%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL009-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 12:33:41 PM UTC 2026
% Result : Unsatisfiable 6.78s 2.01s
% Output : Refutation 6.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 54 ( 43 unt; 9 def)
% Number of atoms : 65 ( 47 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 9 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f17,negated_conjecture,
join(sk1,sk2) = sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
sk2 = join(sk1,sk2),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( join(composition(sk1,sk3),composition(sk2,sk3)) != composition(sk2,sk3)
| join(composition(sk3,sk1),composition(sk3,sk2)) != composition(sk3,sk2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_15) ).
fof(f20,plain,
( composition(sk2,sk3) != join(composition(sk1,sk3),composition(sk2,sk3))
| composition(sk3,sk2) != join(composition(sk3,sk1),composition(sk3,sk2)) ),
inference(reorient_equations,[],[f19]) ).
fof(f22,definition,
sF0 = join(sk1,sk2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f23,plain,
join(sk1,sk2) = sF0,
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
sk2 = sF0,
inference(definition_folding,[],[f18,f23]) ).
fof(f25,definition,
sF1 = composition(sk2,sk3),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f26,plain,
composition(sk2,sk3) = sF1,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF2 = composition(sk1,sk3),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f28,plain,
composition(sk1,sk3) = sF2,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF3 = join(sF2,sF1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f30,plain,
join(sF2,sF1) = sF3,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF4 = composition(sk3,sk2),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f32,plain,
composition(sk3,sk2) = sF4,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF5 = composition(sk3,sk1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f34,plain,
composition(sk3,sk1) = sF5,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF6 = join(sF5,sF4),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f36,plain,
join(sF5,sF4) = sF6,
inference(reorient_equations,[],[f35]) ).
fof(f37,plain,
( sF1 != sF3
| sF4 != sF6 ),
inference(definition_folding,[],[f20,f36,f32,f34,f32,f30,f26,f28,f26]) ).
fof(f39,definition,
( spl7_1
<=> sF4 = sF6 ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f41,plain,
( sF4 != sF6
| spl7_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f43,definition,
( spl7_2
<=> sF1 = sF3 ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f45,plain,
( sF1 != sF3
| spl7_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f37,f43,f39]) ).
fof(f47,plain,
sk2 = join(sk1,sk2),
inference(forward_demodulation,[],[f23,f24]) ).
fof(f52,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f9,f12]) ).
fof(f53,plain,
! [X0] : composition(join(sk1,X0),sk3) = join(sF2,composition(X0,sk3)),
inference(superposition,[],[f9,f28]) ).
fof(f98,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f52,f12]) ).
fof(f107,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f98,f11]) ).
fof(f110,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f107,f11]) ).
fof(f112,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f110,f12]) ).
fof(f134,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f112]) ).
fof(f135,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f134,f10]) ).
fof(f159,plain,
! [X0] : composition(sk3,join(sk1,X0)) = join(sF5,composition(sk3,X0)),
inference(superposition,[],[f135,f34]) ).
fof(f195,plain,
composition(sk3,sk2) = join(sF5,composition(sk3,sk2)),
inference(superposition,[],[f159,f47]) ).
fof(f210,plain,
sF4 = join(sF5,sF4),
inference(forward_demodulation,[],[f195,f32]) ).
fof(f213,plain,
sF4 = sF6,
inference(forward_demodulation,[],[f210,f36]) ).
fof(f216,plain,
( $false
| spl7_1 ),
inference(forward_subsumption_resolution,[],[f213,f41]) ).
fof(f217,plain,
spl7_1,
inference(avatar_contradiction_clause,[],[f216]) ).
fof(f497,plain,
composition(sk2,sk3) = join(sF2,composition(sk2,sk3)),
inference(superposition,[],[f53,f47]) ).
fof(f514,plain,
sF1 = join(sF2,sF1),
inference(forward_demodulation,[],[f497,f26]) ).
fof(f516,plain,
sF1 = sF3,
inference(forward_demodulation,[],[f514,f30]) ).
fof(f518,plain,
( $false
| spl7_2 ),
inference(forward_subsumption_resolution,[],[f516,f45]) ).
fof(f519,plain,
spl7_2,
inference(avatar_contradiction_clause,[],[f518]) ).
cnf(s1,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f46]) ).
cnf(s2,plain,
spl7_1,
inference(sat_conversion,[],[f217]) ).
cnf(s3,plain,
spl7_2,
inference(sat_conversion,[],[f519]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f520,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL009-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n013.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 22:49:36 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.23/1.77 % (633598)Input is clausal, will run a generic CNF schedule.
% 5.23/1.77 % (633648)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=3857764020:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.23/1.77 % (633649)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=189193222:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.23/1.77 % (633653)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2417519604:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.23/1.77 % (633651)lrs+10_1_sil=8000:sp=occurrence:random_seed=1448692288:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.23/1.77 % (633650)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1204274882:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.23/1.77 % (633654)dis-21_1_sil=8000:lcm=predicate:random_seed=1278999477:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 5.23/1.77 % (633654)Refutation not found, incomplete strategy
% 5.23/1.77 % (633654)------------------------------
% 5.23/1.77 % (633654)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/1.77 % (633654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/1.77 % (633654)CaDiCaL version: 2.1.3
% 5.23/1.77 % (633654)Termination reason: Refutation not found, incomplete strategy
% 5.23/1.77 % (633654)Time elapsed: 0.001 s
% 5.23/1.77 % (633654)Peak memory usage: 88 MB
% 5.23/1.77 % (633654)Instructions burned: 1 (million)
% 5.23/1.77 % (633652)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1820902515:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.23/1.77 % (633651)Instruction limit reached!
% 5.23/1.77 % (633651)------------------------------
% 5.23/1.77 % (633651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/1.77 % (633651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/1.77 % (633651)CaDiCaL version: 2.1.3
% 5.23/1.77 % (633651)Termination reason: Instruction limit
% 5.23/1.77 % (633651)Termination phase: Saturation
% 5.23/1.77 % (633651)Time elapsed: 0.097 s
% 5.23/1.77 % (633651)Peak memory usage: 89 MB
% 5.23/1.77 % (633651)Instructions burned: 108 (million)
% 5.23/1.77 % (633652)Instruction limit reached!
% 5.23/1.77 % (633652)------------------------------
% 5.23/1.77 % (633652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/1.77 % (633652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/1.77 % (633652)CaDiCaL version: 2.1.3
% 5.23/1.77 % (633652)Termination reason: Instruction limit
% 5.23/1.77 % (633652)Termination phase: Saturation
% 5.23/1.77 % (633652)Time elapsed: 0.107 s
% 5.23/1.77 % (633652)Peak memory usage: 89 MB
% 5.23/1.77 % (633652)Instructions burned: 115 (million)
% 5.23/1.77 % (633653)Instruction limit reached!
% 5.23/1.77 % (633653)------------------------------
% 5.23/1.77 % (633653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/1.77 % (633653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/1.77 % (633653)CaDiCaL version: 2.1.3
% 5.23/1.77 % (633653)Termination reason: Instruction limit
% 5.23/1.77 % (633653)Termination phase: Saturation
% 5.23/1.77 % (633653)Time elapsed: 0.153 s
% 5.23/1.77 % (633653)Peak memory usage: 89 MB
% 5.23/1.77 % (633653)Instructions burned: 185 (million)
% 5.23/1.77 % (633654)------------------------------
% 5.23/1.77 % (633654)------------------------------
% 5.23/1.77 % (633670)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=386664790:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.23/1.77 % (633671)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1119207803:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 5.23/1.77 % (633672)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=462313701:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 5.23/1.77 % (633648)First to succeed.
% 5.23/1.77 % (633648)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-633598"
% 5.23/1.77 % (633672)Also succeeded, but the first one will report.
% 6.78/2.01 % (633670)Instruction limit reached!
% 6.78/2.01 % (633670)------------------------------
% 6.78/2.01 % (633670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/2.01 % (633670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/2.01 % (633670)CaDiCaL version: 2.1.3
% 6.78/2.01 % (633670)Termination reason: Instruction limit
% 6.78/2.01 % (633670)Termination phase: Saturation
% 6.78/2.01 % (633670)Time elapsed: 0.110 s
% 6.78/2.01 % (633670)Peak memory usage: 89 MB
% 6.78/2.01 % (633670)Instructions burned: 144 (million)
% 6.78/2.01 % (633671)Instruction limit reached!
% 6.78/2.01 % (633671)------------------------------
% 6.78/2.01 % (633671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/2.01 % (633671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/2.01 % (633671)CaDiCaL version: 2.1.3
% 6.78/2.01 % (633671)Termination reason: Instruction limit
% 6.78/2.01 % (633671)Termination phase: Saturation
% 6.78/2.01 % (633671)Time elapsed: 0.168 s
% 6.78/2.01 % (633671)Peak memory usage: 89 MB
% 6.78/2.01 % (633671)Instructions burned: 190 (million)
% 6.78/2.01 % (633683)lrs+10_64_to=lpo:sil=8000:random_seed=3265985662:i=126:bd=preordered_2994 on theBenchmark for (2994ds/126Mi)
% 6.78/2.01 % (633648)Refutation found. Thanks to Tanya!
% 6.78/2.01 % SZS status Unsatisfiable for theBenchmark
% 6.78/2.01 % SZS output start Proof for theBenchmark
% See solution above
% 6.78/2.01 % (633648)------------------------------
% 6.78/2.01 % (633648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/2.01 % (633648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/2.01 % (633648)CaDiCaL version: 2.1.3
% 6.78/2.01 % (633648)Termination reason: Refutation
% 6.78/2.01 % (633648)Time elapsed: 0.468 s
% 6.78/2.01 % (633648)Peak memory usage: 129 MB
% 6.78/2.01 % (633648)Instructions burned: 1005 (million)
% 6.78/2.01 % (633648)------------------------------
% 6.78/2.01 % (633648)------------------------------
% 6.78/2.01 % (633598)Success in time 0.898 s
% 6.78/2.01 % Vampire exiting
%------------------------------------------------------------------------------