%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS099+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 11:41:39 AM UTC 2026
% Result : Unsatisfiable 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 12 unt; 6 def)
% Number of atoms : 250 ( 54 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 316 ( 114 ~; 94 |; 91 &)
% ( 11 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 109 ( 0 sgn 79 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1,X2,X3] :
( rtt(X0,X1)
& rtt(X0,X2)
& rtt(X0,X3)
& X1 != X2
& X1 != X3
& X2 != X3 )
& ! [X4] :
( rtt(X0,X4)
=> ca(X4) )
& ! [X1,X2] :
( ( rtt(X0,X1)
& rtt(X0,X2) )
=> X1 = X2 )
& ! [X1,X2] :
( ( rtt(X0,X1)
& rtt(X0,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f16,axiom,
cUnsatisfiable(i2003_11_14_17_20_29215),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f17,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1,X2,X3] :
( rtt(X0,X1)
& rtt(X0,X2)
& rtt(X0,X3)
& X1 != X2
& X1 != X3
& X2 != X3 )
& ! [X4] :
( rtt(X0,X4)
=> ca(X4) )
& ! [X5,X6] :
( ( rtt(X0,X5)
& rtt(X0,X6) )
=> X5 = X6 )
& ! [X7,X8] :
( ( rtt(X0,X7)
& rtt(X0,X8) )
=> X7 = X8 ) ) ),
inference(rectify,[],[f13]) ).
fof(f38,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1,X2,X3] :
( rtt(X0,X1)
& rtt(X0,X2)
& rtt(X0,X3)
& X1 != X2
& X1 != X3
& X2 != X3 )
& ! [X4] :
( ca(X4)
| ~ rtt(X0,X4) )
& ! [X5,X6] :
( X5 = X6
| ~ rtt(X0,X5)
| ~ rtt(X0,X6) )
& ! [X7,X8] :
( X7 = X8
| ~ rtt(X0,X7)
| ~ rtt(X0,X8) ) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f39,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1,X2,X3] :
( rtt(X0,X1)
& rtt(X0,X2)
& rtt(X0,X3)
& X1 != X2
& X1 != X3
& X2 != X3 )
& ! [X4] :
( ca(X4)
| ~ rtt(X0,X4) )
& ! [X5,X6] :
( X5 = X6
| ~ rtt(X0,X5)
| ~ rtt(X0,X6) )
& ! [X7,X8] :
( X7 = X8
| ~ rtt(X0,X7)
| ~ rtt(X0,X8) ) ) ),
inference(flattening,[],[f38]) ).
fof(f43,definition,
! [X0] :
( sP0(X0)
<=> ! [X7,X8] :
( X7 = X8
| ~ rtt(X0,X7)
| ~ rtt(X0,X8) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f44,definition,
! [X0] :
( sP1(X0)
<=> ? [X1,X2,X3] :
( rtt(X0,X1)
& rtt(X0,X2)
& rtt(X0,X3)
& X1 != X2
& X1 != X3
& X2 != X3 ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f45,definition,
! [X0] :
( sP2(X0)
<=> ( sP1(X0)
& ! [X4] :
( ca(X4)
| ~ rtt(X0,X4) )
& ! [X5,X6] :
( X5 = X6
| ~ rtt(X0,X5)
| ~ rtt(X0,X6) )
& sP0(X0) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f46,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> sP2(X0) ),
inference(definition_folding,[],[f39,f45,f44,f43]) ).
fof(f48,plain,
! [X0] :
( ( sP2(X0)
| ~ sP1(X0)
| ? [X4] :
( ~ ca(X4)
& rtt(X0,X4) )
| ? [X5,X6] :
( X5 != X6
& rtt(X0,X5)
& rtt(X0,X6) )
| ~ sP0(X0) )
& ( ( sP1(X0)
& ! [X4] :
( ca(X4)
| ~ rtt(X0,X4) )
& ! [X5,X6] :
( X5 = X6
| ~ rtt(X0,X5)
| ~ rtt(X0,X6) )
& sP0(X0) )
| ~ sP2(X0) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f49,plain,
! [X0] :
( ( sP2(X0)
| ~ sP1(X0)
| ? [X4] :
( ~ ca(X4)
& rtt(X0,X4) )
| ? [X5,X6] :
( X5 != X6
& rtt(X0,X5)
& rtt(X0,X6) )
| ~ sP0(X0) )
& ( ( sP1(X0)
& ! [X4] :
( ca(X4)
| ~ rtt(X0,X4) )
& ! [X5,X6] :
( X5 = X6
| ~ rtt(X0,X5)
| ~ rtt(X0,X6) )
& sP0(X0) )
| ~ sP2(X0) ) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ( sP2(X0)
| ~ sP1(X0)
| ? [X1] :
( ~ ca(X1)
& rtt(X0,X1) )
| ? [X2,X3] :
( X2 != X3
& rtt(X0,X2)
& rtt(X0,X3) )
| ~ sP0(X0) )
& ( ( sP1(X0)
& ! [X4] :
( ca(X4)
| ~ rtt(X0,X4) )
& ! [X5,X6] :
( X5 = X6
| ~ rtt(X0,X5)
| ~ rtt(X0,X6) )
& sP0(X0) )
| ~ sP2(X0) ) ),
inference(rectify,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ( sP2(X0)
| ~ sP1(X0)
| ( ~ ca(sK3(X0))
& rtt(X0,sK3(X0)) )
| ( sK4(X0) != sK5(X0)
& rtt(X0,sK4(X0))
& rtt(X0,sK5(X0)) )
| ~ sP0(X0) )
& ( ( sP1(X0)
& ! [X4] :
( ca(X4)
| ~ rtt(X0,X4) )
& ! [X5,X6] :
( X5 = X6
| ~ rtt(X0,X5)
| ~ rtt(X0,X6) )
& sP0(X0) )
| ~ sP2(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X1,sK3(X0)),skolemize(X2,sK4(X0)),skolemize(X3,sK5(X0))],[f50]) ).
fof(f52,plain,
! [X0] :
( ( sP1(X0)
| ! [X1,X2,X3] :
( ~ rtt(X0,X1)
| ~ rtt(X0,X2)
| ~ rtt(X0,X3)
| X1 = X2
| X1 = X3
| X2 = X3 ) )
& ( ? [X1,X2,X3] :
( rtt(X0,X1)
& rtt(X0,X2)
& rtt(X0,X3)
& X1 != X2
& X1 != X3
& X2 != X3 )
| ~ sP1(X0) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f53,plain,
! [X0] :
( ( sP1(X0)
| ! [X1,X2,X3] :
( ~ rtt(X0,X1)
| ~ rtt(X0,X2)
| ~ rtt(X0,X3)
| X1 = X2
| X1 = X3
| X2 = X3 ) )
& ( ? [X4,X5,X6] :
( rtt(X0,X4)
& rtt(X0,X5)
& rtt(X0,X6)
& X4 != X5
& X4 != X6
& X5 != X6 )
| ~ sP1(X0) ) ),
inference(rectify,[],[f52]) ).
fof(f54,plain,
! [X0] :
( ( sP1(X0)
| ! [X1,X2,X3] :
( ~ rtt(X0,X1)
| ~ rtt(X0,X2)
| ~ rtt(X0,X3)
| X1 = X2
| X1 = X3
| X2 = X3 ) )
& ( ( rtt(X0,sK6(X0))
& rtt(X0,sK7(X0))
& rtt(X0,sK8(X0))
& sK6(X0) != sK7(X0)
& sK6(X0) != sK8(X0)
& sK7(X0) != sK8(X0) )
| ~ sP1(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X4,sK6(X0)),skolemize(X5,sK7(X0)),skolemize(X6,sK8(X0))],[f53]) ).
fof(f58,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ~ sP2(X0) )
& ( sP2(X0)
| ~ cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f74,plain,
! [X0,X6,X5] :
( X5 = X6
| ~ rtt(X0,X5)
| ~ rtt(X0,X6)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f76,plain,
! [X0] :
( ~ sP2(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f85,plain,
! [X0] :
( sK6(X0) != sK7(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f87,plain,
! [X0] :
( ~ sP1(X0)
| rtt(X0,sK7(X0)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f88,plain,
! [X0] :
( ~ sP1(X0)
| rtt(X0,sK6(X0)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f94,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sP2(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f98,plain,
cUnsatisfiable(i2003_11_14_17_20_29215),
inference(cnf_transformation,[],[f16]) ).
fof(f109,definition,
! [X0,X1] :
( sQ11_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ11_eqProxy])],[equality_proxy_definition]) ).
fof(f112,plain,
! [X0,X6,X5] :
( sQ11_eqProxy(X5,X6)
| ~ rtt(X0,X5)
| ~ rtt(X0,X6)
| ~ sP2(X0) ),
inference(equality_proxy_replacement,[],[f74,f109]) ).
fof(f114,plain,
! [X0] :
( ~ sQ11_eqProxy(sK6(X0),sK7(X0))
| ~ sP1(X0) ),
inference(equality_proxy_replacement,[],[f85,f109]) ).
fof(f122,plain,
sP2(i2003_11_14_17_20_29215),
inference(resolution,[],[f94,f98]) ).
fof(f124,plain,
sP1(i2003_11_14_17_20_29215),
inference(resolution,[],[f122,f76]) ).
fof(f126,plain,
rtt(i2003_11_14_17_20_29215,sK7(i2003_11_14_17_20_29215)),
inference(resolution,[],[f87,f124]) ).
fof(f127,plain,
rtt(i2003_11_14_17_20_29215,sK6(i2003_11_14_17_20_29215)),
inference(resolution,[],[f88,f124]) ).
fof(f134,plain,
! [X0,X1] :
( ~ sP2(X0)
| ~ rtt(X0,sK7(X1))
| ~ rtt(X0,sK6(X1))
| ~ sP1(X1) ),
inference(resolution,[],[f112,f114]) ).
fof(f155,plain,
! [X0] :
( ~ sP1(X0)
| ~ rtt(i2003_11_14_17_20_29215,sK6(X0))
| ~ rtt(i2003_11_14_17_20_29215,sK7(X0)) ),
inference(resolution,[],[f134,f122]) ).
fof(f159,plain,
( ~ rtt(i2003_11_14_17_20_29215,sK6(i2003_11_14_17_20_29215))
| ~ rtt(i2003_11_14_17_20_29215,sK7(i2003_11_14_17_20_29215)) ),
inference(resolution,[],[f155,f124]) ).
fof(f161,definition,
( spl12_1
<=> rtt(i2003_11_14_17_20_29215,sK7(i2003_11_14_17_20_29215)) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f162,plain,
( ~ rtt(i2003_11_14_17_20_29215,sK7(i2003_11_14_17_20_29215))
| spl12_1 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,definition,
( spl12_2
<=> rtt(i2003_11_14_17_20_29215,sK6(i2003_11_14_17_20_29215)) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f165,plain,
( ~ rtt(i2003_11_14_17_20_29215,sK6(i2003_11_14_17_20_29215))
| spl12_2 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f166,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f159,f164,f161]) ).
fof(f167,plain,
( $false
| spl12_1 ),
inference(resolution,[],[f162,f126]) ).
fof(f168,plain,
spl12_1,
inference(avatar_contradiction_clause,[],[f167]) ).
fof(f169,plain,
( $false
| spl12_2 ),
inference(resolution,[],[f165,f127]) ).
fof(f170,plain,
spl12_2,
inference(avatar_contradiction_clause,[],[f169]) ).
cnf(s1,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(sat_conversion,[],[f166]) ).
cnf(s2,plain,
spl12_1,
inference(sat_conversion,[],[f168]) ).
cnf(s3,plain,
spl12_2,
inference(sat_conversion,[],[f170]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f171,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS099+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 13:27:32 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 3.64/1.50 % (2648967)Detected formulas, will run a generic FOF schedule.
% 3.64/1.50 % (2648975)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1395040403:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.64/1.50 % (2648975)Refutation not found, incomplete strategy
% 3.64/1.50 % (2648975)------------------------------
% 3.64/1.50 % (2648975)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.50 % (2648975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.50 % (2648975)CaDiCaL version: 2.1.3
% 3.64/1.50 % (2648975)Termination reason: Refutation not found, incomplete strategy
% 3.64/1.50 % (2648975)Time elapsed: 0.0000 s
% 3.64/1.50 % (2648975)Peak memory usage: 86 MB
% 3.64/1.50 % (2648976)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=747778548:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.64/1.50 % (2648974)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=2454762441:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.64/1.50 % (2648973)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=4188358577:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.64/1.50 % (2648978)dis-21_1_sil=8000:lcm=predicate:random_seed=1741044722: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)
% 3.64/1.50 % (2648972)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=313797479:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.64/1.50 % (2648976)Refutation not found, incomplete strategy
% 3.64/1.50 % (2648976)------------------------------
% 3.64/1.50 % (2648976)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.50 % (2648976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.50 % (2648976)CaDiCaL version: 2.1.3
% 3.64/1.50 % (2648976)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (2648976)Time elapsed: 0.0000 s
% 0.17/1.50 % (2648976)Peak memory usage: 86 MB
% 0.17/1.50 % (2648978)First to succeed.
% 0.17/1.50 % (2648978)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2648967"
% 0.17/1.50 % (2648977)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2918071370:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.50 % (2648977)Also succeeded, but the first one will report.
% 0.17/1.50 % (2648975)------------------------------
% 0.17/1.50 % (2648975)------------------------------
% 0.17/1.50 % (2648976)------------------------------
% 0.17/1.50 % (2648976)------------------------------
% 0.17/1.50 % (2648978)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (2648978)------------------------------
% 0.17/1.50 % (2648978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2648978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2648978)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2648978)Termination reason: Refutation
% 0.17/1.50 % (2648978)Time elapsed: 0.004 s
% 0.17/1.50 % (2648978)Peak memory usage: 89 MB
% 0.17/1.50 % (2648978)Instructions burned: 4 (million)
% 0.17/1.50 % (2648978)------------------------------
% 0.17/1.50 % (2648978)------------------------------
% 0.17/1.50 % (2648967)Success in time 0.434 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------