%------------------------------------------------------------------------------
% 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 : n004.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 : Theorem 2.71s 1.36s
% Output : Refutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 61 unt; 0 def)
% Number of atoms : 61 ( 60 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 82 ( 81 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
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) ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero) ).
fof(f14,conjecture,
! [X0] : join(zero,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0] : join(zero,X0) = X0,
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0] : join(zero,X0) != X0,
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
sK0 != join(zero,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f16]) ).
fof(f18,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f20,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f22,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f23,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f25,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f27,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f29,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f30,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f31,plain,
sK0 != join(zero,sK0),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
! [X0] : meet(X0,complement(X0)) = complement(top),
inference(superposition,[],[f21,f29]) ).
fof(f35,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X1,X0),
inference(superposition,[],[f21,f18]) ).
fof(f40,plain,
zero = complement(top),
inference(forward_demodulation,[],[f34,f30]) ).
fof(f54,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f27,f25]) ).
fof(f69,plain,
! [X0,X1] : composition(X0,X1) = composition(X0,composition(one,X1)),
inference(superposition,[],[f22,f23]) ).
fof(f112,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(forward_demodulation,[],[f28,f18]) ).
fof(f123,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(superposition,[],[f112,f25]) ).
fof(f146,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(forward_demodulation,[],[f20,f18]) ).
fof(f147,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),meet(X0,X1)) = X0,
inference(forward_demodulation,[],[f146,f21]) ).
fof(f148,plain,
! [X0,X1] : join(meet(X0,X1),complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f147,f18]) ).
fof(f158,plain,
! [X0] : join(meet(X0,complement(complement(X0))),complement(top)) = X0,
inference(superposition,[],[f148,f29]) ).
fof(f159,plain,
! [X0,X1] : join(meet(X1,X0),complement(join(X0,complement(X1)))) = X1,
inference(superposition,[],[f148,f18]) ).
fof(f161,plain,
! [X0,X1] : join(meet(X0,complement(X1)),meet(X0,X1)) = X0,
inference(superposition,[],[f148,f21]) ).
fof(f163,plain,
! [X0,X1] : join(meet(X0,X1),meet(X0,complement(X1))) = X0,
inference(forward_demodulation,[],[f161,f18]) ).
fof(f164,plain,
! [X0] : join(complement(top),meet(X0,complement(complement(X0)))) = X0,
inference(forward_demodulation,[],[f158,f18]) ).
fof(f172,plain,
! [X0] : join(zero,meet(X0,complement(complement(X0)))) = X0,
inference(forward_demodulation,[],[f164,f40]) ).
fof(f199,plain,
! [X0] : complement(top) = meet(complement(X0),X0),
inference(superposition,[],[f35,f29]) ).
fof(f202,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(superposition,[],[f35,f21]) ).
fof(f218,plain,
! [X0] : zero = meet(complement(X0),X0),
inference(forward_demodulation,[],[f199,f40]) ).
fof(f455,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f54,f23]) ).
fof(f478,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f455,f25]) ).
fof(f497,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(superposition,[],[f69,f478]) ).
fof(f501,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[],[f497,f478]) ).
fof(f633,plain,
! [X0] : complement(complement(X0)) = join(meet(complement(complement(X0)),X0),zero),
inference(superposition,[],[f163,f218]) ).
fof(f637,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(complement(complement(X0)),X0)),
inference(forward_demodulation,[],[f633,f18]) ).
fof(f646,plain,
! [X0] : complement(complement(X0)) = join(zero,meet(X0,complement(complement(X0)))),
inference(forward_demodulation,[],[f637,f202]) ).
fof(f647,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f646,f172]) ).
fof(f1243,plain,
! [X0] : complement(X0) = join(complement(X0),composition(one,complement(X0))),
inference(superposition,[],[f123,f478]) ).
fof(f1264,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f1243,f501]) ).
fof(f1674,plain,
! [X0] : join(meet(X0,complement(X0)),complement(complement(X0))) = X0,
inference(superposition,[],[f159,f1264]) ).
fof(f1681,plain,
! [X0] : join(complement(complement(X0)),meet(X0,complement(X0))) = X0,
inference(forward_demodulation,[],[f1674,f18]) ).
fof(f1689,plain,
! [X0] : join(complement(complement(X0)),zero) = X0,
inference(forward_demodulation,[],[f1681,f30]) ).
fof(f1691,plain,
! [X0] : join(zero,complement(complement(X0))) = X0,
inference(forward_demodulation,[],[f1689,f18]) ).
fof(f1693,plain,
! [X0] : join(zero,X0) = X0,
inference(forward_demodulation,[],[f1691,f647]) ).
fof(f2299,plain,
sK0 != sK0,
inference(superposition,[],[f31,f1693]) ).
fof(f2319,plain,
$false,
inference(trivial_inequality_removal,[],[f2299]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL001+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n004.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 22:50:07 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 2.71/1.36 % (3971016)Detected formulas, will run a generic FOF schedule.
% 2.71/1.36 % (3971119)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1549316299:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.36 % (3971119)Refutation not found, incomplete strategy
% 2.71/1.36 % (3971119)------------------------------
% 2.71/1.36 % (3971119)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.36 % (3971119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.36 % (3971119)CaDiCaL version: 2.1.3
% 2.71/1.36 % (3971119)Termination reason: Refutation not found, incomplete strategy
% 2.71/1.36 % (3971119)Time elapsed: 0.001 s
% 2.71/1.36 % (3971119)Peak memory usage: 88 MB
% 2.71/1.36 % (3971116)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=3586699276:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.36 % (3971121)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1286170926:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.36 % (3971120)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2747121144:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.36 % (3971117)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=552735721:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.36 % (3971122)dis-21_1_sil=8000:lcm=predicate:random_seed=1443108779: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)
% 2.71/1.36 % (3971118)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=679406042:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.36 % (3971122)Refutation not found, incomplete strategy
% 2.71/1.36 % (3971122)------------------------------
% 2.71/1.36 % (3971122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.36 % (3971122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.36 % (3971122)CaDiCaL version: 2.1.3
% 2.71/1.36 % (3971122)Termination reason: Refutation not found, incomplete strategy
% 2.71/1.36 % (3971122)Time elapsed: 0.001 s
% 2.71/1.36 % (3971122)Peak memory usage: 88 MB
% 2.71/1.36 % (3971122)Instructions burned: 1 (million)
% 2.71/1.36 % (3971121)First to succeed.
% 2.71/1.36 % (3971121)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3971016"
% 2.71/1.36 % (3971120)Instruction limit reached!
% 2.71/1.36 % (3971120)------------------------------
% 2.71/1.36 % (3971120)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.36 % (3971120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.36 % (3971120)CaDiCaL version: 2.1.3
% 2.71/1.36 % (3971120)Termination reason: Instruction limit
% 2.71/1.36 % (3971120)Termination phase: Saturation
% 2.71/1.36 % (3971120)Time elapsed: 0.063 s
% 2.71/1.36 % (3971120)Peak memory usage: 89 MB
% 2.71/1.36 % (3971120)Instructions burned: 119 (million)
% 2.71/1.36 % (3971119)------------------------------
% 2.71/1.36 % (3971119)------------------------------
% 2.71/1.36 % (3971130)lrs+10_1_sil=8000:sp=occurrence:random_seed=2813338194:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.71/1.36 % (3971122)------------------------------
% 2.71/1.36 % (3971122)------------------------------
% 2.71/1.36 % (3971131)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2029962551:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.71/1.36 % (3971130)Also succeeded, but the first one will report.
% 2.71/1.36 % (3971131)Instruction limit reached!
% 2.71/1.36 % (3971131)------------------------------
% 2.71/1.36 % (3971131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.36 % (3971131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.36 % (3971131)CaDiCaL version: 2.1.3
% 2.71/1.36 % (3971131)Termination reason: Instruction limit
% 2.71/1.36 % (3971131)Termination phase: Saturation
% 2.71/1.36 % (3971131)Time elapsed: 0.039 s
% 2.71/1.36 % (3971131)Peak memory usage: 88 MB
% 2.71/1.36 % (3971131)Instructions burned: 160 (million)
% 2.71/1.36 % (3971121)Refutation found. Thanks to Tanya!
% 2.71/1.36 % SZS status Theorem for theBenchmark
% 3.93/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.93/1.46 % (3971121)------------------------------
% 3.93/1.46 % (3971121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.46 % (3971121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.46 % (3971121)CaDiCaL version: 2.1.3
% 3.93/1.46 % (3971121)Termination reason: Refutation
% 3.93/1.46 % (3971121)Time elapsed: 0.052 s
% 3.93/1.46 % (3971121)Peak memory usage: 90 MB
% 3.93/1.46 % (3971121)Instructions burned: 87 (million)
% 3.93/1.46 % (3971121)------------------------------
% 3.93/1.46 % (3971121)------------------------------
% 3.93/1.46 % (3971016)Success in time 0.484 s
% 3.93/1.46 % Vampire exiting
%------------------------------------------------------------------------------