%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS121+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 : n012.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 11:41:42 AM UTC 2026
% Result : Unsatisfiable 2.30s 0.94s
% Output : Refutation 2.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 9 unt; 0 def)
% Number of atoms : 190 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 225 ( 90 ~; 82 |; 43 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 98 ( 82 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rr(X0,X1)
& ca_Vx3(X1) )
& cp1(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f23,axiom,
! [X0] :
( cp1(X0)
<=> ~ ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f24,axiom,
! [X0] :
( cp1xcomp(X0)
<=> ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f25,axiom,
! [X0] :
( ca_Ax2(X0)
<=> ( cp1(X0)
& ! [X1] :
( rinvR(X0,X1)
=> cp1xcomp(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f26,axiom,
! [X0] :
( ca_Vx3(X0)
<=> ? [X1] :
( rr(X0,X1)
& ca_Ax2(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
fof(f29,axiom,
! [X0,X1] :
( rinvR(X0,X1)
<=> rr(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
fof(f30,axiom,
! [X0,X1,X2] :
( ( rr(X0,X1)
& rr(X1,X2) )
=> rr(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
fof(f31,axiom,
cUnsatisfiable(i2003_11_14_17_21_5199),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
fof(f70,plain,
! [X0] :
( cp1(X0)
<=> ! [X1] : ~ ra_Px1(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f71,plain,
! [X0] :
( ca_Ax2(X0)
<=> ( cp1(X0)
& ! [X1] :
( cp1xcomp(X1)
| ~ rinvR(X0,X1) ) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f74,plain,
! [X0,X1,X2] :
( rr(X0,X2)
| ~ rr(X0,X1)
| ~ rr(X1,X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f75,plain,
! [X0,X1,X2] :
( rr(X0,X2)
| ~ rr(X0,X1)
| ~ rr(X1,X2) ),
inference(flattening,[],[f74]) ).
fof(f77,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rr(X0,X1)
| ~ ca_Vx3(X1) )
| ~ cp1(X0) )
& ( ( ? [X1] :
( rr(X0,X1)
& ca_Vx3(X1) )
& cp1(X0) )
| ~ cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f78,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rr(X0,X1)
| ~ ca_Vx3(X1) )
| ~ cp1(X0) )
& ( ( ? [X1] :
( rr(X0,X1)
& ca_Vx3(X1) )
& cp1(X0) )
| ~ cUnsatisfiable(X0) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rr(X0,X1)
| ~ ca_Vx3(X1) )
| ~ cp1(X0) )
& ( ( ? [X2] :
( rr(X0,X2)
& ca_Vx3(X2) )
& cp1(X0) )
| ~ cUnsatisfiable(X0) ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rr(X0,X1)
| ~ ca_Vx3(X1) )
| ~ cp1(X0) )
& ( ( rr(X0,sK0(X0))
& ca_Vx3(sK0(X0))
& cp1(X0) )
| ~ cUnsatisfiable(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0))],[f79]) ).
fof(f81,plain,
! [X0] :
( ( cp1(X0)
| ? [X1] : ra_Px1(X0,X1) )
& ( ! [X1] : ~ ra_Px1(X0,X1)
| ~ cp1(X0) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f82,plain,
! [X0] :
( ( cp1(X0)
| ? [X1] : ra_Px1(X0,X1) )
& ( ! [X2] : ~ ra_Px1(X0,X2)
| ~ cp1(X0) ) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X0] :
( ( cp1(X0)
| ra_Px1(X0,sK1(X0)) )
& ( ! [X2] : ~ ra_Px1(X0,X2)
| ~ cp1(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f82]) ).
fof(f84,plain,
! [X0] :
( ( cp1xcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ? [X1] : ra_Px1(X0,X1)
| ~ cp1xcomp(X0) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f85,plain,
! [X0] :
( ( cp1xcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ? [X2] : ra_Px1(X0,X2)
| ~ cp1xcomp(X0) ) ),
inference(rectify,[],[f84]) ).
fof(f86,plain,
! [X0] :
( ( cp1xcomp(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ra_Px1(X0,sK2(X0))
| ~ cp1xcomp(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0))],[f85]) ).
fof(f87,plain,
! [X0] :
( ( ca_Ax2(X0)
| ~ cp1(X0)
| ? [X1] :
( ~ cp1xcomp(X1)
& rinvR(X0,X1) ) )
& ( ( cp1(X0)
& ! [X1] :
( cp1xcomp(X1)
| ~ rinvR(X0,X1) ) )
| ~ ca_Ax2(X0) ) ),
inference(nnf_transformation,[],[f71]) ).
fof(f88,plain,
! [X0] :
( ( ca_Ax2(X0)
| ~ cp1(X0)
| ? [X1] :
( ~ cp1xcomp(X1)
& rinvR(X0,X1) ) )
& ( ( cp1(X0)
& ! [X1] :
( cp1xcomp(X1)
| ~ rinvR(X0,X1) ) )
| ~ ca_Ax2(X0) ) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0] :
( ( ca_Ax2(X0)
| ~ cp1(X0)
| ? [X1] :
( ~ cp1xcomp(X1)
& rinvR(X0,X1) ) )
& ( ( cp1(X0)
& ! [X2] :
( cp1xcomp(X2)
| ~ rinvR(X0,X2) ) )
| ~ ca_Ax2(X0) ) ),
inference(rectify,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ( ca_Ax2(X0)
| ~ cp1(X0)
| ( ~ cp1xcomp(sK3(X0))
& rinvR(X0,sK3(X0)) ) )
& ( ( cp1(X0)
& ! [X2] :
( cp1xcomp(X2)
| ~ rinvR(X0,X2) ) )
| ~ ca_Ax2(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f89]) ).
fof(f91,plain,
! [X0] :
( ( ca_Vx3(X0)
| ! [X1] :
( ~ rr(X0,X1)
| ~ ca_Ax2(X1) ) )
& ( ? [X1] :
( rr(X0,X1)
& ca_Ax2(X1) )
| ~ ca_Vx3(X0) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f92,plain,
! [X0] :
( ( ca_Vx3(X0)
| ! [X1] :
( ~ rr(X0,X1)
| ~ ca_Ax2(X1) ) )
& ( ? [X2] :
( rr(X0,X2)
& ca_Ax2(X2) )
| ~ ca_Vx3(X0) ) ),
inference(rectify,[],[f91]) ).
fof(f93,plain,
! [X0] :
( ( ca_Vx3(X0)
| ! [X1] :
( ~ rr(X0,X1)
| ~ ca_Ax2(X1) ) )
& ( ( rr(X0,sK4(X0))
& ca_Ax2(sK4(X0)) )
| ~ ca_Vx3(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0))],[f92]) ).
fof(f95,plain,
! [X0,X1] :
( ( rinvR(X0,X1)
| ~ rr(X1,X0) )
& ( rr(X1,X0)
| ~ rinvR(X0,X1) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f119,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| cp1(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f120,plain,
! [X0] :
( ca_Vx3(sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f121,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| rr(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f123,plain,
! [X2,X0] :
( ~ ra_Px1(X0,X2)
| ~ cp1(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f125,plain,
! [X0] :
( ~ cp1xcomp(X0)
| ra_Px1(X0,sK2(X0)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f127,plain,
! [X2,X0] :
( cp1xcomp(X2)
| ~ rinvR(X0,X2)
| ~ ca_Ax2(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f131,plain,
! [X0] :
( ~ ca_Vx3(X0)
| ca_Ax2(sK4(X0)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f132,plain,
! [X0] :
( ~ ca_Vx3(X0)
| rr(X0,sK4(X0)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f138,plain,
! [X0,X1] :
( rinvR(X0,X1)
| ~ rr(X1,X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f139,plain,
! [X2,X0,X1] :
( rr(X0,X2)
| ~ rr(X0,X1)
| ~ rr(X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f140,plain,
cUnsatisfiable(i2003_11_14_17_21_5199),
inference(cnf_transformation,[],[f31]) ).
fof(f165,plain,
cp1(i2003_11_14_17_21_5199),
inference(resolution,[],[f119,f140]) ).
fof(f166,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ca_Ax2(sK4(sK0(X0))) ),
inference(resolution,[],[f131,f120]) ).
fof(f167,plain,
rr(i2003_11_14_17_21_5199,sK0(i2003_11_14_17_21_5199)),
inference(resolution,[],[f121,f140]) ).
fof(f170,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| rr(sK0(X0),sK4(sK0(X0))) ),
inference(resolution,[],[f132,f120]) ).
fof(f173,plain,
! [X0,X1] :
( ~ rinvR(X0,X1)
| ~ ca_Ax2(X0)
| ra_Px1(X1,sK2(X1)) ),
inference(resolution,[],[f127,f125]) ).
fof(f174,plain,
ca_Ax2(sK4(sK0(i2003_11_14_17_21_5199))),
inference(resolution,[],[f166,f140]) ).
fof(f184,plain,
rr(sK0(i2003_11_14_17_21_5199),sK4(sK0(i2003_11_14_17_21_5199))),
inference(resolution,[],[f170,f140]) ).
fof(f194,plain,
! [X0,X1] :
( ra_Px1(X1,sK2(X1))
| ~ ca_Ax2(X0)
| ~ rr(X1,X0) ),
inference(resolution,[],[f173,f138]) ).
fof(f200,plain,
! [X0,X1] :
( ~ ca_Ax2(X0)
| ~ rr(X1,X0)
| ~ cp1(X1) ),
inference(resolution,[],[f194,f123]) ).
fof(f205,plain,
! [X0] :
( ~ cp1(X0)
| ~ rr(X0,sK4(sK0(i2003_11_14_17_21_5199))) ),
inference(resolution,[],[f200,f174]) ).
fof(f213,plain,
~ rr(i2003_11_14_17_21_5199,sK4(sK0(i2003_11_14_17_21_5199))),
inference(resolution,[],[f205,f165]) ).
fof(f220,plain,
! [X0] :
( ~ rr(X0,sK4(sK0(i2003_11_14_17_21_5199)))
| ~ rr(i2003_11_14_17_21_5199,X0) ),
inference(resolution,[],[f213,f139]) ).
fof(f230,plain,
~ rr(i2003_11_14_17_21_5199,sK0(i2003_11_14_17_21_5199)),
inference(resolution,[],[f220,f184]) ).
fof(f234,plain,
$false,
inference(resolution,[],[f230,f167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KRS121+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 % Computer : n012.cluster.edu
% 0.04/0.32 % Model : x86_64 x86_64
% 0.04/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.32 % Memory : 8046.5625MB
% 0.04/0.32 % OS : Linux 6.8.0-71-generic
% 0.04/0.32 % CPULimit : 300
% 0.04/0.32 % WCLimit : 300
% 0.04/0.32 % DateTime : Sun Sep 27 13:26:50 UTC 2026
% 0.06/0.32 % CPUTime :
% 0.06/0.32 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.34 Running first-order theorem proving
% 0.06/0.34 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
% 2.30/0.94 % (2388925)Detected formulas, will run a generic FOF schedule.
% 2.30/0.94 % (2388934)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2335742765:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.30/0.94 % (2388935)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3002581634:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.30/0.94 % (2388931)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=3163022839:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.30/0.94 % (2388936)dis-21_1_sil=8000:lcm=predicate:random_seed=1379206709: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)
% 2.30/0.94 % (2388933)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2999107094:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.30/0.94 % (2388930)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=1621861496:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.30/0.94 % (2388932)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=116966066:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.30/0.94 % (2388934)Refutation not found, incomplete strategy
% 2.30/0.94 % (2388934)------------------------------
% 2.30/0.94 % (2388934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.30/0.94 % (2388934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.94 % (2388933)Refutation not found, incomplete strategy
% 2.30/0.94 % (2388933)------------------------------
% 2.30/0.94 % (2388933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.30/0.94 % (2388934)CaDiCaL version: 2.1.3
% 2.30/0.94 % (2388933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.94 % (2388934)Termination reason: Refutation not found, incomplete strategy
% 2.30/0.94 % (2388934)Time elapsed: 0.0000 s
% 2.30/0.94 % (2388934)Peak memory usage: 85 MB
% 2.30/0.94 % (2388933)CaDiCaL version: 2.1.3
% 2.30/0.94 % (2388933)Termination reason: Refutation not found, incomplete strategy
% 2.30/0.94 % (2388933)Time elapsed: 0.0000 s
% 2.30/0.94 % (2388933)Peak memory usage: 86 MB
% 2.30/0.94 % (2388936)First to succeed.
% 2.30/0.94 % (2388936)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2388925"
% 2.30/0.94 % (2388935)Also succeeded, but the first one will report.
% 2.30/0.94 % (2388934)------------------------------
% 2.30/0.94 % (2388934)------------------------------
% 2.30/0.94 % (2388933)------------------------------
% 2.30/0.94 % (2388933)------------------------------
% 2.30/0.94 % (2388936)Refutation found. Thanks to Tanya!
% 2.30/0.94 % SZS status Unsatisfiable for theBenchmark
% 2.30/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 2.30/0.94 % (2388936)------------------------------
% 2.30/0.94 % (2388936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.30/0.94 % (2388936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.94 % (2388936)CaDiCaL version: 2.1.3
% 2.30/0.94 % (2388936)Termination reason: Refutation
% 2.30/0.94 % (2388936)Time elapsed: 0.002 s
% 2.30/0.94 % (2388936)Peak memory usage: 88 MB
% 2.30/0.94 % (2388936)Instructions burned: 4 (million)
% 2.30/0.94 % (2388936)------------------------------
% 2.30/0.94 % (2388936)------------------------------
% 2.30/0.94 % (2388925)Success in time 0.3 s
% 2.30/0.94 % Vampire exiting
%------------------------------------------------------------------------------