],[f18]) ).
fof(f53,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf2(X0,X1)
| ~ rf2(X0,X2) ),
inference(flattening,[],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( rf1(X0,X1)
| ~ rf3(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f57,plain,
! [X0,X1] :
( rf2(X0,X1)
| ~ rf3(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f59,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf1(X0,X1)
| ~ cp1(X1) )
| ! [X2] :
( ~ rf2(X0,X2)
| cp1(X2) )
| ! [X3] :
( ~ rf3(X0,X3)
| ~ cp2(X3) ) )
& ( ( ? [X1] :
( rf1(X0,X1)
& cp1(X1) )
& ? [X2] :
( rf2(X0,X2)
& ~ cp1(X2) )
& ? [X3] :
( rf3(X0,X3)
& cp2(X3) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f60,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf1(X0,X1)
| ~ cp1(X1) )
| ! [X2] :
( ~ rf2(X0,X2)
| cp1(X2) )
| ! [X3] :
( ~ rf3(X0,X3)
| ~ cp2(X3) ) )
& ( ( ? [X1] :
( rf1(X0,X1)
& cp1(X1) )
& ? [X2] :
( rf2(X0,X2)
& ~ cp1(X2) )
& ? [X3] :
( rf3(X0,X3)
& cp2(X3) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf1(X0,X1)
| ~ cp1(X1) )
| ! [X2] :
( ~ rf2(X0,X2)
| cp1(X2) )
| ! [X3] :
( ~ rf3(X0,X3)
| ~ cp2(X3) ) )
& ( ( ? [X4] :
( rf1(X0,X4)
& cp1(X4) )
& ? [X5] :
( rf2(X0,X5)
& ~ cp1(X5) )
& ? [X6] :
( rf3(X0,X6)
& cp2(X6) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf1(X0,X1)
| ~ cp1(X1) )
| ! [X2] :
( ~ rf2(X0,X2)
| cp1(X2) )
| ! [X3] :
( ~ rf3(X0,X3)
| ~ cp2(X3) ) )
& ( ( rf1(X0,sK0(X0))
& cp1(sK0(X0))
& rf2(X0,sK1(X0))
& ~ cp1(sK1(X0))
& rf3(X0,sK2(X0))
& cp2(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))],[f61]) ).
fof(f81,plain,
! [X0] :
( rf3(X0,sK2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f82,plain,
! [X0] :
( ~ cp1(sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f83,plain,
! [X0] :
( rf2(X0,sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f84,plain,
! [X0] :
( cp1(sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f85,plain,
! [X0] :
( rf1(X0,sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ rf1(X0,X1)
| X1 = X2
| ~ rf1(X0,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ rf2(X0,X1)
| X1 = X2
| ~ rf2(X0,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f90,plain,
cUnsatisfiable(i2003_11_14_17_18_2750),
inference(cnf_transformation,[],[f20]) ).
fof(f91,plain,
! [X0,X1] :
( rf1(X0,X1)
| ~ rf3(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f92,plain,
! [X0,X1] :
( rf2(X0,X1)
| ~ rf3(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f106,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| ~ rf1(X0,X1)
| sK0(X0) = X1 ),
inference(resolution,[],[f87,f85]) ).
fof(f109,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| ~ rf2(X0,X1)
| sK1(X0) = X1 ),
inference(resolution,[],[f88,f83]) ).
fof(f114,plain,
! [X0] :
( ~ rf1(i2003_11_14_17_18_2750,X0)
| sK0(i2003_11_14_17_18_2750) = X0 ),
inference(resolution,[],[f106,f90]) ).
fof(f117,plain,
! [X0] :
( ~ rf3(i2003_11_14_17_18_2750,X0)
| sK0(i2003_11_14_17_18_2750) = X0 ),
inference(resolution,[],[f114,f91]) ).
fof(f119,plain,
( sK0(i2003_11_14_17_18_2750) = sK2(i2003_11_14_17_18_2750)
| ~ cUnsatisfiable(i2003_11_14_17_18_2750) ),
inference(resolution,[],[f117,f81]) ).
fof(f120,plain,
sK0(i2003_11_14_17_18_2750) = sK2(i2003_11_14_17_18_2750),
inference(forward_subsumption_resolution,[],[f119,f90]) ).
fof(f121,plain,
! [X0] :
( ~ rf2(i2003_11_14_17_18_2750,X0)
| sK1(i2003_11_14_17_18_2750) = X0 ),
inference(resolution,[],[f109,f90]) ).
fof(f136,plain,
! [X0] :
( ~ rf3(i2003_11_14_17_18_2750,X0)
| sK1(i2003_11_14_17_18_2750) = X0 ),
inference(resolution,[],[f121,f92]) ).
fof(f140,plain,
( sK2(i2003_11_14_17_18_2750) = sK1(i2003_11_14_17_18_2750)
| ~ cUnsatisfiable(i2003_11_14_17_18_2750) ),
inference(resolution,[],[f136,f81]) ).
fof(f141,plain,
sK2(i2003_11_14_17_18_2750) = sK1(i2003_11_14_17_18_2750),
inference(forward_subsumption_resolution,[],[f140,f90]) ).
fof(f142,plain,
sK0(i2003_11_14_17_18_2750) = sK1(i2003_11_14_17_18_2750),
inference(forward_demodulation,[],[f141,f120]) ).
fof(f146,plain,
( ~ cp1(sK0(i2003_11_14_17_18_2750))
| ~ cUnsatisfiable(i2003_11_14_17_18_2750) ),
inference(superposition,[],[f82,f142]) ).
fof(f147,plain,
~ cUnsatisfiable(i2003_11_14_17_18_2750),
inference(forward_subsumption_resolution,[],[f146,f84]) ).
fof(f149,plain,
$false,
inference(forward_subsumption_resolution,[],[f147,f90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS069+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 13:20:24 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 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
% 3.62/1.47 % (1222466)Detected formulas, will run a generic FOF schedule.
% 3.62/1.47 % (1222474)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2266729055:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.62/1.47 % (1222474)Refutation not found, incomplete strategy
% 3.62/1.47 % (1222474)------------------------------
% 3.62/1.47 % (1222474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.47 % (1222474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.47 % (1222474)CaDiCaL version: 2.1.3
% 3.62/1.47 % (1222474)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.47 % (1222474)Time elapsed: 0.0000 s
% 3.62/1.47 % (1222474)Peak memory usage: 86 MB
% 3.62/1.47 % (1222473)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=3376954307:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.62/1.47 % (1222472)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=3584304291:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.62/1.47 % (1222471)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=770064116:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.62/1.47 % (1222477)dis-21_1_sil=8000:lcm=predicate:random_seed=2047625615: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)
% 3.62/1.47 % (1222475)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1865074623:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.62/1.47 % (1222476)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3515620196:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.62/1.47 % (1222475)Refutation not found, incomplete strategy
% 3.62/1.47 % (1222475)------------------------------
% 3.62/1.47 % (1222475)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.47 % (1222475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.47 % (1222475)CaDiCaL version: 2.1.3
% 3.62/1.47 % (1222475)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.47 % (1222475)Time elapsed: 0.0000 s
% 3.62/1.47 % (1222475)Peak memory usage: 86 MB
% 3.62/1.47 % (1222477)Refutation not found, incomplete strategy
% 3.62/1.47 % (1222477)------------------------------
% 3.62/1.47 % (1222477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.47 % (1222477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.47 % (1222477)CaDiCaL version: 2.1.3
% 3.62/1.47 % (1222477)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.47 % (1222477)Time elapsed: 0.002 s
% 3.62/1.47 % (1222477)Peak memory usage: 88 MB
% 3.62/1.47 % (1222477)Instructions burned: 1 (million)
% 3.62/1.47 % (1222476)First to succeed.
% 3.62/1.47 % (1222476)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1222466"
% 3.62/1.47 % (1222474)------------------------------
% 3.62/1.47 % (1222474)------------------------------
% 3.62/1.47 % (1222485)lrs+10_1_sil=8000:sp=occurrence:random_seed=3771840410:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.62/1.47 % (1222485)Refutation not found, incomplete strategy
% 3.62/1.47 % (1222485)------------------------------
% 3.62/1.47 % (1222485)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.47 % (1222485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.47 % (1222485)CaDiCaL version: 2.1.3
% 3.62/1.47 % (1222485)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.47 % (1222485)Time elapsed: 0.0000 s
% 3.62/1.47 % (1222485)Peak memory usage: 86 MB
% 3.62/1.47 % (1222477)------------------------------
% 3.62/1.47 % (1222477)------------------------------
% 3.62/1.47 % (1222475)------------------------------
% 3.62/1.47 % (1222475)------------------------------
% 3.62/1.47 % (1222476)Refutation found. Thanks to Tanya!
% 3.62/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.62/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.47 % (1222476)------------------------------
% 3.62/1.47 % (1222476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.47 % (1222476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.47 % (1222476)CaDiCaL version: 2.1.3
% 3.62/1.47 % (1222476)Termination reason: Refutation
% 3.62/1.47 % (1222476)Time elapsed: 0.005 s
% 3.62/1.47 % (1222476)Peak memory usage: 89 MB
% 3.62/1.47 % (1222476)Instructions burned: 4 (million)
% 3.62/1.47 % (1222476)------------------------------
% 3.62/1.47 % (1222476)------------------------------
% 3.62/1.47 % (1222466)Success in time 0.433 s
% 3.62/1.47 % Vampire exiting
%------------------------------------------------------------------------------