%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS088+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 11:41:37 AM UTC 2026
% Result : Unsatisfiable 3.61s 1.45s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 9 unt; 3 def)
% Number of atoms : 137 ( 9 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 162 ( 70 ~; 61 |; 23 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 58 ( 0 sgn 48 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ? [X1] :
( rf(X0,X1)
& ! [X2] :
( rinvF(X1,X2)
=> ? [X3] :
( rf(X2,X3)
& ~ cp1(X3) ) )
& cp1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f18,axiom,
! [X0,X1,X2] :
( ( rf(X0,X1)
& rf(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f19,axiom,
! [X0,X1] :
( rinvF(X0,X1)
<=> rf(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
fof(f22,axiom,
cUnsatisfiable(i2003_11_14_17_19_49673),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f51,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ? [X1] :
( rf(X0,X1)
& ! [X2] :
( ? [X3] :
( rf(X2,X3)
& ~ cp1(X3) )
| ~ rinvF(X1,X2) )
& cp1(X1) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f52,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf(X0,X1)
| ~ rf(X0,X2) ),
inference(ennf_transformation,[],[f18]) ).
fof(f53,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf(X0,X1)
| ~ rf(X0,X2) ),
inference(flattening,[],[f52]) ).
fof(f57,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf(X0,X1)
| ? [X2] :
( ! [X3] :
( ~ rf(X2,X3)
| cp1(X3) )
& rinvF(X1,X2) )
| ~ cp1(X1) ) )
& ( ? [X1] :
( rf(X0,X1)
& ! [X2] :
( ? [X3] :
( rf(X2,X3)
& ~ cp1(X3) )
| ~ rinvF(X1,X2) )
& cp1(X1) )
| ~ cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f58,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf(X0,X1)
| ? [X2] :
( ! [X3] :
( ~ rf(X2,X3)
| cp1(X3) )
& rinvF(X1,X2) )
| ~ cp1(X1) ) )
& ( ? [X4] :
( rf(X0,X4)
& ! [X5] :
( ? [X6] :
( rf(X5,X6)
& ~ cp1(X6) )
| ~ rinvF(X4,X5) )
& cp1(X4) )
| ~ cUnsatisfiable(X0) ) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf(X0,X1)
| ( ! [X3] :
( ~ rf(sK0(X1),X3)
| cp1(X3) )
& rinvF(X1,sK0(X1)) )
| ~ cp1(X1) ) )
& ( ( rf(X0,sK1(X0))
& ! [X5] :
( ( rf(X5,sK2(X5))
& ~ cp1(sK2(X5)) )
| ~ rinvF(sK1(X0),X5) )
& cp1(sK1(X0)) )
| ~ cUnsatisfiable(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X1)),skolemize(X4,sK1(X0)),skolemize(X6,sK2(X5))],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( ( rinvF(X0,X1)
| ~ rf(X1,X0) )
& ( rf(X1,X0)
| ~ rinvF(X0,X1) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f80,plain,
! [X0] :
( cp1(sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f81,plain,
! [X0,X5] :
( ~ cp1(sK2(X5))
| ~ rinvF(sK1(X0),X5)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f82,plain,
! [X0,X5] :
( rf(X5,sK2(X5))
| ~ rinvF(sK1(X0),X5)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f83,plain,
! [X0] :
( rf(X0,sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f86,plain,
! [X2,X0,X1] :
( ~ rf(X0,X1)
| X1 = X2
| ~ rf(X0,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f88,plain,
! [X0,X1] :
( rinvF(X0,X1)
| ~ rf(X1,X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f92,plain,
cUnsatisfiable(i2003_11_14_17_19_49673),
inference(cnf_transformation,[],[f22]) ).
fof(f108,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| ~ rf(X0,X1)
| sK1(X0) = X1 ),
inference(resolution,[],[f86,f83]) ).
fof(f110,plain,
! [X0] :
( ~ rf(i2003_11_14_17_19_49673,X0)
| sK1(i2003_11_14_17_19_49673) = X0 ),
inference(resolution,[],[f108,f92]) ).
fof(f113,plain,
! [X0] :
( sK1(i2003_11_14_17_19_49673) = sK2(i2003_11_14_17_19_49673)
| ~ rinvF(sK1(X0),i2003_11_14_17_19_49673)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f110,f82]) ).
fof(f115,definition,
( spl3_1
<=> ! [X0] :
( ~ rinvF(sK1(X0),i2003_11_14_17_19_49673)
| ~ cUnsatisfiable(X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f116,plain,
( ! [X0] :
( ~ rinvF(sK1(X0),i2003_11_14_17_19_49673)
| ~ cUnsatisfiable(X0) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,definition,
( spl3_2
<=> sK1(i2003_11_14_17_19_49673) = sK2(i2003_11_14_17_19_49673) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f120,plain,
( sK1(i2003_11_14_17_19_49673) = sK2(i2003_11_14_17_19_49673)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f113,f118,f115]) ).
fof(f124,plain,
( ! [X0] :
( ~ cp1(sK1(i2003_11_14_17_19_49673))
| ~ rinvF(sK1(X0),i2003_11_14_17_19_49673)
| ~ cUnsatisfiable(X0) )
| ~ spl3_2 ),
inference(superposition,[],[f81,f120]) ).
fof(f126,definition,
( spl3_3
<=> cp1(sK1(i2003_11_14_17_19_49673)) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f128,plain,
( ~ cp1(sK1(i2003_11_14_17_19_49673))
| spl3_3 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl3_1
| ~ spl3_3
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f124,f118,f126,f115]) ).
fof(f136,plain,
( ! [X0] :
( ~ rf(i2003_11_14_17_19_49673,sK1(X0))
| ~ cUnsatisfiable(X0) )
| ~ spl3_1 ),
inference(resolution,[],[f116,f88]) ).
fof(f138,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_49673)
| ~ cUnsatisfiable(i2003_11_14_17_19_49673)
| ~ spl3_1 ),
inference(resolution,[],[f136,f83]) ).
fof(f139,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_49673)
| ~ spl3_1 ),
inference(duplicate_literal_removal,[],[f138]) ).
fof(f140,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f139,f92]) ).
fof(f141,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f140]) ).
fof(f143,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_49673)
| spl3_3 ),
inference(resolution,[],[f128,f80]) ).
fof(f145,plain,
( $false
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f143,f92]) ).
fof(f146,plain,
spl3_3,
inference(avatar_contradiction_clause,[],[f145]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f121]) ).
cnf(s2,plain,
( spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f129]) ).
cnf(s4,plain,
~ spl3_1,
inference(sat_conversion,[],[f141]) ).
cnf(s5,plain,
spl3_3,
inference(sat_conversion,[],[f146]) ).
cnf(s7,plain,
~ spl3_2,
inference(rat,[],[s2,s5,s4]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s4]) ).
fof(f147,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS088+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 : n020.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 13:22:49 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
% 3.61/1.45 % (3380795)Detected formulas, will run a generic FOF schedule.
% 3.61/1.45 % (3380803)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1986674089:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.61/1.45 % (3380803)Refutation not found, incomplete strategy
% 3.61/1.45 % (3380803)------------------------------
% 3.61/1.45 % (3380803)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.45 % (3380803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.45 % (3380803)CaDiCaL version: 2.1.3
% 3.61/1.45 % (3380803)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.45 % (3380803)Time elapsed: 0.0000 s
% 3.61/1.45 % (3380803)Peak memory usage: 86 MB
% 3.61/1.45 % (3380800)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=2786011590:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.61/1.45 % (3380804)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3237761591:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.61/1.45 % (3380802)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=839773909:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.61/1.45 % (3380805)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2067313720:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.61/1.45 % (3380801)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=1711730564:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.61/1.45 % (3380806)dis-21_1_sil=8000:lcm=predicate:random_seed=3094631247: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)
% 3.61/1.45 % (3380804)Refutation not found, incomplete strategy
% 3.61/1.45 % (3380804)------------------------------
% 3.61/1.45 % (3380804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.45 % (3380804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.45 % (3380804)CaDiCaL version: 2.1.3
% 3.61/1.45 % (3380804)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.45 % (3380804)Time elapsed: 0.001 s
% 3.61/1.45 % (3380804)Peak memory usage: 86 MB
% 3.61/1.45 % (3380805)First to succeed.
% 3.61/1.45 % (3380805)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3380795"
% 3.61/1.45 % (3380806)Instruction limit reached!
% 3.61/1.45 % (3380806)------------------------------
% 3.61/1.45 % (3380806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.45 % (3380806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.45 % (3380806)CaDiCaL version: 2.1.3
% 3.61/1.45 % (3380806)Termination reason: Instruction limit
% 3.61/1.45 % (3380806)Termination phase: Saturation
% 3.61/1.45 % (3380806)Time elapsed: 0.056 s
% 3.61/1.45 % (3380806)Peak memory usage: 88 MB
% 3.61/1.45 % (3380806)Instructions burned: 132 (million)
% 3.61/1.45 % (3380803)------------------------------
% 3.61/1.45 % (3380803)------------------------------
% 3.61/1.45 % (3380814)lrs+10_1_sil=8000:sp=occurrence:random_seed=2320872354:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.61/1.45 % (3380814)Refutation not found, incomplete strategy
% 3.61/1.45 % (3380814)------------------------------
% 3.61/1.45 % (3380814)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.45 % (3380814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.45 % (3380814)CaDiCaL version: 2.1.3
% 3.61/1.45 % (3380814)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.45 % (3380814)Time elapsed: 0.001 s
% 3.61/1.45 % (3380814)Peak memory usage: 86 MB
% 3.61/1.45 % (3380804)------------------------------
% 3.61/1.45 % (3380804)------------------------------
% 3.61/1.45 % (3380815)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3366036350:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.61/1.45 % (3380815)Refutation not found, incomplete strategy
% 3.61/1.45 % (3380815)------------------------------
% 3.61/1.45 % (3380815)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.45 % (3380815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.45 % (3380815)CaDiCaL version: 2.1.3
% 3.61/1.45 % (3380815)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.45 % (3380815)Time elapsed: 0.0000 s
% 3.61/1.45 % (3380815)Peak memory usage: 87 MB
% 3.61/1.45 % (3380805)Refutation found. Thanks to Tanya!
% 3.61/1.45 % SZS status Unsatisfiable for theBenchmark
% 3.61/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.45 % (3380805)------------------------------
% 3.61/1.45 % (3380805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.45 % (3380805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.45 % (3380805)CaDiCaL version: 2.1.3
% 3.61/1.45 % (3380805)Termination reason: Refutation
% 3.61/1.45 % (3380805)Time elapsed: 0.004 s
% 3.61/1.45 % (3380805)Peak memory usage: 89 MB
% 3.61/1.45 % (3380805)Instructions burned: 3 (million)
% 3.61/1.45 % (3380805)------------------------------
% 3.61/1.45 % (3380805)------------------------------
% 3.61/1.45 % (3380795)Success in time 0.426 s
% 3.61/1.45 % Vampire exiting
%------------------------------------------------------------------------------