%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS097+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 : n016.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 11:41:38 AM UTC 2026
% Result : Unsatisfiable 3.55s 1.45s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 7 unt; 3 def)
% Number of atoms : 195 ( 20 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 242 ( 94 ~; 83 |; 58 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 84 ( 0 sgn 53 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] : rr(X0,X1)
& ? [X2] :
( rr(X0,X2)
& cd(X2) )
& ~ ? [X1,X3] :
( rr(X0,X1)
& rr(X0,X3)
& X1 != X3 )
& ? [X2] :
( rr(X0,X2)
& cc(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f30,axiom,
cUnsatisfiable(i2003_11_14_17_20_21603),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f32,axiom,
! [X0] :
~ ( cd(X0)
& cc(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f40,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] : rr(X0,X1)
& ? [X2] :
( rr(X0,X2)
& cd(X2) )
& ~ ? [X3,X4] :
( rr(X0,X3)
& rr(X0,X4)
& X3 != X4 )
& ? [X5] :
( rr(X0,X5)
& cc(X5) ) ) ),
inference(rectify,[],[f28]) ).
fof(f91,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] : rr(X0,X1)
& ? [X2] :
( rr(X0,X2)
& cd(X2) )
& ! [X3,X4] :
( ~ rr(X0,X3)
| ~ rr(X0,X4)
| X3 = X4 )
& ? [X5] :
( rr(X0,X5)
& cc(X5) ) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f93,plain,
! [X0] :
( ~ cd(X0)
| ~ cc(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f101,definition,
! [X0] :
( sP0(X0)
<=> ( ? [X1] : rr(X0,X1)
& ? [X2] :
( rr(X0,X2)
& cd(X2) )
& ! [X3,X4] :
( ~ rr(X0,X3)
| ~ rr(X0,X4)
| X3 = X4 )
& ? [X5] :
( rr(X0,X5)
& cc(X5) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f102,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> sP0(X0) ),
inference(definition_folding,[],[f91,f101]) ).
fof(f104,plain,
! [X0] :
( ( sP0(X0)
| ! [X1] : ~ rr(X0,X1)
| ! [X2] :
( ~ rr(X0,X2)
| ~ cd(X2) )
| ? [X3,X4] :
( rr(X0,X3)
& rr(X0,X4)
& X3 != X4 )
| ! [X5] :
( ~ rr(X0,X5)
| ~ cc(X5) ) )
& ( ( ? [X1] : rr(X0,X1)
& ? [X2] :
( rr(X0,X2)
& cd(X2) )
& ! [X3,X4] :
( ~ rr(X0,X3)
| ~ rr(X0,X4)
| X3 = X4 )
& ? [X5] :
( rr(X0,X5)
& cc(X5) ) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f105,plain,
! [X0] :
( ( sP0(X0)
| ! [X1] : ~ rr(X0,X1)
| ! [X2] :
( ~ rr(X0,X2)
| ~ cd(X2) )
| ? [X3,X4] :
( rr(X0,X3)
& rr(X0,X4)
& X3 != X4 )
| ! [X5] :
( ~ rr(X0,X5)
| ~ cc(X5) ) )
& ( ( ? [X1] : rr(X0,X1)
& ? [X2] :
( rr(X0,X2)
& cd(X2) )
& ! [X3,X4] :
( ~ rr(X0,X3)
| ~ rr(X0,X4)
| X3 = X4 )
& ? [X5] :
( rr(X0,X5)
& cc(X5) ) )
| ~ sP0(X0) ) ),
inference(flattening,[],[f104]) ).
fof(f106,plain,
! [X0] :
( ( sP0(X0)
| ! [X1] : ~ rr(X0,X1)
| ! [X2] :
( ~ rr(X0,X2)
| ~ cd(X2) )
| ? [X3,X4] :
( rr(X0,X3)
& rr(X0,X4)
& X3 != X4 )
| ! [X5] :
( ~ rr(X0,X5)
| ~ cc(X5) ) )
& ( ( ? [X6] : rr(X0,X6)
& ? [X7] :
( rr(X0,X7)
& cd(X7) )
& ! [X8,X9] :
( ~ rr(X0,X8)
| ~ rr(X0,X9)
| X8 = X9 )
& ? [X10] :
( rr(X0,X10)
& cc(X10) ) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f105]) ).
fof(f107,plain,
! [X0] :
( ( sP0(X0)
| ! [X1] : ~ rr(X0,X1)
| ! [X2] :
( ~ rr(X0,X2)
| ~ cd(X2) )
| ( rr(X0,sK1(X0))
& rr(X0,sK2(X0))
& sK1(X0) != sK2(X0) )
| ! [X5] :
( ~ rr(X0,X5)
| ~ cc(X5) ) )
& ( ( rr(X0,sK3(X0))
& rr(X0,sK4(X0))
& cd(sK4(X0))
& ! [X8,X9] :
( ~ rr(X0,X8)
| ~ rr(X0,X9)
| X8 = X9 )
& rr(X0,sK5(X0))
& cc(sK5(X0)) )
| ~ sP0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5]),skolemize(X3,sK1(X0)),skolemize(X4,sK2(X0)),skolemize(X6,sK3(X0)),skolemize(X7,sK4(X0)),skolemize(X10,sK5(X0))],[f106]) ).
fof(f108,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f140,plain,
! [X0] :
( cc(sK5(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f141,plain,
! [X0] :
( rr(X0,sK5(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f142,plain,
! [X0,X8,X9] :
( ~ sP0(X0)
| ~ rr(X0,X9)
| X8 = X9
| ~ rr(X0,X8) ),
inference(cnf_transformation,[],[f107]) ).
fof(f143,plain,
! [X0] :
( ~ sP0(X0)
| cd(sK4(X0)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f144,plain,
! [X0] :
( rr(X0,sK4(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f149,plain,
! [X0] :
( sP0(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f154,plain,
cUnsatisfiable(i2003_11_14_17_20_21603),
inference(cnf_transformation,[],[f30]) ).
fof(f156,plain,
! [X0] :
( ~ cd(X0)
| ~ cc(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f195,plain,
! [X2,X0,X1] :
( ~ cUnsatisfiable(X0)
| X1 = X2
| ~ rr(X0,X2)
| ~ rr(X0,X1) ),
inference(resolution,[],[f142,f149]) ).
fof(f196,plain,
! [X0,X1] :
( ~ rr(i2003_11_14_17_20_21603,X1)
| X0 = X1
| ~ rr(i2003_11_14_17_20_21603,X0) ),
inference(resolution,[],[f195,f154]) ).
fof(f202,plain,
! [X0] :
( sK5(i2003_11_14_17_20_21603) = X0
| ~ rr(i2003_11_14_17_20_21603,X0)
| ~ sP0(i2003_11_14_17_20_21603) ),
inference(resolution,[],[f196,f141]) ).
fof(f205,definition,
( spl6_1
<=> sP0(i2003_11_14_17_20_21603) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f206,plain,
( sP0(i2003_11_14_17_20_21603)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f207,plain,
( ~ sP0(i2003_11_14_17_20_21603)
| spl6_1 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f209,definition,
( spl6_2
<=> ! [X0] :
( sK5(i2003_11_14_17_20_21603) = X0
| ~ rr(i2003_11_14_17_20_21603,X0) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f210,plain,
( ! [X0] :
( ~ rr(i2003_11_14_17_20_21603,X0)
| sK5(i2003_11_14_17_20_21603) = X0 )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f211,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f202,f209,f205]) ).
fof(f237,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| spl6_1 ),
inference(resolution,[],[f207,f149]) ).
fof(f238,plain,
( $false
| spl6_1 ),
inference(forward_subsumption_resolution,[],[f237,f154]) ).
fof(f239,plain,
spl6_1,
inference(avatar_contradiction_clause,[],[f238]) ).
fof(f241,plain,
( cd(sK4(i2003_11_14_17_20_21603))
| ~ spl6_1 ),
inference(resolution,[],[f206,f143]) ).
fof(f242,plain,
( ~ cc(sK4(i2003_11_14_17_20_21603))
| ~ spl6_1 ),
inference(resolution,[],[f241,f156]) ).
fof(f248,plain,
( sK4(i2003_11_14_17_20_21603) = sK5(i2003_11_14_17_20_21603)
| ~ sP0(i2003_11_14_17_20_21603)
| ~ spl6_2 ),
inference(resolution,[],[f210,f144]) ).
fof(f250,plain,
( sK4(i2003_11_14_17_20_21603) = sK5(i2003_11_14_17_20_21603)
| ~ spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f248,f206]) ).
fof(f261,plain,
( cc(sK4(i2003_11_14_17_20_21603))
| ~ sP0(i2003_11_14_17_20_21603)
| ~ spl6_1
| ~ spl6_2 ),
inference(superposition,[],[f140,f250]) ).
fof(f262,plain,
( ~ sP0(i2003_11_14_17_20_21603)
| ~ spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f261,f242]) ).
fof(f263,plain,
( $false
| ~ spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f262,f206]) ).
fof(f264,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_contradiction_clause,[],[f263]) ).
cnf(s1,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f211]) ).
cnf(s6,plain,
spl6_1,
inference(sat_conversion,[],[f239]) ).
cnf(s7,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f264]) ).
cnf(s8,plain,
~ spl6_2,
inference(rat,[],[s7,s6]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s8,s6]) ).
fof(f265,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS097+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n016.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 13:27:47 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 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
% 3.55/1.45 % (2649367)Detected formulas, will run a generic FOF schedule.
% 3.55/1.45 % (2649376)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2597990886:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.55/1.45 % (2649376)Refutation not found, incomplete strategy
% 3.55/1.45 % (2649376)------------------------------
% 3.55/1.45 % (2649376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.45 % (2649376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.45 % (2649376)CaDiCaL version: 2.1.3
% 3.55/1.45 % (2649376)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.45 % (2649376)Time elapsed: 0.0000 s
% 3.55/1.45 % (2649376)Peak memory usage: 86 MB
% 3.55/1.45 % (2649375)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1250417669:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.55/1.45 % (2649378)dis-21_1_sil=8000:lcm=predicate:random_seed=3794914004: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)
% 3.55/1.45 % (2649375)Refutation not found, incomplete strategy
% 3.55/1.45 % (2649375)------------------------------
% 3.55/1.45 % (2649375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.45 % (2649375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.45 % (2649375)CaDiCaL version: 2.1.3
% 3.55/1.45 % (2649375)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.45 % (2649375)Time elapsed: 0.0000 s
% 3.55/1.45 % (2649375)Peak memory usage: 86 MB
% 3.55/1.45 % (2649372)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=1385232237:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.55/1.45 % (2649374)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=397073386:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.55/1.45 % (2649373)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=3123995545:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.55/1.45 % (2649378)Refutation not found, incomplete strategy
% 3.55/1.45 % (2649378)------------------------------
% 3.55/1.45 % (2649378)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.45 % (2649378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.45 % (2649378)CaDiCaL version: 2.1.3
% 3.55/1.45 % (2649378)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.45 % (2649378)Time elapsed: 0.003 s
% 3.55/1.45 % (2649378)Peak memory usage: 88 MB
% 3.55/1.45 % (2649378)Instructions burned: 3 (million)
% 3.55/1.45 % (2649377)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=548741715:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.55/1.45 % (2649377)First to succeed.
% 3.55/1.45 % (2649377)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2649367"
% 3.55/1.45 % (2649376)------------------------------
% 3.55/1.45 % (2649376)------------------------------
% 3.55/1.45 % (2649386)lrs+10_1_sil=8000:sp=occurrence:random_seed=763340268:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.55/1.45 % (2649386)Refutation not found, incomplete strategy
% 3.55/1.45 % (2649386)------------------------------
% 3.55/1.45 % (2649386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.45 % (2649386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.45 % (2649386)CaDiCaL version: 2.1.3
% 3.55/1.45 % (2649386)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.45 % (2649386)Time elapsed: 0.0000 s
% 3.55/1.45 % (2649386)Peak memory usage: 86 MB
% 3.55/1.45 % (2649378)------------------------------
% 3.55/1.45 % (2649378)------------------------------
% 3.55/1.45 % (2649375)------------------------------
% 3.55/1.45 % (2649375)------------------------------
% 3.55/1.45 % (2649377)Refutation found. Thanks to Tanya!
% 3.55/1.45 % SZS status Unsatisfiable for theBenchmark
% 3.55/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.45 % (2649377)------------------------------
% 3.55/1.45 % (2649377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.45 % (2649377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.45 % (2649377)CaDiCaL version: 2.1.3
% 3.55/1.45 % (2649377)Termination reason: Refutation
% 3.55/1.45 % (2649377)Time elapsed: 0.007 s
% 3.55/1.45 % (2649377)Peak memory usage: 89 MB
% 3.55/1.45 % (2649377)Instructions burned: 5 (million)
% 3.55/1.45 % (2649377)------------------------------
% 3.55/1.45 % (2649377)------------------------------
% 3.55/1.45 % (2649367)Success in time 0.415 s
% 3.55/1.45 % Vampire exiting
%------------------------------------------------------------------------------