%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM017+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 09:40:09 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 15 unt; 2 def)
% Number of atoms : 254 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 280 ( 91 ~; 158 |; 22 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 104 ( 0 sgn 99 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aRewritingSystem0(X1) )
=> ! [X2] :
( aReductOfIn0(X2,X0,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mReduct) ).
fof(f11,axiom,
! [X0] :
( aRewritingSystem0(X0)
=> ( isLocallyConfluent0(X0)
<=> ! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3)
& aReductOfIn0(X2,X1,X0)
& aReductOfIn0(X3,X1,X0) )
=> ? [X4] :
( aElement0(X4)
& sdtmndtasgtdt0(X2,X0,X4)
& sdtmndtasgtdt0(X3,X0,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mWCRDef) ).
fof(f15,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
fof(f16,axiom,
( isLocallyConfluent0(xR)
& isTerminating0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656_01) ).
fof(f17,axiom,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731) ).
fof(f20,axiom,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& sdtmndtasgtdt0(xu,xR,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__755) ).
fof(f21,axiom,
( aElement0(xv)
& aReductOfIn0(xv,xa,xR)
& sdtmndtasgtdt0(xv,xR,xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__779) ).
fof(f22,conjecture,
? [X0] :
( aElement0(X0)
& sdtmndtasgtdt0(xu,xR,X0)
& sdtmndtasgtdt0(xv,xR,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f23,negated_conjecture,
~ ? [X0] :
( aElement0(X0)
& sdtmndtasgtdt0(xu,xR,X0)
& sdtmndtasgtdt0(xv,xR,X0) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f26,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f27,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(flattening,[],[f26]) ).
fof(f42,plain,
! [X0] :
( ( isLocallyConfluent0(X0)
<=> ! [X1,X2,X3] :
( ? [X4] :
( aElement0(X4)
& sdtmndtasgtdt0(X2,X0,X4)
& sdtmndtasgtdt0(X3,X0,X4) )
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aReductOfIn0(X3,X1,X0) ) )
| ~ aRewritingSystem0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f43,plain,
! [X0] :
( ( isLocallyConfluent0(X0)
<=> ! [X1,X2,X3] :
( ? [X4] :
( aElement0(X4)
& sdtmndtasgtdt0(X2,X0,X4)
& sdtmndtasgtdt0(X3,X0,X4) )
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aReductOfIn0(X3,X1,X0) ) )
| ~ aRewritingSystem0(X0) ),
inference(flattening,[],[f42]) ).
fof(f52,plain,
! [X0] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| ~ sdtmndtasgtdt0(xv,xR,X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f74,plain,
! [X2,X3,X0,X1] :
( ~ aRewritingSystem0(X0)
| ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| sdtmndtasgtdt0(X3,X0,sK8(X0,X2,X3))
| ~ isLocallyConfluent0(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( ~ aRewritingSystem0(X0)
| ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| sdtmndtasgtdt0(X2,X0,sK8(X0,X2,X3))
| ~ isLocallyConfluent0(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( ~ aRewritingSystem0(X0)
| ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sK8(X0,X2,X3))
| ~ isLocallyConfluent0(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f92,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f94,plain,
isLocallyConfluent0(xR),
inference(cnf_transformation,[],[f16]) ).
fof(f97,plain,
aElement0(xa),
inference(cnf_transformation,[],[f17]) ).
fof(f104,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f20]) ).
fof(f107,plain,
aReductOfIn0(xv,xa,xR),
inference(cnf_transformation,[],[f21]) ).
fof(f109,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xv,xR,X0)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| aElement0(X0)
| aReductOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1) ),
inference(consistent_polarity_flipping,[],[f53]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( ~ aRewritingSystem0(X0)
| aReductOfIn0(X3,X1,X0)
| aReductOfIn0(X2,X1,X0)
| aElement0(X3)
| aElement0(X2)
| aElement0(X1)
| ~ aElement0(sK8(X0,X2,X3))
| isLocallyConfluent0(X0) ),
inference(consistent_polarity_flipping,[],[f76]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( ~ aRewritingSystem0(X0)
| aReductOfIn0(X3,X1,X0)
| aReductOfIn0(X2,X1,X0)
| aElement0(X3)
| aElement0(X2)
| aElement0(X1)
| ~ sdtmndtasgtdt0(X2,X0,sK8(X0,X2,X3))
| isLocallyConfluent0(X0) ),
inference(consistent_polarity_flipping,[],[f75]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( ~ aRewritingSystem0(X0)
| aReductOfIn0(X3,X1,X0)
| aReductOfIn0(X2,X1,X0)
| aElement0(X3)
| aElement0(X2)
| aElement0(X1)
| ~ sdtmndtasgtdt0(X3,X0,sK8(X0,X2,X3))
| isLocallyConfluent0(X0) ),
inference(consistent_polarity_flipping,[],[f74]) ).
fof(f150,plain,
~ isLocallyConfluent0(xR),
inference(consistent_polarity_flipping,[],[f94]) ).
fof(f152,plain,
~ aElement0(xa),
inference(consistent_polarity_flipping,[],[f97]) ).
fof(f159,plain,
~ aReductOfIn0(xu,xa,xR),
inference(consistent_polarity_flipping,[],[f104]) ).
fof(f162,plain,
~ aReductOfIn0(xv,xa,xR),
inference(consistent_polarity_flipping,[],[f107]) ).
fof(f164,plain,
! [X0] :
( sdtmndtasgtdt0(xv,xR,X0)
| sdtmndtasgtdt0(xu,xR,X0)
| aElement0(X0) ),
inference(consistent_polarity_flipping,[],[f109]) ).
fof(f221,plain,
! [X2,X3,X0,X1] :
( ~ aRewritingSystem0(X0)
| aReductOfIn0(X3,X1,X0)
| aReductOfIn0(X2,X1,X0)
| aElement0(X2)
| aElement0(X1)
| ~ aElement0(sK8(X0,X2,X3))
| isLocallyConfluent0(X0) ),
inference(forward_subsumption_resolution,[],[f136,f111]) ).
fof(f222,plain,
! [X2,X3,X0,X1] :
( ~ aElement0(sK8(X0,X2,X3))
| aReductOfIn0(X3,X1,X0)
| aReductOfIn0(X2,X1,X0)
| aElement0(X1)
| ~ aRewritingSystem0(X0)
| isLocallyConfluent0(X0) ),
inference(forward_subsumption_resolution,[],[f221,f111]) ).
fof(f251,plain,
! [X2,X3,X0,X1] :
( ~ aRewritingSystem0(X0)
| aReductOfIn0(X3,X1,X0)
| aReductOfIn0(X2,X1,X0)
| aElement0(X2)
| aElement0(X1)
| ~ sdtmndtasgtdt0(X2,X0,sK8(X0,X2,X3))
| isLocallyConfluent0(X0) ),
inference(forward_subsumption_resolution,[],[f137,f111]) ).
fof(f252,plain,
! [X2,X3,X0,X1] :
( ~ aRewritingSystem0(X0)
| aReductOfIn0(X3,X1,X0)
| aReductOfIn0(X2,X1,X0)
| aElement0(X1)
| ~ sdtmndtasgtdt0(X2,X0,sK8(X0,X2,X3))
| isLocallyConfluent0(X0) ),
inference(forward_subsumption_resolution,[],[f251,f111]) ).
fof(f253,plain,
! [X2,X0,X1] :
( aReductOfIn0(X0,X1,xR)
| aReductOfIn0(X2,X1,xR)
| aElement0(X1)
| ~ sdtmndtasgtdt0(X2,xR,sK8(xR,X2,X0))
| isLocallyConfluent0(xR) ),
inference(resolution,[],[f252,f92]) ).
fof(f254,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X2,xR,sK8(xR,X2,X0))
| aReductOfIn0(X2,X1,xR)
| aElement0(X1)
| aReductOfIn0(X0,X1,xR) ),
inference(forward_subsumption_resolution,[],[f253,f150]) ).
fof(f255,plain,
! [X2,X3,X0,X1] :
( ~ aRewritingSystem0(X0)
| aReductOfIn0(X3,X1,X0)
| aReductOfIn0(X2,X1,X0)
| aElement0(X2)
| aElement0(X1)
| ~ sdtmndtasgtdt0(X3,X0,sK8(X0,X2,X3))
| isLocallyConfluent0(X0) ),
inference(forward_subsumption_resolution,[],[f138,f111]) ).
fof(f256,plain,
! [X2,X3,X0,X1] :
( ~ aRewritingSystem0(X0)
| aReductOfIn0(X3,X1,X0)
| aReductOfIn0(X2,X1,X0)
| aElement0(X1)
| ~ sdtmndtasgtdt0(X3,X0,sK8(X0,X2,X3))
| isLocallyConfluent0(X0) ),
inference(forward_subsumption_resolution,[],[f255,f111]) ).
fof(f257,plain,
! [X2,X0,X1] :
( aReductOfIn0(X0,X1,xR)
| aReductOfIn0(X2,X1,xR)
| aElement0(X1)
| ~ sdtmndtasgtdt0(X0,xR,sK8(xR,X2,X0))
| isLocallyConfluent0(xR) ),
inference(resolution,[],[f256,f92]) ).
fof(f258,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,xR,sK8(xR,X2,X0))
| aReductOfIn0(X2,X1,xR)
| aElement0(X1)
| aReductOfIn0(X0,X1,xR) ),
inference(forward_subsumption_resolution,[],[f257,f150]) ).
fof(f373,plain,
! [X0,X1] :
( aReductOfIn0(xv,X0,xR)
| aReductOfIn0(X1,X0,xR)
| sdtmndtasgtdt0(xu,xR,sK8(xR,xv,X1))
| aElement0(X0)
| aElement0(sK8(xR,xv,X1)) ),
inference(resolution,[],[f254,f164]) ).
fof(f533,plain,
! [X0,X1] :
( aReductOfIn0(xv,X0,xR)
| aReductOfIn0(xu,X0,xR)
| aElement0(X0)
| aElement0(sK8(xR,xv,xu))
| aReductOfIn0(xv,X1,xR)
| aElement0(X1)
| aReductOfIn0(xu,X1,xR) ),
inference(resolution,[],[f373,f258]) ).
fof(f553,definition,
( spl14_30
<=> ! [X1] :
( aReductOfIn0(xv,X1,xR)
| aReductOfIn0(xu,X1,xR)
| aElement0(X1) ) ),
introduced(definition,[new_symbols(definition,[spl14_30])],[avatar_definition]) ).
fof(f554,plain,
( ! [X1] :
( aReductOfIn0(xv,X1,xR)
| aReductOfIn0(xu,X1,xR)
| aElement0(X1) )
| ~ spl14_30 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f556,definition,
( spl14_31
<=> aElement0(sK8(xR,xv,xu)) ),
introduced(definition,[new_symbols(definition,[spl14_31])],[avatar_definition]) ).
fof(f558,plain,
( aElement0(sK8(xR,xv,xu))
| ~ spl14_31 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f559,plain,
( spl14_30
| spl14_31
| spl14_30 ),
inference(avatar_split_clause,[],[f533,f553,f556,f553]) ).
fof(f1048,plain,
( aReductOfIn0(xu,xa,xR)
| aElement0(xa)
| ~ spl14_30 ),
inference(resolution,[],[f554,f162]) ).
fof(f1049,plain,
( aElement0(xa)
| ~ spl14_30 ),
inference(forward_subsumption_resolution,[],[f1048,f159]) ).
fof(f1050,plain,
( $false
| ~ spl14_30 ),
inference(forward_subsumption_resolution,[],[f1049,f152]) ).
fof(f1051,plain,
~ spl14_30,
inference(avatar_contradiction_clause,[],[f1050]) ).
fof(f1052,plain,
( ! [X0] :
( aReductOfIn0(xu,X0,xR)
| aReductOfIn0(xv,X0,xR)
| aElement0(X0)
| ~ aRewritingSystem0(xR)
| isLocallyConfluent0(xR) )
| ~ spl14_31 ),
inference(resolution,[],[f558,f222]) ).
fof(f1055,plain,
( ! [X0] :
( aReductOfIn0(xu,X0,xR)
| aReductOfIn0(xv,X0,xR)
| aElement0(X0)
| isLocallyConfluent0(xR) )
| ~ spl14_31 ),
inference(forward_subsumption_resolution,[],[f1052,f92]) ).
fof(f1056,plain,
( ! [X0] :
( aReductOfIn0(xu,X0,xR)
| aReductOfIn0(xv,X0,xR)
| aElement0(X0) )
| ~ spl14_31 ),
inference(forward_subsumption_resolution,[],[f1055,f150]) ).
fof(f1057,plain,
( spl14_30
| ~ spl14_31 ),
inference(avatar_split_clause,[],[f1056,f556,f553]) ).
cnf(s23,plain,
( spl14_30
| spl14_30
| spl14_31 ),
inference(sat_conversion,[],[f559]) ).
cnf(s24,plain,
( spl14_30
| spl14_31 ),
inference(rat,[],[s23]) ).
cnf(s34,plain,
~ spl14_30,
inference(sat_conversion,[],[f1051]) ).
cnf(s35,plain,
( spl14_30
| ~ spl14_31 ),
inference(sat_conversion,[],[f1057]) ).
cnf(s36,plain,
~ spl14_31,
inference(rat,[],[s35,s34]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s24,s36,s34]) ).
fof(f1058,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM017+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n020.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 21:46:35 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 0.08/0.26 % (607099)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (607105)% WARNING: option uhcvi not known.
% 0.08/0.26 % (607105)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1771402196:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.26 % (607104)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1374328256_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.26 % (607107)dis+10_1_sil=32000:sp=arity:random_seed=4282419177:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.26 % (607106)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1784727444:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.26 % (607108)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=625261392:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.26 % (607109)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3882144463:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.26 % (607110)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2967835973:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.26 % TRYING [1]
% 0.08/0.26 % TRYING [2]
% 0.08/0.26 % TRYING [3]
% 0.08/0.26 % (607105) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-607099-607105"...
% 0.08/0.26 % TRYING [4]
% 0.08/0.26 % (607105)...printing done.
% 0.08/0.26 % (607105)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (607105)------------------------------
% 0.08/0.26 % (607105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (607105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (607105)CaDiCaL version: 2.1.3
% 0.08/0.26 % (607105)Termination reason: Refutation
% 0.08/0.26 % (607105)Time elapsed: 0.017 s
% 0.08/0.26 % (607105)Peak memory usage: 12 MB
% 0.08/0.26 % (607105)Instructions burned: 50 (million)
% 0.08/0.26 % (607099)Success in time 0.048 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------