%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM012+3 : 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 : n013.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 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 70 ( 21 unt; 5 def)
% Number of atoms : 293 ( 29 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 314 ( 91 ~; 139 |; 70 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 58 ( 0 sgn 45 !; 13 ?)
% 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mTCRDef) ).
fof(f9,axiom,
( aElement0(xx)
& aRewritingSystem0(xR)
& aElement0(xy)
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__349) ).
fof(f10,conjecture,
( ( ( xx = xy
| ( ( aReductOfIn0(xy,xx,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xx,xR)
& sdtmndtplgtdt0(X0,xR,xy) ) )
& sdtmndtplgtdt0(xx,xR,xy) ) )
& sdtmndtasgtdt0(xx,xR,xy)
& ( xy = xz
| ( ( aReductOfIn0(xz,xy,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xy,xR)
& sdtmndtplgtdt0(X0,xR,xz) ) )
& sdtmndtplgtdt0(xy,xR,xz) ) )
& sdtmndtasgtdt0(xy,xR,xz) )
=> ( xx = xz
| aReductOfIn0(xz,xx,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xx,xR)
& sdtmndtplgtdt0(X0,xR,xz) )
| sdtmndtplgtdt0(xx,xR,xz)
| sdtmndtasgtdt0(xx,xR,xz) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f11,negated_conjecture,
~ ( ( ( xx = xy
| ( ( aReductOfIn0(xy,xx,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xx,xR)
& sdtmndtplgtdt0(X0,xR,xy) ) )
& sdtmndtplgtdt0(xx,xR,xy) ) )
& sdtmndtasgtdt0(xx,xR,xy)
& ( xy = xz
| ( ( aReductOfIn0(xz,xy,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xy,xR)
& sdtmndtplgtdt0(X0,xR,xz) ) )
& sdtmndtplgtdt0(xy,xR,xz) ) )
& sdtmndtasgtdt0(xy,xR,xz) )
=> ( xx = xz
| aReductOfIn0(xz,xx,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xx,xR)
& sdtmndtplgtdt0(X0,xR,xz) )
| sdtmndtplgtdt0(xx,xR,xz)
| sdtmndtasgtdt0(xx,xR,xz) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
~ ( ( ( xx = xy
| ( ( aReductOfIn0(xy,xx,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xx,xR)
& sdtmndtplgtdt0(X0,xR,xy) ) )
& sdtmndtplgtdt0(xx,xR,xy) ) )
& sdtmndtasgtdt0(xx,xR,xy)
& ( xy = xz
| ( ( aReductOfIn0(xz,xy,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xy,xR)
& sdtmndtplgtdt0(X1,xR,xz) ) )
& sdtmndtplgtdt0(xy,xR,xz) ) )
& sdtmndtasgtdt0(xy,xR,xz) )
=> ( xx = xz
| aReductOfIn0(xz,xx,xR)
| ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,xx,xR)
& sdtmndtplgtdt0(X2,xR,xz) )
| sdtmndtplgtdt0(xx,xR,xz)
| sdtmndtasgtdt0(xx,xR,xz) ) ),
inference(rectify,[],[f11]) ).
fof(f22,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(f23,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,[],[f22]) ).
fof(f24,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(f25,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
( xx != xz
& ~ aReductOfIn0(xz,xx,xR)
& ! [X2] :
( ~ aElement0(X2)
| ~ aReductOfIn0(X2,xx,xR)
| ~ sdtmndtplgtdt0(X2,xR,xz) )
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ~ sdtmndtasgtdt0(xx,xR,xz)
& ( xx = xy
| ( ( aReductOfIn0(xy,xx,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xx,xR)
& sdtmndtplgtdt0(X0,xR,xy) ) )
& sdtmndtplgtdt0(xx,xR,xy) ) )
& sdtmndtasgtdt0(xx,xR,xy)
& ( xy = xz
| ( ( aReductOfIn0(xz,xy,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xy,xR)
& sdtmndtplgtdt0(X1,xR,xz) ) )
& sdtmndtplgtdt0(xy,xR,xz) ) )
& sdtmndtasgtdt0(xy,xR,xz) ),
inference(ennf_transformation,[],[f12]) ).
fof(f27,plain,
( xx != xz
& ~ aReductOfIn0(xz,xx,xR)
& ! [X2] :
( ~ aElement0(X2)
| ~ aReductOfIn0(X2,xx,xR)
| ~ sdtmndtplgtdt0(X2,xR,xz) )
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ~ sdtmndtasgtdt0(xx,xR,xz)
& ( xx = xy
| ( ( aReductOfIn0(xy,xx,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xx,xR)
& sdtmndtplgtdt0(X0,xR,xy) ) )
& sdtmndtplgtdt0(xx,xR,xy) ) )
& sdtmndtasgtdt0(xx,xR,xy)
& ( xy = xz
| ( ( aReductOfIn0(xz,xy,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xy,xR)
& sdtmndtplgtdt0(X1,xR,xz) ) )
& sdtmndtplgtdt0(xy,xR,xz) ) )
& sdtmndtasgtdt0(xy,xR,xz) ),
inference(flattening,[],[f26]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X3) ),
inference(cnf_transformation,[],[f23]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2
| ~ sdtmndtasgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
aElement0(xz),
inference(cnf_transformation,[],[f9]) ).
fof(f39,plain,
aElement0(xy),
inference(cnf_transformation,[],[f9]) ).
fof(f40,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f9]) ).
fof(f41,plain,
aElement0(xx),
inference(cnf_transformation,[],[f9]) ).
fof(f50,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| xy = xz ),
inference(cnf_transformation,[],[f27]) ).
fof(f51,plain,
sdtmndtasgtdt0(xy,xR,xz),
inference(cnf_transformation,[],[f27]) ).
fof(f52,plain,
sdtmndtasgtdt0(xx,xR,xy),
inference(cnf_transformation,[],[f27]) ).
fof(f53,plain,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(cnf_transformation,[],[f27]) ).
fof(f54,plain,
~ sdtmndtplgtdt0(xx,xR,xz),
inference(cnf_transformation,[],[f27]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( ~ aRewritingSystem0(X1)
| aElement0(X2)
| aElement0(X3)
| aElement0(X0)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X3) ),
inference(consistent_polarity_flipping,[],[f34]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ aRewritingSystem0(X1)
| aElement0(X2)
| aElement0(X0)
| sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2
| ~ sdtmndtasgtdt0(X0,X1,X2) ),
inference(consistent_polarity_flipping,[],[f35]) ).
fof(f68,plain,
~ aElement0(xx),
inference(consistent_polarity_flipping,[],[f41]) ).
fof(f69,plain,
~ aElement0(xy),
inference(consistent_polarity_flipping,[],[f39]) ).
fof(f70,plain,
~ aElement0(xz),
inference(consistent_polarity_flipping,[],[f38]) ).
fof(f81,definition,
( spl3_1
<=> xx = xy ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f83,plain,
( xx = xy
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f104,definition,
( spl3_6
<=> xy = xz ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f106,plain,
( xy = xz
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f127,definition,
( spl3_11
<=> sdtmndtplgtdt0(xx,xR,xy) ),
introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition]) ).
fof(f129,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f132,definition,
( spl3_12
<=> sdtmndtplgtdt0(xy,xR,xz) ),
introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition]) ).
fof(f134,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( spl3_6
| spl3_12 ),
inference(avatar_split_clause,[],[f50,f132,f104]) ).
fof(f139,plain,
( ~ sdtmndtasgtdt0(xx,xR,xy)
| ~ spl3_6 ),
inference(forward_demodulation,[],[f53,f106]) ).
fof(f140,plain,
( $false
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f139,f52]) ).
fof(f141,plain,
~ spl3_6,
inference(avatar_contradiction_clause,[],[f140]) ).
fof(f147,definition,
( spl3_13
<=> aElement0(xy) ),
introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition]) ).
fof(f148,plain,
( ~ aElement0(xy)
| spl3_13 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f151,plain,
~ spl3_13,
inference(avatar_split_clause,[],[f69,f147]) ).
fof(f165,plain,
! [X0,X1] :
( ~ sdtmndtasgtdt0(X1,xR,X0)
| aElement0(X1)
| sdtmndtplgtdt0(X1,xR,X0)
| X0 = X1
| aElement0(X0) ),
inference(resolution,[],[f67,f40]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ sdtmndtplgtdt0(X2,xR,X0)
| aElement0(X1)
| aElement0(X2)
| ~ sdtmndtplgtdt0(X0,xR,X1)
| aElement0(X0)
| sdtmndtplgtdt0(X2,xR,X1) ),
inference(resolution,[],[f64,f40]) ).
fof(f175,plain,
( aElement0(xx)
| sdtmndtplgtdt0(xx,xR,xy)
| xx = xy
| aElement0(xy) ),
inference(resolution,[],[f165,f52]) ).
fof(f190,plain,
( ! [X0] :
( aElement0(X0)
| aElement0(xx)
| ~ sdtmndtplgtdt0(xy,xR,X0)
| aElement0(xy)
| sdtmndtplgtdt0(xx,xR,X0) )
| ~ spl3_11 ),
inference(resolution,[],[f172,f129]) ).
fof(f197,plain,
( ! [X0] :
( aElement0(X0)
| ~ sdtmndtplgtdt0(xy,xR,X0)
| aElement0(xy)
| sdtmndtplgtdt0(xx,xR,X0) )
| ~ spl3_11 ),
inference(forward_subsumption_resolution,[],[f190,f68]) ).
fof(f201,plain,
( ! [X0] :
( ~ sdtmndtplgtdt0(xy,xR,X0)
| aElement0(X0)
| sdtmndtplgtdt0(xx,xR,X0) )
| ~ spl3_11
| spl3_13 ),
inference(forward_subsumption_resolution,[],[f197,f148]) ).
fof(f219,plain,
( aElement0(xz)
| sdtmndtplgtdt0(xx,xR,xz)
| ~ spl3_11
| ~ spl3_12
| spl3_13 ),
inference(resolution,[],[f201,f134]) ).
fof(f220,plain,
( sdtmndtplgtdt0(xx,xR,xz)
| ~ spl3_11
| ~ spl3_12
| spl3_13 ),
inference(forward_subsumption_resolution,[],[f219,f70]) ).
fof(f221,plain,
( $false
| ~ spl3_11
| ~ spl3_12
| spl3_13 ),
inference(forward_subsumption_resolution,[],[f220,f54]) ).
fof(f222,plain,
( ~ spl3_11
| ~ spl3_12
| spl3_13 ),
inference(avatar_contradiction_clause,[],[f221]) ).
fof(f223,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| xx = xy
| aElement0(xy) ),
inference(forward_subsumption_resolution,[],[f175,f68]) ).
fof(f226,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| xx = xy
| spl3_13 ),
inference(forward_subsumption_resolution,[],[f223,f148]) ).
fof(f229,plain,
( spl3_1
| spl3_11
| spl3_13 ),
inference(avatar_split_clause,[],[f226,f147,f127,f81]) ).
fof(f231,plain,
( ~ sdtmndtasgtdt0(xy,xR,xz)
| ~ spl3_1 ),
inference(superposition,[],[f53,f83]) ).
fof(f240,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f231,f51]) ).
fof(f241,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f240]) ).
cnf(s8,plain,
( spl3_6
| spl3_12 ),
inference(sat_conversion,[],[f135]) ).
cnf(s10,plain,
~ spl3_6,
inference(sat_conversion,[],[f141]) ).
cnf(s13,plain,
~ spl3_13,
inference(sat_conversion,[],[f151]) ).
cnf(s14,plain,
( ~ spl3_11
| ~ spl3_12
| spl3_13 ),
inference(sat_conversion,[],[f222]) ).
cnf(s17,plain,
( spl3_1
| spl3_11
| spl3_13 ),
inference(sat_conversion,[],[f229]) ).
cnf(s20,plain,
~ spl3_1,
inference(sat_conversion,[],[f241]) ).
cnf(s21,plain,
( spl3_11
| spl3_13 ),
inference(rat,[],[s17,s20]) ).
cnf(s22,plain,
spl3_11,
inference(rat,[],[s21,s13]) ).
cnf(s23,plain,
~ spl3_12,
inference(rat,[],[s14,s13,s22]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s8,s23,s10]) ).
fof(f242,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM012+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n013.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 21:44:36 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.19/0.28 % (1610963)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (1610969)% WARNING: option uhcvi not known.
% 0.19/0.28 % (1610969)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=578771296:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (1610969) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1610963-1610969"...
% 0.19/0.28 % (1610969)...printing done.
% 0.19/0.28 % (1610969)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (1610969)------------------------------
% 0.19/0.28 % (1610969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (1610969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (1610969)CaDiCaL version: 2.1.3
% 0.19/0.28 % (1610969)Termination reason: Refutation
% 0.19/0.28 % (1610969)Time elapsed: 0.004 s
% 0.19/0.28 % (1610969)Peak memory usage: 12 MB
% 0.19/0.28 % (1610969)Instructions burned: 7 (million)
% 0.19/0.28 % (1610963)Success in time 0.038 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------