%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS106+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 2.78s 1.15s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 7 unt; 0 def)
% Number of atoms : 183 ( 18 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 212 ( 84 ~; 77 |; 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(f19,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rf3(X0,X1)
& cp2(X1) )
& ? [X1] :
( rf1(X0,X1)
& cp1(X1) )
& ? [X1] :
( rf2(X0,X1)
& cp1xcomp(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f20,axiom,
! [X0] :
( cp1(X0)
<=> ~ ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f21,axiom,
! [X0] :
( cp1xcomp(X0)
<=> ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( rf1(X0,X1)
& rf1(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f23,axiom,
! [X0,X1,X2] :
( ( rf2(X0,X1)
& rf2(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
fof(f25,axiom,
cUnsatisfiable(i2003_11_14_17_20_57644),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
fof(f26,axiom,
! [X0,X1] :
( rf3(X0,X1)
=> rf1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
fof(f27,axiom,
! [X0,X1] :
( rf3(X0,X1)
=> rf2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
fof(f28,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rf3(X0,X1)
& cp2(X1) )
& ? [X2] :
( rf1(X0,X2)
& cp1(X2) )
& ? [X3] :
( rf2(X0,X3)
& cp1xcomp(X3) ) ) ),
inference(rectify,[],[f19]) ).
fof(f61,plain,
! [X0] :
( cp1(X0)
<=> ! [X1] : ~ ra_Px1(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f62,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf1(X0,X1)
| ~ rf1(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f63,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf1(X0,X1)
| ~ rf1(X0,X2) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf2(X0,X1)
| ~ rf2(X0,X2) ),
inference(ennf_transformation,[],[f23]) ).
fof(f65,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf2(X0,X1)
| ~ rf2(X0,X2) ),
inference(flattening,[],[f64]) ).
fof(f68,plain,
! [X0,X1] :
( rf1(X0,X1)
| ~ rf3(X0,X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f69,plain,
! [X0,X1] :
( rf2(X0,X1)
| ~ rf3(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f71,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf3(X0,X1)
| ~ cp2(X1) )
| ! [X2] :
( ~ rf1(X0,X2)
| ~ cp1(X2) )
| ! [X3] :
( ~ rf2(X0,X3)
| ~ cp1xcomp(X3) ) )
& ( ( ? [X1] :
( rf3(X0,X1)
& cp2(X1) )
& ? [X2] :
( rf1(X0,X2)
& cp1(X2) )
& ? [X3] :
( rf2(X0,X3)
& cp1xcomp(X3) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f72,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf3(X0,X1)
| ~ cp2(X1) )
| ! [X2] :
( ~ rf1(X0,X2)
| ~ cp1(X2) )
| ! [X3] :
( ~ rf2(X0,X3)
| ~ cp1xcomp(X3) ) )
& ( ( ? [X1] :
( rf3(X0,X1)
& cp2(X1) )
& ? [X2] :
( rf1(X0,X2)
& cp1(X2) )
& ? [X3] :
( rf2(X0,X3)
& cp1xcomp(X3) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf3(X0,X1)
| ~ cp2(X1) )
| ! [X2] :
( ~ rf1(X0,X2)
| ~ cp1(X2) )
| ! [X3] :
( ~ rf2(X0,X3)
| ~ cp1xcomp(X3) ) )
& ( ( ? [X4] :
( rf3(X0,X4)
& cp2(X4) )
& ? [X5] :
( rf1(X0,X5)
& cp1(X5) )
& ? [X6] :
( rf2(X0,X6)
& cp1xcomp(X6) ) )
| ~ cUnsatisfiable(X0) ) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rf3(X0,X1)
| ~ cp2(X1) )
| ! [X2] :
( ~ rf1(X0,X2)
| ~ cp1(X2) )
| ! [X3] :
( ~ rf2(X0,X3)
| ~ cp1xcomp(X3) ) )
& ( ( rf3(X0,sK0(X0))
& cp2(sK0(X0))
& rf1(X0,sK1(X0))
& cp1(sK1(X0))
& rf2(X0,sK2(X0))
& cp1xcomp(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))],[f73]) ).
fof(f75,plain,
! [X0] :
( ( cp1(X0)
| ? [X1] : ra_Px1(X0,X1) )
& ( ! [X1] : ~ ra_Px1(X0,X1)
| ~ cp1(X0) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f76,plain,
! [X0] :
( ( cp1(X0)
| ? [X1] : ra_Px1(X0,X1) )
& ( ! [X2] : ~ ra_Px1(X0,X2)
| ~ cp1(X0) ) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0] :
( ( cp1(X0)
| ra_Px1(X0,sK3(X0)) )
& ( ! [X2] : ~ ra_Px1(X0,X2)
| ~ cp1(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f76]) ).
fof(f78,plain,
! [X0] :
( ( cp1xcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ? [X1] : ra_Px1(X0,X1)
| ~ cp1xcomp(X0) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f79,plain,
! [X0] :
( ( cp1xcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ? [X2] : ra_Px1(X0,X2)
| ~ cp1xcomp(X0) ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ( cp1xcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ra_Px1(X0,sK4(X0))
| ~ cp1xcomp(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0))],[f79]) ).
fof(f101,plain,
! [X0] :
( cp1xcomp(sK2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f102,plain,
! [X0] :
( rf2(X0,sK2(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f103,plain,
! [X0] :
( cp1(sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f104,plain,
! [X0] :
( rf1(X0,sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f106,plain,
! [X0] :
( rf3(X0,sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f108,plain,
! [X2,X0] :
( ~ ra_Px1(X0,X2)
| ~ cp1(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f110,plain,
! [X0] :
( ra_Px1(X0,sK4(X0))
| ~ cp1xcomp(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ rf1(X0,X1)
| X1 = X2
| ~ rf1(X0,X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ rf2(X0,X1)
| X1 = X2
| ~ rf2(X0,X2) ),
inference(cnf_transformation,[],[f65]) ).
fof(f115,plain,
cUnsatisfiable(i2003_11_14_17_20_57644),
inference(cnf_transformation,[],[f25]) ).
fof(f116,plain,
! [X0,X1] :
( rf1(X0,X1)
| ~ rf3(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f117,plain,
! [X0,X1] :
( rf2(X0,X1)
| ~ rf3(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f134,plain,
! [X0] :
( ~ cp1xcomp(X0)
| ~ cp1(X0) ),
inference(resolution,[],[f110,f108]) ).
fof(f135,plain,
! [X0] :
( ~ cp1(sK2(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f134,f101]) ).
fof(f138,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| ~ rf1(X0,X1)
| sK1(X0) = X1 ),
inference(resolution,[],[f112,f104]) ).
fof(f142,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| ~ rf2(X0,X1)
| sK2(X0) = X1 ),
inference(resolution,[],[f113,f102]) ).
fof(f147,plain,
! [X0] :
( ~ rf1(i2003_11_14_17_20_57644,X0)
| sK1(i2003_11_14_17_20_57644) = X0 ),
inference(resolution,[],[f138,f115]) ).
fof(f151,plain,
! [X0] :
( ~ rf3(i2003_11_14_17_20_57644,X0)
| sK1(i2003_11_14_17_20_57644) = X0 ),
inference(resolution,[],[f147,f116]) ).
fof(f152,plain,
! [X0] :
( ~ rf2(i2003_11_14_17_20_57644,X0)
| sK2(i2003_11_14_17_20_57644) = X0 ),
inference(resolution,[],[f142,f115]) ).
fof(f155,plain,
! [X0] :
( ~ rf3(i2003_11_14_17_20_57644,X0)
| sK2(i2003_11_14_17_20_57644) = X0 ),
inference(resolution,[],[f152,f117]) ).
fof(f157,plain,
( sK1(i2003_11_14_17_20_57644) = sK0(i2003_11_14_17_20_57644)
| ~ cUnsatisfiable(i2003_11_14_17_20_57644) ),
inference(resolution,[],[f151,f106]) ).
fof(f158,plain,
sK1(i2003_11_14_17_20_57644) = sK0(i2003_11_14_17_20_57644),
inference(forward_subsumption_resolution,[],[f157,f115]) ).
fof(f162,plain,
( cp1(sK0(i2003_11_14_17_20_57644))
| ~ cUnsatisfiable(i2003_11_14_17_20_57644) ),
inference(superposition,[],[f103,f158]) ).
fof(f163,plain,
cp1(sK0(i2003_11_14_17_20_57644)),
inference(forward_subsumption_resolution,[],[f162,f115]) ).
fof(f172,plain,
( sK2(i2003_11_14_17_20_57644) = sK0(i2003_11_14_17_20_57644)
| ~ cUnsatisfiable(i2003_11_14_17_20_57644) ),
inference(resolution,[],[f155,f106]) ).
fof(f173,plain,
sK2(i2003_11_14_17_20_57644) = sK0(i2003_11_14_17_20_57644),
inference(forward_subsumption_resolution,[],[f172,f115]) ).
fof(f176,plain,
( ~ cp1(sK0(i2003_11_14_17_20_57644))
| ~ cUnsatisfiable(i2003_11_14_17_20_57644) ),
inference(superposition,[],[f135,f173]) ).
fof(f181,plain,
~ cUnsatisfiable(i2003_11_14_17_20_57644),
inference(forward_subsumption_resolution,[],[f176,f163]) ).
fof(f183,plain,
$false,
inference(forward_subsumption_resolution,[],[f181,f115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS106+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n007.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 13:22:10 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.78/1.15 % (1418523)Detected formulas, will run a generic FOF schedule.
% 2.78/1.15 % (1418529)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=1024943943:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.78/1.15 % (1418528)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=2877128058:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.78/1.15 % (1418531)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2009352267:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.78/1.15 % (1418530)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=2109815671:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.78/1.15 % (1418532)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2481614239:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.78/1.15 % (1418534)dis-21_1_sil=8000:lcm=predicate:random_seed=2442547727: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)
% 2.78/1.15 % (1418533)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2903168267:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.78/1.15 % (1418532)Refutation not found, incomplete strategy
% 2.78/1.15 % (1418532)------------------------------
% 2.78/1.15 % (1418532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.15 % (1418532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.15 % (1418532)CaDiCaL version: 2.1.3
% 2.78/1.15 % (1418532)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.15 % (1418532)Time elapsed: 0.0000 s
% 2.78/1.15 % (1418531)Refutation not found, incomplete strategy
% 2.78/1.15 % (1418531)------------------------------
% 2.78/1.15 % (1418531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.15 % (1418532)Peak memory usage: 85 MB
% 2.78/1.15 % (1418531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.15 % (1418531)CaDiCaL version: 2.1.3
% 2.78/1.15 % (1418531)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.15 % (1418531)Time elapsed: 0.0000 s
% 2.78/1.15 % (1418531)Peak memory usage: 86 MB
% 2.78/1.15 % (1418533)First to succeed.
% 2.78/1.15 % (1418533)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1418523"
% 2.78/1.15 % (1418534)Instruction limit reached!
% 2.78/1.15 % (1418534)------------------------------
% 2.78/1.15 % (1418534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.15 % (1418534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.15 % (1418534)CaDiCaL version: 2.1.3
% 2.78/1.15 % (1418534)Termination reason: Instruction limit
% 2.78/1.15 % (1418534)Termination phase: Saturation
% 2.78/1.15 % (1418534)Time elapsed: 0.044 s
% 2.78/1.15 % (1418534)Peak memory usage: 87 MB
% 2.78/1.15 % (1418534)Instructions burned: 129 (million)
% 2.78/1.15 % (1418533)Refutation found. Thanks to Tanya!
% 2.78/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.78/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/1.15 % (1418533)------------------------------
% 2.78/1.15 % (1418533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.15 % (1418533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.15 % (1418533)CaDiCaL version: 2.1.3
% 2.78/1.15 % (1418533)Termination reason: Refutation
% 2.78/1.15 % (1418533)Time elapsed: 0.004 s
% 2.78/1.15 % (1418533)Peak memory usage: 88 MB
% 2.78/1.15 % (1418533)Instructions burned: 5 (million)
% 2.78/1.15 % (1418533)------------------------------
% 2.78/1.15 % (1418533)------------------------------
% 2.78/1.15 % (1418523)Success in time 0.334 s
% 2.78/1.15 % Vampire exiting
%------------------------------------------------------------------------------