%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KRS107+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 11:42:17 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.44s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 11 unt; 1 def)
% Number of atoms : 219 ( 8 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 251 ( 100 ~; 93 |; 47 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 103 ( 0 sgn 84 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rrx3(X0,X1)
& cc1(X1) )
& ? [X1] :
( rrx4(X0,X1)
& cc2(X1) )
& ca_Cx1(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f36,axiom,
! [X0] :
( ca_Ax2(X0)
<=> ( cc2(X0)
& cc1(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f37,axiom,
! [X0] :
( ca_Cx1(X0)
<=> ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f38,axiom,
! [X0] :
( ca_Cx1xcomp(X0)
<=> ? [X1] :
( rrx3(X0,X1)
& ca_Ax2(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f39,axiom,
! [X0] :
( ca_Cx1xcomp(X0)
<=> ~ ? [X1] : ra_Px1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( rrx(X0,X1)
& rrx(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
fof(f45,axiom,
cUnsatisfiable(i2003_11_14_17_21_01226),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).
fof(f50,axiom,
! [X0,X1] :
( rrx4(X0,X1)
=> rrx(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).
fof(f53,axiom,
! [X0,X1] :
( rrx3(X0,X1)
=> rrx(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
fof(f54,plain,
! [X0] :
( cUnsatisfiable(X0)
<=> ( ? [X1] :
( rrx3(X0,X1)
& cc1(X1) )
& ? [X2] :
( rrx4(X0,X2)
& cc2(X2) )
& ca_Cx1(X0) ) ),
inference(rectify,[],[f35]) ).
fof(f119,plain,
! [X0] :
( ca_Cx1xcomp(X0)
<=> ! [X1] : ~ ra_Px1(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f120,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rrx(X0,X1)
| ~ rrx(X0,X2) ),
inference(ennf_transformation,[],[f40]) ).
fof(f121,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rrx(X0,X1)
| ~ rrx(X0,X2) ),
inference(flattening,[],[f120]) ).
fof(f134,plain,
! [X0,X1] :
( rrx(X0,X1)
| ~ rrx4(X0,X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f137,plain,
! [X0,X1] :
( rrx(X0,X1)
| ~ rrx3(X0,X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f139,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rrx3(X0,X1)
| ~ cc1(X1) )
| ! [X2] :
( ~ rrx4(X0,X2)
| ~ cc2(X2) )
| ~ ca_Cx1(X0) )
& ( ( ? [X1] :
( rrx3(X0,X1)
& cc1(X1) )
& ? [X2] :
( rrx4(X0,X2)
& cc2(X2) )
& ca_Cx1(X0) )
| ~ cUnsatisfiable(X0) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f140,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rrx3(X0,X1)
| ~ cc1(X1) )
| ! [X2] :
( ~ rrx4(X0,X2)
| ~ cc2(X2) )
| ~ ca_Cx1(X0) )
& ( ( ? [X1] :
( rrx3(X0,X1)
& cc1(X1) )
& ? [X2] :
( rrx4(X0,X2)
& cc2(X2) )
& ca_Cx1(X0) )
| ~ cUnsatisfiable(X0) ) ),
inference(flattening,[],[f139]) ).
fof(f141,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rrx3(X0,X1)
| ~ cc1(X1) )
| ! [X2] :
( ~ rrx4(X0,X2)
| ~ cc2(X2) )
| ~ ca_Cx1(X0) )
& ( ( ? [X3] :
( rrx3(X0,X3)
& cc1(X3) )
& ? [X4] :
( rrx4(X0,X4)
& cc2(X4) )
& ca_Cx1(X0) )
| ~ cUnsatisfiable(X0) ) ),
inference(rectify,[],[f140]) ).
fof(f142,plain,
! [X0] :
( ( cUnsatisfiable(X0)
| ! [X1] :
( ~ rrx3(X0,X1)
| ~ cc1(X1) )
| ! [X2] :
( ~ rrx4(X0,X2)
| ~ cc2(X2) )
| ~ ca_Cx1(X0) )
& ( ( rrx3(X0,sK0(X0))
& cc1(sK0(X0))
& rrx4(X0,sK1(X0))
& cc2(sK1(X0))
& ca_Cx1(X0) )
| ~ cUnsatisfiable(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0)),skolemize(X4,sK1(X0))],[f141]) ).
fof(f143,plain,
! [X0] :
( ( ca_Ax2(X0)
| ~ cc2(X0)
| ~ cc1(X0) )
& ( ( cc2(X0)
& cc1(X0) )
| ~ ca_Ax2(X0) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f144,plain,
! [X0] :
( ( ca_Ax2(X0)
| ~ cc2(X0)
| ~ cc1(X0) )
& ( ( cc2(X0)
& cc1(X0) )
| ~ ca_Ax2(X0) ) ),
inference(flattening,[],[f143]) ).
fof(f145,plain,
! [X0] :
( ( ca_Cx1(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ? [X1] : ra_Px1(X0,X1)
| ~ ca_Cx1(X0) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f146,plain,
! [X0] :
( ( ca_Cx1(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ? [X2] : ra_Px1(X0,X2)
| ~ ca_Cx1(X0) ) ),
inference(rectify,[],[f145]) ).
fof(f147,plain,
! [X0] :
( ( ca_Cx1(X0)
| ! [X1] : ~ ra_Px1(X0,X1) )
& ( ra_Px1(X0,sK2(X0))
| ~ ca_Cx1(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0))],[f146]) ).
fof(f148,plain,
! [X0] :
( ( ca_Cx1xcomp(X0)
| ! [X1] :
( ~ rrx3(X0,X1)
| ~ ca_Ax2(X1) ) )
& ( ? [X1] :
( rrx3(X0,X1)
& ca_Ax2(X1) )
| ~ ca_Cx1xcomp(X0) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f149,plain,
! [X0] :
( ( ca_Cx1xcomp(X0)
| ! [X1] :
( ~ rrx3(X0,X1)
| ~ ca_Ax2(X1) ) )
& ( ? [X2] :
( rrx3(X0,X2)
& ca_Ax2(X2) )
| ~ ca_Cx1xcomp(X0) ) ),
inference(rectify,[],[f148]) ).
fof(f150,plain,
! [X0] :
( ( ca_Cx1xcomp(X0)
| ! [X1] :
( ~ rrx3(X0,X1)
| ~ ca_Ax2(X1) ) )
& ( ( rrx3(X0,sK3(X0))
& ca_Ax2(sK3(X0)) )
| ~ ca_Cx1xcomp(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0))],[f149]) ).
fof(f151,plain,
! [X0] :
( ( ca_Cx1xcomp(X0)
| ? [X1] : ra_Px1(X0,X1) )
& ( ! [X1] : ~ ra_Px1(X0,X1)
| ~ ca_Cx1xcomp(X0) ) ),
inference(nnf_transformation,[],[f119]) ).
fof(f152,plain,
! [X0] :
( ( ca_Cx1xcomp(X0)
| ? [X1] : ra_Px1(X0,X1) )
& ( ! [X2] : ~ ra_Px1(X0,X2)
| ~ ca_Cx1xcomp(X0) ) ),
inference(rectify,[],[f151]) ).
fof(f153,plain,
! [X0] :
( ( ca_Cx1xcomp(X0)
| ra_Px1(X0,sK4(X0)) )
& ( ! [X2] : ~ ra_Px1(X0,X2)
| ~ ca_Cx1xcomp(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f152]) ).
fof(f190,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ca_Cx1(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f191,plain,
! [X0] :
( cc2(sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f192,plain,
! [X0] :
( rrx4(X0,sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f193,plain,
! [X0] :
( cc1(sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f194,plain,
! [X0] :
( rrx3(X0,sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f198,plain,
! [X0] :
( ~ cc2(X0)
| ca_Ax2(X0)
| ~ cc1(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f199,plain,
! [X0] :
( ra_Px1(X0,sK2(X0))
| ~ ca_Cx1(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f203,plain,
! [X0,X1] :
( ~ rrx3(X0,X1)
| ca_Cx1xcomp(X0)
| ~ ca_Ax2(X1) ),
inference(cnf_transformation,[],[f150]) ).
fof(f204,plain,
! [X2,X0] :
( ~ ra_Px1(X0,X2)
| ~ ca_Cx1xcomp(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f206,plain,
! [X2,X0,X1] :
( ~ rrx(X0,X2)
| ~ rrx(X0,X1)
| X1 = X2 ),
inference(cnf_transformation,[],[f121]) ).
fof(f211,plain,
cUnsatisfiable(i2003_11_14_17_21_01226),
inference(cnf_transformation,[],[f45]) ).
fof(f216,plain,
! [X0,X1] :
( ~ rrx4(X0,X1)
| rrx(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f219,plain,
! [X0,X1] :
( ~ rrx3(X0,X1)
| rrx(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f253,plain,
ca_Cx1(i2003_11_14_17_21_01226),
inference(resolution,[],[f190,f211]) ).
fof(f256,plain,
! [X0] :
( ~ cc1(sK1(X0))
| ca_Ax2(sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f198,f191]) ).
fof(f258,plain,
! [X0] :
( ~ ca_Cx1xcomp(X0)
| ~ ca_Cx1(X0) ),
inference(resolution,[],[f199,f204]) ).
fof(f266,plain,
! [X0] :
( rrx(X0,sK1(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f216,f192]) ).
fof(f267,plain,
! [X0] :
( rrx(X0,sK0(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f219,f194]) ).
fof(f269,plain,
! [X0] :
( ~ ca_Ax2(sK0(X0))
| ca_Cx1xcomp(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f203,f194]) ).
fof(f273,plain,
! [X0,X1] :
( ~ rrx(X0,X1)
| ~ cUnsatisfiable(X0)
| sK1(X0) = X1 ),
inference(resolution,[],[f266,f206]) ).
fof(f287,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sK0(X0) = sK1(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[],[f273,f267]) ).
fof(f289,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sK0(X0) = sK1(X0) ),
inference(duplicate_literal_removal,[],[f287]) ).
fof(f296,plain,
sK0(i2003_11_14_17_21_01226) = sK1(i2003_11_14_17_21_01226),
inference(resolution,[],[f289,f211]) ).
fof(f301,plain,
( ~ cc1(sK0(i2003_11_14_17_21_01226))
| ca_Ax2(sK0(i2003_11_14_17_21_01226))
| ~ cUnsatisfiable(i2003_11_14_17_21_01226) ),
inference(superposition,[],[f256,f296]) ).
fof(f309,plain,
( ca_Ax2(sK0(i2003_11_14_17_21_01226))
| ~ cUnsatisfiable(i2003_11_14_17_21_01226) ),
inference(forward_subsumption_resolution,[],[f301,f193]) ).
fof(f310,plain,
ca_Ax2(sK0(i2003_11_14_17_21_01226)),
inference(forward_subsumption_resolution,[],[f309,f211]) ).
fof(f318,definition,
( spl5_2
<=> ca_Ax2(sK0(i2003_11_14_17_21_01226)) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f320,plain,
( ca_Ax2(sK0(i2003_11_14_17_21_01226))
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f322,plain,
spl5_2,
inference(avatar_split_clause,[],[f310,f318]) ).
fof(f327,plain,
( ca_Cx1xcomp(i2003_11_14_17_21_01226)
| ~ cUnsatisfiable(i2003_11_14_17_21_01226)
| ~ spl5_2 ),
inference(resolution,[],[f320,f269]) ).
fof(f330,plain,
( ca_Cx1xcomp(i2003_11_14_17_21_01226)
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f327,f211]) ).
fof(f333,plain,
( ~ ca_Cx1(i2003_11_14_17_21_01226)
| ~ spl5_2 ),
inference(resolution,[],[f330,f258]) ).
fof(f334,plain,
( $false
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f333,f253]) ).
fof(f335,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f334]) ).
cnf(s2,plain,
spl5_2,
inference(sat_conversion,[],[f322]) ).
cnf(s4,plain,
~ spl5_2,
inference(sat_conversion,[],[f335]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4]) ).
fof(f339,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS107+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n007.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 13:21:55 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.44 % (1418107)Will run a generic schedule for satisfiability detection.
% 0.11/0.44 % (1418112)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2546800599_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.44 % TRYING [1]
% 0.11/0.44 % TRYING [2]
% 0.11/0.44 % TRYING [3]
% 0.11/0.44 % TRYING [4]
% 0.11/0.44 % TRYING [5]
% 0.11/0.44 % TRYING [6]
% 0.11/0.44 % TRYING [7]
% 0.11/0.44 % TRYING [8]
% 0.11/0.44 % TRYING [9]
% 0.11/0.44 % TRYING [10]
% 0.11/0.44 % TRYING [11]
% 0.11/0.44 % TRYING [12]
% 0.11/0.44 % TRYING [13]
% 0.11/0.44 % TRYING [14]
% 0.11/0.44 % (1418114)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=560700730:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.44 % (1418113)% WARNING: option uhcvi not known.
% 0.11/0.44 % TRYING [15]
% 0.11/0.44 % (1418115)dis+10_1_sil=32000:sp=arity:random_seed=3946356404:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.44 % (1418116)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2666833283:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.44 % (1418117)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1709364901:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.44 % (1418118)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2445041878:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.44 % TRYING [16]
% 0.11/0.44 % TRYING [17]
% 0.11/0.44 % TRYING [18]
% 0.11/0.44 % (1418115) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1418107-1418115"...
% 0.11/0.44 % (1418118) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1418107-1418118"...
% 0.11/0.44 % (1418113)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4090121487:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.44 % TRYING [19]
% 0.11/0.44 % (1418116) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1418107-1418116"...
% 0.11/0.44 % (1418117) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1418107-1418117"...
% 0.11/0.44 % (1418115)...printing done.
% 0.11/0.44 % TRYING [20]
% 0.11/0.44 % (1418118)...printing done.
% 0.11/0.44 % (1418116)...printing done.
% 0.11/0.44 % (1418117)...printing done.
% 0.11/0.44 % (1418115)Refutation found. Thanks to Tanya!
% 0.11/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (1418115)------------------------------
% 0.11/0.45 % (1418115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (1418115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (1418115)CaDiCaL version: 2.1.3
% 0.11/0.45 % (1418115)Termination reason: Refutation
% 0.11/0.45 % (1418115)Time elapsed: 0.005 s
% 0.11/0.45 % (1418115)Peak memory usage: 12 MB
% 0.11/0.45 % (1418115)Instructions burned: 6 (million)
% 0.11/0.45 % (1418107)Success in time 0.038 s
% 0.11/0.45 % Vampire exiting
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