%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM012+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 09:40:07 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 77 ( 16 unt; 4 def)
% Number of atoms : 245 ( 16 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 298 ( 130 ~; 137 |; 19 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1,X2,X3] :
( ( aElement0(X0)
& aRewritingSystem0(X1)
& aElement0(X2)
& aElement0(X3) )
=> ( ( sdtmndtplgtdt0(X0,X1,X2)
& sdtmndtplgtdt0(X2,X1,X3) )
=> sdtmndtplgtdt0(X0,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCTrans) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aRewritingSystem0(X1)
& aElement0(X2) )
=> ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRDef) ).
fof(f9,axiom,
( aElement0(xx)
& aRewritingSystem0(xR)
& aElement0(xy)
& aElement0(xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__349) ).
fof(f10,conjecture,
( ( sdtmndtasgtdt0(xx,xR,xy)
& sdtmndtasgtdt0(xy,xR,xz) )
=> sdtmndtasgtdt0(xx,xR,xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f11,negated_conjecture,
~ ( ( sdtmndtasgtdt0(xx,xR,xy)
& sdtmndtasgtdt0(xy,xR,xz) )
=> sdtmndtasgtdt0(xx,xR,xz) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( sdtmndtplgtdt0(X0,X1,X3)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(ennf_transformation,[],[f7]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( sdtmndtplgtdt0(X0,X1,X3)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f8]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
( ~ sdtmndtasgtdt0(xx,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy)
& sdtmndtasgtdt0(xy,xR,xz) ),
inference(ennf_transformation,[],[f11]) ).
fof(f25,plain,
( ~ sdtmndtasgtdt0(xx,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy)
& sdtmndtasgtdt0(xy,xR,xz) ),
inference(flattening,[],[f24]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,X1,X2)
| ( X0 != X2
& ~ sdtmndtplgtdt0(X0,X1,X2) ) )
& ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2)
| ~ sdtmndtasgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(nnf_transformation,[],[f23]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,X1,X2)
| ( X0 != X2
& ~ sdtmndtplgtdt0(X0,X1,X2) ) )
& ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2)
| ~ sdtmndtasgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f30]) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X3)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f42,plain,
aElement0(xz),
inference(cnf_transformation,[],[f9]) ).
fof(f43,plain,
aElement0(xy),
inference(cnf_transformation,[],[f9]) ).
fof(f44,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f9]) ).
fof(f45,plain,
aElement0(xx),
inference(cnf_transformation,[],[f9]) ).
fof(f46,plain,
sdtmndtasgtdt0(xy,xR,xz),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
sdtmndtasgtdt0(xx,xR,xy),
inference(cnf_transformation,[],[f25]) ).
fof(f48,plain,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(cnf_transformation,[],[f25]) ).
fof(f186,definition,
( spl1_11
<=> xx = xy ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f187,plain,
( xx != xy
| spl1_11 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f188,plain,
( xx = xy
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f190,definition,
( spl1_12
<=> sdtmndtplgtdt0(xx,xR,xy) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f191,plain,
( ~ sdtmndtplgtdt0(xx,xR,xy)
| spl1_12 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f192,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f196,plain,
( sdtmndtasgtdt0(xx,xR,xz)
| ~ spl1_11 ),
inference(superposition,[],[f46,f188]) ).
fof(f197,plain,
( $false
| ~ spl1_11 ),
inference(forward_subsumption_resolution,[],[f196,f48]) ).
fof(f198,plain,
~ spl1_11,
inference(avatar_contradiction_clause,[],[f197]) ).
fof(f201,definition,
( spl1_13
<=> xy = xz ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f202,plain,
( xy != xz
| spl1_13 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f203,plain,
( xy = xz
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f205,definition,
( spl1_14
<=> sdtmndtplgtdt0(xy,xR,xz) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f206,plain,
( ~ sdtmndtplgtdt0(xy,xR,xz)
| spl1_14 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f207,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| ~ spl1_14 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f211,plain,
( ~ sdtmndtasgtdt0(xx,xR,xy)
| ~ spl1_13 ),
inference(superposition,[],[f48,f203]) ).
fof(f212,plain,
( $false
| ~ spl1_13 ),
inference(forward_subsumption_resolution,[],[f211,f47]) ).
fof(f213,plain,
~ spl1_13,
inference(avatar_contradiction_clause,[],[f212]) ).
fof(f255,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| xy = xz
| ~ aElement0(xy)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xz) ),
inference(resolution,[],[f39,f46]) ).
fof(f256,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| xx = xy
| ~ aElement0(xx)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xy) ),
inference(resolution,[],[f39,f47]) ).
fof(f267,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| ~ aElement0(xx)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xy)
| spl1_11 ),
inference(forward_subsumption_resolution,[],[f256,f187]) ).
fof(f268,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xy)
| spl1_11 ),
inference(forward_subsumption_resolution,[],[f267,f45]) ).
fof(f269,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| ~ aElement0(xy)
| spl1_11 ),
inference(forward_subsumption_resolution,[],[f268,f44]) ).
fof(f270,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| spl1_11 ),
inference(forward_subsumption_resolution,[],[f269,f43]) ).
fof(f271,plain,
( $false
| spl1_11
| spl1_12 ),
inference(forward_subsumption_resolution,[],[f270,f191]) ).
fof(f272,plain,
( spl1_11
| spl1_12 ),
inference(avatar_contradiction_clause,[],[f271]) ).
fof(f318,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| ~ aElement0(xy)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xz)
| spl1_13 ),
inference(forward_subsumption_resolution,[],[f255,f202]) ).
fof(f319,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xz)
| spl1_13 ),
inference(forward_subsumption_resolution,[],[f318,f43]) ).
fof(f320,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| ~ aElement0(xz)
| spl1_13 ),
inference(forward_subsumption_resolution,[],[f319,f44]) ).
fof(f321,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| spl1_13 ),
inference(forward_subsumption_resolution,[],[f320,f42]) ).
fof(f322,plain,
( $false
| spl1_13
| spl1_14 ),
inference(forward_subsumption_resolution,[],[f321,f206]) ).
fof(f323,plain,
( spl1_13
| spl1_14 ),
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f326,plain,
( ! [X0] :
( ~ sdtmndtplgtdt0(X0,xR,xy)
| sdtmndtplgtdt0(X0,xR,xz)
| ~ aElement0(X0)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xy)
| ~ aElement0(xz) )
| ~ spl1_14 ),
inference(resolution,[],[f207,f38]) ).
fof(f328,plain,
( ! [X0] :
( ~ sdtmndtplgtdt0(X0,xR,xy)
| sdtmndtplgtdt0(X0,xR,xz)
| ~ aElement0(X0)
| ~ aElement0(xy)
| ~ aElement0(xz) )
| ~ spl1_14 ),
inference(forward_subsumption_resolution,[],[f326,f44]) ).
fof(f329,plain,
( ! [X0] :
( ~ sdtmndtplgtdt0(X0,xR,xy)
| sdtmndtplgtdt0(X0,xR,xz)
| ~ aElement0(X0)
| ~ aElement0(xz) )
| ~ spl1_14 ),
inference(forward_subsumption_resolution,[],[f328,f43]) ).
fof(f330,plain,
( ! [X0] :
( ~ sdtmndtplgtdt0(X0,xR,xy)
| sdtmndtplgtdt0(X0,xR,xz)
| ~ aElement0(X0) )
| ~ spl1_14 ),
inference(forward_subsumption_resolution,[],[f329,f42]) ).
fof(f362,plain,
( sdtmndtplgtdt0(xx,xR,xz)
| ~ aElement0(xx)
| ~ spl1_12
| ~ spl1_14 ),
inference(resolution,[],[f330,f192]) ).
fof(f365,plain,
( sdtmndtplgtdt0(xx,xR,xz)
| ~ spl1_12
| ~ spl1_14 ),
inference(forward_subsumption_resolution,[],[f362,f45]) ).
fof(f367,plain,
( sdtmndtasgtdt0(xx,xR,xz)
| ~ aElement0(xx)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xz)
| ~ spl1_12
| ~ spl1_14 ),
inference(resolution,[],[f365,f40]) ).
fof(f368,plain,
( ~ aElement0(xx)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xz)
| ~ spl1_12
| ~ spl1_14 ),
inference(forward_subsumption_resolution,[],[f367,f48]) ).
fof(f369,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0(xz)
| ~ spl1_12
| ~ spl1_14 ),
inference(forward_subsumption_resolution,[],[f368,f45]) ).
fof(f370,plain,
( ~ aElement0(xz)
| ~ spl1_12
| ~ spl1_14 ),
inference(forward_subsumption_resolution,[],[f369,f44]) ).
fof(f371,plain,
( $false
| ~ spl1_12
| ~ spl1_14 ),
inference(forward_subsumption_resolution,[],[f370,f42]) ).
fof(f372,plain,
( ~ spl1_12
| ~ spl1_14 ),
inference(avatar_contradiction_clause,[],[f371]) ).
cnf(s108,plain,
~ spl1_11,
inference(sat_conversion,[],[f198]) ).
cnf(s117,plain,
~ spl1_13,
inference(sat_conversion,[],[f213]) ).
cnf(s160,plain,
( spl1_11
| spl1_12 ),
inference(sat_conversion,[],[f272]) ).
cnf(s188,plain,
( spl1_13
| spl1_14 ),
inference(sat_conversion,[],[f323]) ).
cnf(s213,plain,
( ~ spl1_12
| ~ spl1_14 ),
inference(sat_conversion,[],[f372]) ).
cnf(s214,plain,
spl1_14,
inference(rat,[],[s188,s117]) ).
cnf(s215,plain,
~ spl1_12,
inference(rat,[],[s213,s214]) ).
cnf(s218,plain,
spl1_11,
inference(rat,[],[s160,s215]) ).
cnf(s219,plain,
$false,
inference(rat,[],[s108,s218]) ).
fof(f373,plain,
$false,
inference(avatar_sat_refutation,[],[s219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM012+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n008.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 21:45:39 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.26 % (2685671)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (2685678)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3291661986:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.26 % (2685677)% WARNING: option uhcvi not known.
% 0.09/0.26 % (2685678) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2685671-2685678"...
% 0.09/0.26 % (2685678)...printing done.
% 0.09/0.26 % (2685676)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=61147229_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.26 % (2685677)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=452664734:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.26 % (2685679)dis+10_1_sil=32000:sp=arity:random_seed=512372846:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.26 % (2685678)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.26 % (2685678)------------------------------
% 0.09/0.26 % (2685678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (2685678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (2685678)CaDiCaL version: 2.1.3
% 0.09/0.26 % (2685678)Termination reason: Refutation
% 0.09/0.26 % (2685678)Time elapsed: 0.004 s
% 0.09/0.26 % (2685678)Peak memory usage: 12 MB
% 0.09/0.26 % (2685678)Instructions burned: 8 (million)
% 0.09/0.26 % (2685671)Success in time 0.035 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------