%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL001-1 : 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 : n002.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 2.83s 1.43s
% Output : Refutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 55 ( 55 unt; 1 def)
% Number of atoms : 55 ( 50 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f8,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
fof(f17,negated_conjecture,
join(zero,sk1) != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
sk1 != join(zero,sk1),
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f20,definition,
~ sP0(join(zero,sk1)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f21,plain,
sP0(sk1),
inference(inequality_splitting,[],[f18,f20]) ).
fof(f22,plain,
zero = complement(top),
inference(backward_demodulation,[],[f19,f15]) ).
fof(f23,plain,
~ sP0(join(complement(top),sk1)),
inference(backward_demodulation,[],[f20,f22]) ).
fof(f38,plain,
! [X0] : converse(X0) = composition(converse(one),converse(X0)),
inference(superposition,[],[f12,f8]) ).
fof(f53,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(superposition,[],[f38,f10]) ).
fof(f59,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f15]) ).
fof(f61,plain,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X1,join(X0,X2)),
inference(superposition,[],[f2,f1]) ).
fof(f76,plain,
one = converse(one),
inference(superposition,[],[f8,f53]) ).
fof(f79,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f53,f76]) ).
fof(f118,plain,
! [X0] : complement(X0) = join(composition(one,complement(composition(one,X0))),complement(X0)),
inference(superposition,[],[f14,f76]) ).
fof(f130,plain,
! [X0,X1] : complement(X0) = join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))),
inference(superposition,[],[f1,f14]) ).
fof(f134,plain,
! [X0] : complement(X0) = join(complement(composition(one,X0)),complement(X0)),
inference(forward_demodulation,[],[f118,f79]) ).
fof(f137,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f134,f79]) ).
fof(f141,plain,
! [X0] : join(complement(complement(X0)),complement(join(complement(X0),X0))) = X0,
inference(superposition,[],[f4,f137]) ).
fof(f145,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f4,f1]) ).
fof(f146,plain,
! [X0] : join(complement(join(complement(X0),complement(complement(X0)))),complement(complement(X0))) = X0,
inference(superposition,[],[f4,f137]) ).
fof(f158,plain,
! [X0] : join(complement(top),complement(complement(X0))) = X0,
inference(forward_demodulation,[],[f146,f15]) ).
fof(f493,plain,
! [X0] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(superposition,[],[f59,f137]) ).
fof(f496,plain,
! [X0] : join(top,X0) = join(top,complement(complement(X0))),
inference(superposition,[],[f59,f158]) ).
fof(f498,plain,
! [X0,X1] : join(top,X0) = join(X1,join(X0,complement(X1))),
inference(superposition,[],[f59,f1]) ).
fof(f500,plain,
! [X0] : join(top,complement(complement(X0))) = join(X0,top),
inference(superposition,[],[f59,f15]) ).
fof(f510,plain,
! [X0] : top = join(top,complement(X0)),
inference(forward_demodulation,[],[f493,f15]) ).
fof(f512,plain,
! [X0] : top = join(top,X0),
inference(backward_demodulation,[],[f496,f510]) ).
fof(f513,plain,
! [X0] : top = join(X0,top),
inference(backward_demodulation,[],[f500,f510]) ).
fof(f518,plain,
! [X0,X1] : top = join(X1,join(X0,complement(X1))),
inference(backward_demodulation,[],[f498,f512]) ).
fof(f638,plain,
! [X0,X1] : join(top,X1) = join(complement(X0),join(X0,X1)),
inference(superposition,[],[f61,f15]) ).
fof(f681,plain,
! [X0,X1] : top = join(complement(X0),join(X0,X1)),
inference(forward_demodulation,[],[f638,f512]) ).
fof(f847,plain,
! [X0] : top = join(complement(X0),X0),
inference(superposition,[],[f518,f158]) ).
fof(f874,plain,
! [X0] : join(complement(complement(X0)),complement(top)) = X0,
inference(backward_demodulation,[],[f141,f847]) ).
fof(f1073,plain,
! [X0,X1] : top = join(complement(composition(converse(X1),complement(composition(X1,X0)))),complement(X0)),
inference(superposition,[],[f681,f14]) ).
fof(f1658,plain,
! [X0] : complement(X0) = join(complement(X0),complement(join(complement(complement(X0)),top))),
inference(superposition,[],[f4,f874]) ).
fof(f1677,plain,
! [X0] : complement(X0) = join(complement(X0),complement(top)),
inference(forward_demodulation,[],[f1658,f513]) ).
fof(f1692,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f874,f1677]) ).
fof(f1732,plain,
! [X0,X1] : join(complement(join(complement(composition(converse(X1),complement(composition(X1,X0)))),complement(X0))),complement(complement(X0))) = X0,
inference(superposition,[],[f145,f130]) ).
fof(f1774,plain,
! [X0,X1] : join(complement(join(complement(composition(converse(X1),complement(composition(X1,X0)))),complement(X0))),X0) = X0,
inference(forward_demodulation,[],[f1732,f1692]) ).
fof(f1791,plain,
! [X0] : join(complement(top),X0) = X0,
inference(forward_demodulation,[],[f1774,f1073]) ).
fof(f1803,plain,
~ sP0(sk1),
inference(backward_demodulation,[],[f23,f1791]) ).
fof(f1804,plain,
$false,
inference(forward_subsumption_resolution,[],[f1803,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL001-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 % Computer : n002.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 22:52:51 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.48 Running first-order theorem proving
% 0.23/0.48 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
% 2.83/1.43 % (3973672)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.83/1.43 % (3973755)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2061818972:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.83/1.43 % (3973755)First to succeed.
% 2.83/1.43 % (3973755)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3973672"
% 2.83/1.43 % (3973757)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=815658528:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.83/1.43 % (3973754)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2799842202:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.83/1.43 % (3973751)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=3700399409:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.83/1.43 % (3973752)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=1769896541:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.83/1.43 % (3973760)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1151439642:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.83/1.43 % (3973759)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=336915591:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.83/1.43 % (3973757)Also succeeded, but the first one will report.
% 2.83/1.43 % (3973760)Also succeeded, but the first one will report.
% 2.83/1.43 % (3973755)Refutation found. Thanks to Tanya!
% 2.83/1.43 % SZS status Unsatisfiable for theBenchmark
% 2.83/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 2.83/1.43 % (3973755)------------------------------
% 2.83/1.43 % (3973755)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.43 % (3973755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.43 % (3973755)CaDiCaL version: 2.1.3
% 2.83/1.43 % (3973755)Termination reason: Refutation
% 2.83/1.43 % (3973755)Time elapsed: 0.029 s
% 2.83/1.43 % (3973755)Peak memory usage: 89 MB
% 2.83/1.43 % (3973755)Instructions burned: 81 (million)
% 2.83/1.43 % (3973755)------------------------------
% 2.83/1.43 % (3973755)------------------------------
% 2.83/1.43 % (3973672)Success in time 0.294 s
% 2.83/1.43 % Vampire exiting
%------------------------------------------------------------------------------