%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM012+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 09:39:22 AM UTC 2026
% Result : Theorem 2.48s 1.04s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 13 unt; 2 def)
% Number of atoms : 203 ( 20 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 264 ( 117 ~; 118 |; 19 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 57 ( 0 sgn 57 !; 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/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,
( ( sdtmndtasgtdt0(xx,xR,xy)
& sdtmndtasgtdt0(xy,xR,xz) )
=> sdtmndtasgtdt0(xx,xR,xz) ),
file('/export/starexec/sandbox2/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] :
( ~ aRewritingSystem0(X1)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ aElement0(X0)
| sdtmndtplgtdt0(X0,X1,X3)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ aRewritingSystem0(X1)
| sdtmndtplgtdt0(X0,X1,X2)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| X0 = X2
| ~ 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(f52,plain,
! [X0,X1] :
( sdtmndtplgtdt0(X0,xR,X1)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X0)
| X0 = X1
| ~ aElement0(X1) ),
inference(resolution,[],[f39,f44]) ).
fof(f56,plain,
! [X2,X0,X1] :
( sdtmndtplgtdt0(X0,xR,X2)
| ~ sdtmndtplgtdt0(X1,xR,X2)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,xR,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(resolution,[],[f38,f44]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ sdtmndtplgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| sdtmndtasgtdt0(X2,xR,X1)
| ~ aElement0(X2)
| ~ aRewritingSystem0(xR)
| ~ aElement0(X1) ),
inference(resolution,[],[f56,f40]) ).
fof(f58,plain,
! [X2,X0,X1] :
( ~ sdtmndtplgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| sdtmndtasgtdt0(X2,xR,X1)
| ~ aRewritingSystem0(xR) ),
inference(duplicate_literal_removal,[],[f57]) ).
fof(f59,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X2,xR,X1)
| ~ aElement0(X2)
| ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(X0,xR,X1) ),
inference(forward_subsumption_resolution,[],[f58,f44]) ).
fof(f61,plain,
! [X0] :
( ~ aElement0(xx)
| ~ sdtmndtplgtdt0(xx,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(xz)
| ~ sdtmndtplgtdt0(X0,xR,xz) ),
inference(resolution,[],[f59,f48]) ).
fof(f62,plain,
! [X0] :
( ~ sdtmndtplgtdt0(xx,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(xz)
| ~ sdtmndtplgtdt0(X0,xR,xz) ),
inference(forward_subsumption_resolution,[],[f61,f45]) ).
fof(f63,plain,
! [X0] :
( ~ sdtmndtplgtdt0(xx,xR,X0)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,xR,xz) ),
inference(forward_subsumption_resolution,[],[f62,f42]) ).
fof(f66,plain,
! [X0] :
( ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,xR,xz)
| ~ sdtmndtasgtdt0(xx,xR,X0)
| ~ aElement0(xx)
| xx = X0
| ~ aElement0(X0) ),
inference(resolution,[],[f63,f52]) ).
fof(f67,plain,
! [X0] :
( ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,xR,xz)
| ~ sdtmndtasgtdt0(xx,xR,X0)
| ~ aElement0(xx)
| xx = X0 ),
inference(duplicate_literal_removal,[],[f66]) ).
fof(f69,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xx,xR,X0)
| ~ sdtmndtplgtdt0(X0,xR,xz)
| ~ aElement0(X0)
| xx = X0 ),
inference(forward_subsumption_resolution,[],[f67,f45]) ).
fof(f74,plain,
( ~ sdtmndtplgtdt0(xy,xR,xz)
| ~ aElement0(xy)
| xx = xy ),
inference(resolution,[],[f69,f47]) ).
fof(f80,plain,
( ~ sdtmndtplgtdt0(xy,xR,xz)
| xx = xy ),
inference(forward_subsumption_resolution,[],[f74,f43]) ).
fof(f82,definition,
( spl1_1
<=> xx = xy ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f84,plain,
( xx = xy
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f86,definition,
( spl1_2
<=> sdtmndtplgtdt0(xy,xR,xz) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f88,plain,
( ~ sdtmndtplgtdt0(xy,xR,xz)
| spl1_2 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f80,f86,f82]) ).
fof(f97,plain,
( ~ sdtmndtasgtdt0(xy,xR,xz)
| ~ aElement0(xy)
| xy = xz
| ~ aElement0(xz)
| spl1_2 ),
inference(resolution,[],[f88,f52]) ).
fof(f98,plain,
( ~ aElement0(xy)
| xy = xz
| ~ aElement0(xz)
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f97,f46]) ).
fof(f100,plain,
( xy = xz
| ~ aElement0(xz)
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f98,f43]) ).
fof(f102,plain,
( xy = xz
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f100,f42]) ).
fof(f110,plain,
( ~ sdtmndtasgtdt0(xx,xR,xy)
| spl1_2 ),
inference(superposition,[],[f48,f102]) ).
fof(f112,plain,
( $false
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f110,f47]) ).
fof(f113,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f112]) ).
fof(f116,plain,
( sdtmndtasgtdt0(xx,xR,xz)
| ~ spl1_1 ),
inference(superposition,[],[f46,f84]) ).
fof(f117,plain,
( $false
| ~ spl1_1 ),
inference(forward_subsumption_resolution,[],[f116,f48]) ).
fof(f118,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f117]) ).
cnf(s1,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f89]) ).
cnf(s2,plain,
spl1_2,
inference(sat_conversion,[],[f113]) ).
cnf(s3,plain,
~ spl1_1,
inference(sat_conversion,[],[f118]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f119,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM012+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n016.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Mon Sep 28 21:49:49 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running first-order theorem proving
% 0.08/0.20 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
% 2.48/1.04 % (4065633)Detected formulas, will run a generic FOF schedule.
% 2.48/1.04 % (4065642)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2256178410:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.48/1.04 % (4065642)Refutation not found, incomplete strategy
% 2.48/1.04 % (4065642)------------------------------
% 2.48/1.04 % (4065642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.04 % (4065642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.04 % (4065642)CaDiCaL version: 2.1.3
% 2.48/1.04 % (4065642)Termination reason: Refutation not found, incomplete strategy
% 2.48/1.04 % (4065642)Time elapsed: 0.0000 s
% 2.48/1.04 % (4065642)Peak memory usage: 87 MB
% 2.48/1.04 % (4065643)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3856453338:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.48/1.04 % (4065643)First to succeed.
% 2.48/1.04 % (4065640)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=221533674:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.48/1.04 % (4065641)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1906028814:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.48/1.04 % (4065638)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=150178144:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.48/1.04 % (4065644)dis-21_1_sil=8000:lcm=predicate:random_seed=3299651947: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)
% 2.48/1.04 % (4065639)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=132533411:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.48/1.04 % (4065643)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4065633"
% 2.48/1.04 % (4065641)Refutation not found, incomplete strategy
% 2.48/1.04 % (4065641)------------------------------
% 2.48/1.04 % (4065641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.04 % (4065641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.04 % (4065641)CaDiCaL version: 2.1.3
% 2.48/1.04 % (4065641)Termination reason: Refutation not found, incomplete strategy
% 2.48/1.04 % (4065641)Time elapsed: 0.001 s
% 2.48/1.04 % (4065641)Peak memory usage: 87 MB
% 2.48/1.04 % (4065644)Instruction limit reached!
% 2.48/1.04 % (4065644)------------------------------
% 2.48/1.04 % (4065644)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.04 % (4065644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.04 % (4065644)CaDiCaL version: 2.1.3
% 2.48/1.04 % (4065644)Termination reason: Instruction limit
% 2.48/1.04 % (4065644)Termination phase: Saturation
% 2.48/1.04 % (4065644)Time elapsed: 0.051 s
% 2.48/1.04 % (4065644)Peak memory usage: 88 MB
% 2.48/1.04 % (4065644)Instructions burned: 129 (million)
% 2.48/1.04 % (4065642)------------------------------
% 2.48/1.04 % (4065642)------------------------------
% 2.48/1.04 % (4065652)lrs+10_1_sil=8000:sp=occurrence:random_seed=4232952093:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.48/1.04 % (4065653)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1816740664:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.48/1.04 % (4065653)Refutation not found, incomplete strategy
% 2.48/1.04 % (4065653)------------------------------
% 2.48/1.04 % (4065653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.04 % (4065653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.04 % (4065653)CaDiCaL version: 2.1.3
% 2.48/1.04 % (4065653)Termination reason: Refutation not found, incomplete strategy
% 2.48/1.04 % (4065653)Time elapsed: 0.0000 s
% 2.48/1.04 % (4065653)Peak memory usage: 88 MB
% 2.48/1.04 % (4065653)Instructions burned: 1 (million)
% 2.48/1.04 % (4065652)Also succeeded, but the first one will report.
% 2.48/1.04 % (4065641)------------------------------
% 2.48/1.04 % (4065641)------------------------------
% 2.48/1.04 % (4065643)Refutation found. Thanks to Tanya!
% 2.48/1.04 % SZS status Theorem for theBenchmark
% 2.48/1.04 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.24 % (4065643)------------------------------
% 3.49/1.24 % (4065643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.24 % (4065643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.24 % (4065643)CaDiCaL version: 2.1.3
% 3.49/1.24 % (4065643)Termination reason: Refutation
% 3.49/1.24 % (4065643)Time elapsed: 0.005 s
% 3.49/1.24 % (4065643)Peak memory usage: 89 MB
% 3.49/1.24 % (4065643)Instructions burned: 5 (million)
% 3.49/1.24 % (4065643)------------------------------
% 3.49/1.24 % (4065643)------------------------------
% 3.49/1.24 % (4065633)Success in time 0.405 s
% 3.49/1.24 % Vampire exiting
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