%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL023+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 : n005.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 12:33:49 PM UTC 2026
% Result : Theorem 6.96s 1.97s
% Output : Refutation 6.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 47 ( 47 unt; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 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 : 80 ( 77 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f14,conjecture,
! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1,X2] : composition(X0,meet(X1,X2)) != join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
composition(sK0,meet(sK1,sK2)) != join(composition(meet(sK0,converse(sK1)),meet(sK1,sK2)),composition(sK0,meet(sK1,sK2))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16]) ).
fof(f18,plain,
composition(sK0,meet(sK1,sK2)) != join(composition(meet(sK0,converse(sK1)),meet(sK1,sK2)),composition(sK0,meet(sK1,sK2))),
inference(cnf_transformation,[],[f17]) ).
fof(f21,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f24,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f25,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f26,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f27,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f28,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f29,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f30,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f31,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
composition(sK0,complement(join(complement(sK1),complement(sK2)))) != join(composition(complement(join(complement(sK0),complement(converse(sK1)))),complement(join(complement(sK1),complement(sK2)))),composition(sK0,complement(join(complement(sK1),complement(sK2))))),
inference(definition_unfolding,[],[f18,f28,f28,f28,f28]) ).
fof(f34,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(forward_demodulation,[],[f29,f31]) ).
fof(f35,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(forward_demodulation,[],[f21,f31]) ).
fof(f37,plain,
composition(sK0,complement(join(complement(sK1),complement(sK2)))) != join(composition(sK0,complement(join(complement(sK1),complement(sK2)))),composition(complement(join(complement(sK0),complement(converse(sK1)))),complement(join(complement(sK1),complement(sK2))))),
inference(forward_demodulation,[],[f32,f31]) ).
fof(f38,plain,
composition(sK0,complement(join(complement(sK1),complement(sK2)))) != composition(join(sK0,complement(join(complement(sK0),complement(converse(sK1))))),complement(join(complement(sK1),complement(sK2)))),
inference(forward_demodulation,[],[f37,f25]) ).
fof(f41,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f22,f24]) ).
fof(f48,plain,
! [X0,X1] : composition(X0,X1) = composition(X0,composition(one,X1)),
inference(superposition,[],[f27,f26]) ).
fof(f104,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(superposition,[],[f35,f24]) ).
fof(f128,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)),
inference(superposition,[],[f30,f34]) ).
fof(f161,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f41,f26]) ).
fof(f179,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f161,f24]) ).
fof(f196,plain,
! [X0] : composition(one,X0) = composition(converse(one),X0),
inference(superposition,[],[f48,f179]) ).
fof(f200,plain,
! [X0] : composition(one,X0) = X0,
inference(forward_demodulation,[],[f196,f179]) ).
fof(f1083,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(converse(one),X0))),
inference(superposition,[],[f104,f200]) ).
fof(f1097,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f1083,f179]) ).
fof(f2879,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(complement(X1))))) = join(complement(join(complement(X0),X1)),X0),
inference(superposition,[],[f128,f34]) ).
fof(f2882,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(X0,complement(join(complement(X0),complement(X1)))),
inference(superposition,[],[f128,f1097]) ).
fof(f2926,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(X1)))) = X0,
inference(forward_demodulation,[],[f2882,f34]) ).
fof(f2929,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(complement(X1))))) = join(X0,complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f2879,f31]) ).
fof(f2978,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f2929,f2926]) ).
fof(f4137,plain,
composition(sK0,complement(join(complement(sK1),complement(sK2)))) != composition(sK0,complement(join(complement(sK1),complement(sK2)))),
inference(superposition,[],[f38,f2978]) ).
fof(f4161,plain,
$false,
inference(trivial_inequality_removal,[],[f4137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL023+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 22:52:31 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 5.50/1.77 % (266267)Detected formulas, will run a generic FOF schedule.
% 5.50/1.77 % (266379)dis-21_1_sil=8000:lcm=predicate:random_seed=569520605: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)
% 5.50/1.77 % (266379)Refutation not found, incomplete strategy
% 5.50/1.77 % (266379)------------------------------
% 5.50/1.77 % (266379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.50/1.77 % (266379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.50/1.77 % (266379)CaDiCaL version: 2.1.3
% 5.50/1.77 % (266379)Termination reason: Refutation not found, incomplete strategy
% 5.50/1.77 % (266379)Time elapsed: 0.001 s
% 5.50/1.77 % (266379)Peak memory usage: 88 MB
% 5.50/1.77 % (266379)Instructions burned: 1 (million)
% 5.50/1.77 % (266374)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=739305519:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.50/1.77 % (266378)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1196418301:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.50/1.77 % (266377)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2209031776:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.50/1.77 % (266376)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=741207113:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.50/1.77 % (266375)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=2528669549:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.50/1.77 % (266376)Refutation not found, incomplete strategy
% 5.50/1.77 % (266376)------------------------------
% 5.50/1.77 % (266376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.50/1.77 % (266376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.50/1.77 % (266376)CaDiCaL version: 2.1.3
% 5.50/1.77 % (266376)Termination reason: Refutation not found, incomplete strategy
% 5.50/1.77 % (266376)Time elapsed: 0.002 s
% 5.50/1.77 % (266376)Peak memory usage: 88 MB
% 5.50/1.77 % (266376)Instructions burned: 1 (million)
% 5.50/1.77 % (266373)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=3127538547:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.50/1.77 % (266377)Instruction limit reached!
% 5.50/1.77 % (266377)------------------------------
% 5.50/1.77 % (266377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.50/1.77 % (266377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.50/1.77 % (266377)CaDiCaL version: 2.1.3
% 5.50/1.77 % (266377)Termination reason: Instruction limit
% 5.50/1.77 % (266377)Termination phase: Saturation
% 5.50/1.77 % (266377)Time elapsed: 0.086 s
% 5.50/1.77 % (266377)Peak memory usage: 88 MB
% 5.50/1.77 % (266377)Instructions burned: 119 (million)
% 5.50/1.77 % (266378)Instruction limit reached!
% 5.50/1.77 % (266378)------------------------------
% 5.50/1.77 % (266378)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.50/1.77 % (266378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.50/1.77 % (266378)CaDiCaL version: 2.1.3
% 5.50/1.77 % (266378)Termination reason: Instruction limit
% 5.50/1.77 % (266378)Termination phase: Saturation
% 5.50/1.77 % (266378)Time elapsed: 0.115 s
% 5.50/1.77 % (266378)Peak memory usage: 89 MB
% 5.50/1.77 % (266378)Instructions burned: 139 (million)
% 5.50/1.77 % (266379)------------------------------
% 5.50/1.77 % (266379)------------------------------
% 5.50/1.77 % (266414)lrs+10_1_sil=8000:sp=occurrence:random_seed=1631689001:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.50/1.77 % (266376)------------------------------
% 5.50/1.77 % (266376)------------------------------
% 5.50/1.77 % (266416)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3088687767:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.50/1.77 % (266422)lrs+1011_1_sil=32000:sp=occurrence:random_seed=795327011:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 5.50/1.77 % (266422)First to succeed.
% 5.50/1.77 % (266422)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-266267"
% 5.50/1.77 % (266416)Instruction limit reached!
% 6.96/1.97 % (266416)------------------------------
% 6.96/1.97 % (266416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.96/1.97 % (266416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.96/1.97 % (266416)CaDiCaL version: 2.1.3
% 6.96/1.97 % (266416)Termination reason: Instruction limit
% 6.96/1.97 % (266416)Termination phase: Saturation
% 6.96/1.97 % (266416)Time elapsed: 0.152 s
% 6.96/1.97 % (266416)Peak memory usage: 90 MB
% 6.96/1.97 % (266416)Instructions burned: 158 (million)
% 6.96/1.97 % (266414)Instruction limit reached!
% 6.96/1.97 % (266414)------------------------------
% 6.96/1.97 % (266414)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.96/1.97 % (266414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.96/1.97 % (266414)CaDiCaL version: 2.1.3
% 6.96/1.97 % (266414)Termination reason: Instruction limit
% 6.96/1.97 % (266414)Termination phase: Saturation
% 6.96/1.97 % (266414)Time elapsed: 0.276 s
% 6.96/1.97 % (266414)Peak memory usage: 91 MB
% 6.96/1.97 % (266414)Instructions burned: 286 (million)
% 6.96/1.97 % (266430)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3379696866:s2a=on:i=248:s2at=1.23:gtg=position_2994 on theBenchmark for (2994ds/248Mi)
% 6.96/1.97 % (266422)Refutation found. Thanks to Tanya!
% 6.96/1.97 % SZS status Theorem for theBenchmark
% 6.96/1.97 % SZS output start Proof for theBenchmark
% See solution above
% 6.96/1.97 % (266422)------------------------------
% 6.96/1.97 % (266422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.96/1.97 % (266422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.96/1.97 % (266422)CaDiCaL version: 2.1.3
% 6.96/1.97 % (266422)Termination reason: Refutation
% 6.96/1.97 % (266422)Time elapsed: 0.068 s
% 6.96/1.97 % (266422)Peak memory usage: 91 MB
% 6.96/1.97 % (266422)Instructions burned: 146 (million)
% 6.96/1.97 % (266422)------------------------------
% 6.96/1.97 % (266422)------------------------------
% 6.96/1.97 % (266267)Success in time 0.899 s
% 6.96/1.97 % Vampire exiting
%------------------------------------------------------------------------------