%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL002-1 : 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 : n018.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 12:33:36 PM UTC 2026
% Result : Unsatisfiable 3.03s 1.35s
% Output : Refutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 25 unt; 1 def)
% Number of atoms : 25 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
fof(f8,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
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(f13,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f15,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
fof(f17,negated_conjecture,
join(sk1,top) != top,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
top != join(sk1,top),
inference(reorient_equations,[],[f17]) ).
fof(f20,definition,
~ sP0(join(sk1,top)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f21,plain,
sP0(top),
inference(inequality_splitting,[],[f18,f20]) ).
fof(f44,plain,
! [X0] : converse(X0) = composition(converse(one),converse(X0)),
inference(superposition,[],[f12,f8]) ).
fof(f59,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(superposition,[],[f44,f10]) ).
fof(f65,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f15]) ).
fof(f84,plain,
one = converse(one),
inference(superposition,[],[f8,f59]) ).
fof(f87,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f59,f84]) ).
fof(f126,plain,
! [X0] : complement(X0) = join(composition(one,complement(composition(one,X0))),complement(X0)),
inference(superposition,[],[f14,f84]) ).
fof(f143,plain,
! [X0] : complement(X0) = join(complement(composition(one,X0)),complement(X0)),
inference(forward_demodulation,[],[f126,f87]) ).
fof(f146,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f143,f87]) ).
fof(f486,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(superposition,[],[f65,f146]) ).
fof(f488,plain,
! [X0] : join(top,complement(complement(X0))) = join(X0,top),
inference(superposition,[],[f65,f15]) ).
fof(f523,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[],[f486,f15]) ).
fof(f528,plain,
! [X0] : top = join(X0,top),
inference(backward_demodulation,[],[f488,f523]) ).
fof(f545,plain,
~ sP0(top),
inference(backward_demodulation,[],[f20,f528]) ).
fof(f551,plain,
$false,
inference(forward_subsumption_resolution,[],[f545,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL002-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n018.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 22:52:24 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 3.03/1.35 % (2815403)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.03/1.35 % (2815512)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1609470907:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.03/1.35 % (2815512)First to succeed.
% 3.03/1.35 % (2815512)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2815403"
% 3.03/1.35 % (2815509)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3201642983:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.03/1.35 % (2815513)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=470795603:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.03/1.35 % (2815510)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3616861245:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.03/1.35 % (2815514)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3423613370:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.03/1.35 % (2815511)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2522390573:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.03/1.35 % (2815515)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1615690216:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.03/1.35 % (2815513)Also succeeded, but the first one will report.
% 3.03/1.35 % (2815515)Also succeeded, but the first one will report.
% 3.03/1.35 % (2815514)Also succeeded, but the first one will report.
% 3.03/1.35 % (2815512)Refutation found. Thanks to Tanya!
% 3.03/1.35 % SZS status Unsatisfiable for theBenchmark
% 3.03/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.03/1.35 % (2815512)------------------------------
% 3.03/1.35 % (2815512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.03/1.35 % (2815512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.35 % (2815512)CaDiCaL version: 2.1.3
% 3.03/1.35 % (2815512)Termination reason: Refutation
% 3.03/1.35 % (2815512)Time elapsed: 0.010 s
% 3.03/1.35 % (2815512)Peak memory usage: 88 MB
% 3.03/1.35 % (2815512)Instructions burned: 26 (million)
% 3.03/1.35 % (2815512)------------------------------
% 3.03/1.35 % (2815512)------------------------------
% 3.03/1.35 % (2815403)Success in time 0.352 s
% 3.03/1.35 % Vampire exiting
%------------------------------------------------------------------------------