%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LAT012-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 11:45:49 AM UTC 2026
% Result : Unsatisfiable 4.02s 1.55s
% Output : Refutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 63 ( 63 unt; 10 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 110 ( 110 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : join(X0,meet(X1,meet(X0,X2))) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mckenzie1) ).
fof(f2,negated_conjecture,
! [X2,X0,X1] : meet(X0,join(X1,join(X0,X2))) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mckenzie2) ).
fof(f3,negated_conjecture,
! [X2,X0,X1] : join(join(meet(X0,X1),meet(X1,X2)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mckenzie3) ).
fof(f4,negated_conjecture,
! [X2,X0,X1] : meet(meet(join(X0,X1),join(X1,X2)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mckenzie4) ).
fof(f5,negated_conjecture,
meet(b,a) != meet(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity_of_meet) ).
fof(f6,definition,
! [X2,X0,X1] : sF0(X1,X0,X2) = meet(X1,meet(X0,X2)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f7,plain,
! [X2,X0,X1] : meet(X1,meet(X0,X2)) = sF0(X1,X0,X2),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
! [X2,X0,X1] : sF1(X0,X1,X2) = join(X0,sF0(X1,X0,X2)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f9,plain,
! [X2,X0,X1] : join(X0,sF0(X1,X0,X2)) = sF1(X0,X1,X2),
inference(reorient_equations,[],[f8]) ).
fof(f10,plain,
! [X2,X0,X1] : sF1(X0,X1,X2) = X0,
inference(definition_folding,[],[f1,f9,f7]) ).
fof(f11,definition,
! [X2,X0,X1] : sF2(X1,X0,X2) = join(X1,join(X0,X2)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f12,plain,
! [X2,X0,X1] : join(X1,join(X0,X2)) = sF2(X1,X0,X2),
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
! [X2,X0,X1] : sF3(X0,X1,X2) = meet(X0,sF2(X1,X0,X2)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f14,plain,
! [X2,X0,X1] : meet(X0,sF2(X1,X0,X2)) = sF3(X0,X1,X2),
inference(reorient_equations,[],[f13]) ).
fof(f15,plain,
! [X2,X0,X1] : sF3(X0,X1,X2) = X0,
inference(definition_folding,[],[f2,f14,f12]) ).
fof(f16,definition,
! [X2,X0,X1] : sF4(X0,X1,X2) = join(meet(X0,X1),meet(X1,X2)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f17,plain,
! [X2,X0,X1] : join(meet(X0,X1),meet(X1,X2)) = sF4(X0,X1,X2),
inference(reorient_equations,[],[f16]) ).
fof(f18,definition,
! [X2,X0,X1] : sF5(X0,X1,X2) = join(sF4(X0,X1,X2),X1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f19,plain,
! [X2,X0,X1] : join(sF4(X0,X1,X2),X1) = sF5(X0,X1,X2),
inference(reorient_equations,[],[f18]) ).
fof(f20,plain,
! [X2,X0,X1] : sF5(X0,X1,X2) = X1,
inference(definition_folding,[],[f3,f19,f17]) ).
fof(f21,definition,
! [X2,X0,X1] : sF6(X0,X1,X2) = meet(join(X0,X1),join(X1,X2)),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f22,plain,
! [X2,X0,X1] : meet(join(X0,X1),join(X1,X2)) = sF6(X0,X1,X2),
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
! [X2,X0,X1] : sF7(X0,X1,X2) = meet(sF6(X0,X1,X2),X1),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f24,plain,
! [X2,X0,X1] : meet(sF6(X0,X1,X2),X1) = sF7(X0,X1,X2),
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
! [X2,X0,X1] : sF7(X0,X1,X2) = X1,
inference(definition_folding,[],[f4,f24,f22]) ).
fof(f26,definition,
sF8 = meet(b,a),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f27,plain,
meet(b,a) = sF8,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF9 = meet(a,b),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f29,plain,
meet(a,b) = sF9,
inference(reorient_equations,[],[f28]) ).
fof(f30,plain,
sF8 != sF9,
inference(definition_folding,[],[f5,f29,f27]) ).
fof(f31,plain,
! [X2,X0,X1] : meet(sF6(X0,X1,X2),X1) = X1,
inference(forward_demodulation,[],[f25,f24]) ).
fof(f32,plain,
! [X2,X0,X1] : join(sF4(X0,X1,X2),X1) = X1,
inference(forward_demodulation,[],[f20,f19]) ).
fof(f33,plain,
! [X2,X0,X1] : meet(X0,sF2(X1,X0,X2)) = X0,
inference(forward_demodulation,[],[f15,f14]) ).
fof(f34,plain,
! [X2,X0,X1] : join(X0,sF0(X1,X0,X2)) = X0,
inference(forward_demodulation,[],[f10,f9]) ).
fof(f35,plain,
! [X2,X0,X1] : meet(meet(join(X0,X1),join(X1,X2)),X1) = X1,
inference(forward_demodulation,[],[f31,f22]) ).
fof(f36,plain,
! [X2,X0,X1] : join(join(meet(X0,X1),meet(X1,X2)),X1) = X1,
inference(forward_demodulation,[],[f32,f17]) ).
fof(f37,plain,
! [X2,X0,X1] : meet(X0,join(X1,join(X0,X2))) = X0,
inference(forward_demodulation,[],[f33,f12]) ).
fof(f38,plain,
! [X2,X0,X1] : join(X0,meet(X1,meet(X0,X2))) = X0,
inference(forward_demodulation,[],[f34,f7]) ).
fof(f39,plain,
! [X0] : a = join(a,meet(X0,sF9)),
inference(superposition,[],[f38,f29]) ).
fof(f40,plain,
! [X0] : b = join(b,meet(X0,sF8)),
inference(superposition,[],[f38,f27]) ).
fof(f41,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = X0,
inference(superposition,[],[f38,f37]) ).
fof(f42,plain,
! [X0,X1] : meet(X0,join(X1,X0)) = X0,
inference(superposition,[],[f37,f38]) ).
fof(f45,plain,
b = join(b,sF9),
inference(superposition,[],[f41,f29]) ).
fof(f46,plain,
a = join(a,sF8),
inference(superposition,[],[f41,f27]) ).
fof(f67,plain,
! [X0] : sF9 = meet(meet(b,join(sF9,X0)),sF9),
inference(superposition,[],[f35,f45]) ).
fof(f68,plain,
! [X0] : sF8 = meet(meet(a,join(sF8,X0)),sF8),
inference(superposition,[],[f35,f46]) ).
fof(f79,plain,
! [X0,X1] : join(X0,meet(X0,X1)) = X0,
inference(superposition,[],[f38,f35]) ).
fof(f80,plain,
b = join(b,sF8),
inference(superposition,[],[f40,f35]) ).
fof(f81,plain,
a = join(a,sF9),
inference(superposition,[],[f39,f35]) ).
fof(f89,plain,
sF8 = meet(sF8,b),
inference(superposition,[],[f42,f80]) ).
fof(f93,plain,
sF9 = meet(sF9,a),
inference(superposition,[],[f42,f81]) ).
fof(f150,plain,
! [X0,X1] : meet(X0,X1) = meet(meet(X0,X1),X0),
inference(superposition,[],[f42,f79]) ).
fof(f183,plain,
! [X0,X1] : join(meet(X0,X1),X1) = X1,
inference(superposition,[],[f36,f38]) ).
fof(f212,plain,
b = join(sF8,b),
inference(superposition,[],[f183,f89]) ).
fof(f214,plain,
a = join(sF9,a),
inference(superposition,[],[f183,f93]) ).
fof(f2175,plain,
sF9 = meet(meet(b,a),sF9),
inference(superposition,[],[f67,f214]) ).
fof(f2201,plain,
sF9 = meet(sF8,sF9),
inference(forward_demodulation,[],[f2175,f27]) ).
fof(f2227,plain,
sF9 = meet(sF9,sF8),
inference(superposition,[],[f150,f2201]) ).
fof(f3079,plain,
sF8 = meet(meet(a,b),sF8),
inference(superposition,[],[f68,f212]) ).
fof(f3112,plain,
sF8 = meet(sF9,sF8),
inference(forward_demodulation,[],[f3079,f29]) ).
fof(f3120,plain,
sF8 = sF9,
inference(forward_demodulation,[],[f3112,f2227]) ).
fof(f3121,plain,
sF8 != sF8,
inference(superposition,[],[f30,f3120]) ).
fof(f3167,plain,
$false,
inference(trivial_inequality_removal,[],[f3121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT012-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 13:51:50 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 4.02/1.55 % (2565790)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.02/1.55 % (2565797)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4191215376:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.02/1.55 % (2565801)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3547642726:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.02/1.55 % (2565798)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3941052875:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.02/1.55 % (2565796)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=2630795316:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.02/1.55 % (2565799)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2702749397:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.02/1.55 % (2565800)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3939785317:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.02/1.55 % (2565795)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=2905237661:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.02/1.55 % (2565799)First to succeed.
% 4.02/1.55 % (2565799)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2565790"
% 4.02/1.55 % (2565798)Instruction limit reached!
% 4.02/1.55 % (2565798)------------------------------
% 4.02/1.55 % (2565798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.55 % (2565798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.55 % (2565798)CaDiCaL version: 2.1.3
% 4.02/1.55 % (2565798)Termination reason: Instruction limit
% 4.02/1.55 % (2565798)Termination phase: Saturation
% 4.02/1.55 % (2565798)Time elapsed: 0.088 s
% 4.02/1.55 % (2565798)Peak memory usage: 89 MB
% 4.02/1.55 % (2565798)Instructions burned: 137 (million)
% 4.02/1.55 % (2565800)Instruction limit reached!
% 4.02/1.55 % (2565800)------------------------------
% 4.02/1.55 % (2565800)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.55 % (2565800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.55 % (2565800)CaDiCaL version: 2.1.3
% 4.02/1.55 % (2565800)Termination reason: Instruction limit
% 4.02/1.55 % (2565800)Termination phase: Saturation
% 4.02/1.55 % (2565800)Time elapsed: 0.170 s
% 4.02/1.55 % (2565800)Peak memory usage: 90 MB
% 4.02/1.55 % (2565800)Instructions burned: 257 (million)
% 4.02/1.55 % (2565809)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2676529748:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 4.02/1.55 % (2565799)Refutation found. Thanks to Tanya!
% 4.02/1.55 % SZS status Unsatisfiable for theBenchmark
% 4.02/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 4.02/1.55 % (2565799)------------------------------
% 4.02/1.55 % (2565799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.55 % (2565799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.55 % (2565799)CaDiCaL version: 2.1.3
% 4.02/1.55 % (2565799)Termination reason: Refutation
% 4.02/1.55 % (2565799)Time elapsed: 0.057 s
% 4.02/1.55 % (2565799)Peak memory usage: 89 MB
% 4.02/1.55 % (2565799)Instructions burned: 96 (million)
% 4.02/1.55 % (2565799)------------------------------
% 4.02/1.55 % (2565799)------------------------------
% 4.02/1.55 % (2565790)Success in time 0.485 s
% 4.02/1.55 % Vampire exiting
%------------------------------------------------------------------------------