%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LAT040-1 : TPTP v9.3.1. Released v2.4.0.
% 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 11:45:53 AM UTC 2026
% Result : Unsatisfiable 2.24s 1.14s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 16
% Syntax : Number of formulae : 101 ( 101 unt; 4 def)
% Number of atoms : 101 ( 100 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 54 ( 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : meet(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).
fof(f2,axiom,
! [X0] : join(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_join) ).
fof(f3,axiom,
! [X0,X1] : meet(X0,join(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
fof(f4,axiom,
! [X0,X1] : join(X0,meet(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
fof(f6,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
fof(f7,axiom,
! [X2,X0,X1] : meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_meet) ).
fof(f9,axiom,
! [X2,X0,X1] : join(X0,meet(X1,X2)) = meet(join(X0,X1),join(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dist_join) ).
fof(f10,axiom,
! [X2,X0,X1] : meet(X0,join(X1,X2)) = join(meet(X0,X1),meet(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dist_meet) ).
fof(f11,negated_conjecture,
join(xx,yy) = join(xx,zz),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs1) ).
fof(f12,negated_conjecture,
meet(xx,yy) = meet(xx,zz),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs2) ).
fof(f13,negated_conjecture,
yy != zz,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rhs) ).
fof(f14,definition,
sF0 = join(xx,yy),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f15,plain,
join(xx,yy) = sF0,
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
sF1 = join(xx,zz),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f17,plain,
join(xx,zz) = sF1,
inference(reorient_equations,[],[f16]) ).
fof(f18,plain,
sF0 = sF1,
inference(definition_folding,[],[f11,f17,f15]) ).
fof(f19,definition,
sF2 = meet(xx,yy),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f20,plain,
meet(xx,yy) = sF2,
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
sF3 = meet(xx,zz),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f22,plain,
meet(xx,zz) = sF3,
inference(reorient_equations,[],[f21]) ).
fof(f23,plain,
sF2 = sF3,
inference(definition_folding,[],[f12,f22,f20]) ).
fof(f24,plain,
! [X0] : meet(join(X0,xx),join(X0,zz)) = join(X0,sF3),
inference(superposition,[],[f9,f22]) ).
fof(f25,plain,
! [X0] : meet(join(X0,xx),join(X0,yy)) = join(X0,sF2),
inference(superposition,[],[f9,f20]) ).
fof(f52,plain,
! [X0] : meet(join(X0,xx),join(X0,zz)) = join(X0,sF2),
inference(forward_demodulation,[],[f24,f23]) ).
fof(f77,plain,
sF2 = meet(join(sF2,xx),join(sF2,zz)),
inference(superposition,[],[f2,f52]) ).
fof(f81,plain,
! [X0] : meet(X0,meet(join(X0,xx),join(X0,zz))) = X0,
inference(superposition,[],[f3,f52]) ).
fof(f84,plain,
sF2 = meet(join(sF2,xx),join(zz,sF2)),
inference(forward_demodulation,[],[f77,f6]) ).
fof(f88,plain,
sF2 = meet(join(zz,sF2),join(sF2,xx)),
inference(forward_demodulation,[],[f84,f5]) ).
fof(f92,plain,
sF2 = meet(join(zz,sF2),join(xx,sF2)),
inference(forward_demodulation,[],[f88,f6]) ).
fof(f96,plain,
sF2 = meet(join(xx,sF2),join(zz,sF2)),
inference(forward_demodulation,[],[f92,f5]) ).
fof(f100,plain,
sF2 = meet(join(xx,sF2),meet(join(zz,xx),join(zz,zz))),
inference(forward_demodulation,[],[f96,f52]) ).
fof(f104,plain,
sF2 = meet(join(xx,sF2),meet(join(zz,xx),zz)),
inference(forward_demodulation,[],[f100,f2]) ).
fof(f107,plain,
sF2 = meet(join(xx,sF2),meet(zz,join(zz,xx))),
inference(forward_demodulation,[],[f104,f5]) ).
fof(f109,plain,
sF2 = meet(join(xx,sF2),zz),
inference(forward_demodulation,[],[f107,f3]) ).
fof(f111,plain,
sF2 = meet(zz,join(xx,sF2)),
inference(forward_demodulation,[],[f109,f5]) ).
fof(f113,plain,
sF2 = meet(zz,meet(join(xx,xx),join(xx,zz))),
inference(forward_demodulation,[],[f111,f52]) ).
fof(f115,plain,
sF2 = meet(zz,meet(join(xx,xx),sF1)),
inference(forward_demodulation,[],[f113,f17]) ).
fof(f117,plain,
sF2 = meet(zz,meet(sF1,join(xx,xx))),
inference(forward_demodulation,[],[f115,f5]) ).
fof(f119,plain,
sF2 = meet(zz,meet(sF1,xx)),
inference(forward_demodulation,[],[f117,f2]) ).
fof(f121,plain,
sF2 = meet(zz,meet(xx,sF1)),
inference(forward_demodulation,[],[f119,f5]) ).
fof(f123,plain,
sF2 = meet(zz,meet(xx,sF0)),
inference(forward_demodulation,[],[f121,f18]) ).
fof(f126,plain,
! [X0] : meet(zz,meet(meet(xx,sF0),X0)) = meet(sF2,X0),
inference(superposition,[],[f7,f123]) ).
fof(f129,plain,
! [X0] : meet(sF2,X0) = meet(zz,meet(xx,meet(sF0,X0))),
inference(forward_demodulation,[],[f126,f7]) ).
fof(f186,plain,
! [X0] : meet(X0,meet(join(xx,X0),join(X0,zz))) = X0,
inference(superposition,[],[f81,f6]) ).
fof(f194,plain,
xx = meet(xx,meet(join(xx,xx),sF1)),
inference(superposition,[],[f81,f17]) ).
fof(f207,plain,
xx = meet(xx,meet(sF1,join(xx,xx))),
inference(forward_demodulation,[],[f194,f5]) ).
fof(f216,plain,
xx = meet(xx,meet(sF1,xx)),
inference(forward_demodulation,[],[f207,f2]) ).
fof(f221,plain,
xx = meet(xx,meet(xx,sF1)),
inference(forward_demodulation,[],[f216,f5]) ).
fof(f224,plain,
xx = meet(xx,meet(xx,sF0)),
inference(forward_demodulation,[],[f221,f18]) ).
fof(f299,plain,
! [X2,X0,X1] : meet(X0,join(X1,X2)) = meet(join(meet(X0,X1),X0),join(meet(X0,X1),X2)),
inference(forward_demodulation,[],[f10,f9]) ).
fof(f300,plain,
! [X2,X0,X1] : meet(X0,join(X1,X2)) = meet(join(X0,meet(X0,X1)),join(meet(X0,X1),X2)),
inference(forward_demodulation,[],[f299,f6]) ).
fof(f301,plain,
! [X2,X0,X1] : meet(X0,join(X1,X2)) = meet(X0,join(meet(X0,X1),X2)),
inference(forward_demodulation,[],[f300,f4]) ).
fof(f304,plain,
sF2 = meet(zz,meet(xx,meet(sF0,sF2))),
inference(superposition,[],[f129,f1]) ).
fof(f305,plain,
! [X0] : meet(zz,meet(xx,meet(sF0,X0))) = meet(X0,sF2),
inference(superposition,[],[f129,f5]) ).
fof(f865,plain,
! [X0] : meet(xx,join(zz,X0)) = meet(xx,join(sF3,X0)),
inference(superposition,[],[f301,f22]) ).
fof(f867,plain,
! [X0] : meet(xx,join(meet(xx,sF0),X0)) = meet(xx,join(xx,X0)),
inference(superposition,[],[f301,f224]) ).
fof(f871,plain,
! [X0,X1] : meet(X0,join(X1,meet(X0,X1))) = meet(X0,meet(X0,X1)),
inference(superposition,[],[f301,f2]) ).
fof(f898,plain,
! [X0,X1] : meet(X0,meet(join(X1,X0),join(X1,X1))) = meet(X0,meet(X0,X1)),
inference(forward_demodulation,[],[f871,f9]) ).
fof(f900,plain,
! [X0] : xx = meet(xx,join(meet(xx,sF0),X0)),
inference(forward_demodulation,[],[f867,f3]) ).
fof(f901,plain,
! [X0] : meet(xx,join(zz,X0)) = meet(xx,join(sF2,X0)),
inference(forward_demodulation,[],[f865,f23]) ).
fof(f917,plain,
! [X0,X1] : meet(X0,meet(join(X1,X0),X1)) = meet(X0,meet(X0,X1)),
inference(forward_demodulation,[],[f898,f2]) ).
fof(f919,plain,
! [X0] : xx = meet(xx,join(sF0,X0)),
inference(forward_demodulation,[],[f900,f301]) ).
fof(f930,plain,
! [X0,X1] : meet(X0,meet(X1,join(X1,X0))) = meet(X0,meet(X0,X1)),
inference(forward_demodulation,[],[f917,f5]) ).
fof(f934,plain,
! [X0,X1] : meet(X0,X1) = meet(X0,meet(X0,X1)),
inference(forward_demodulation,[],[f930,f3]) ).
fof(f940,plain,
xx = meet(xx,sF0),
inference(superposition,[],[f919,f2]) ).
fof(f961,plain,
! [X0] : meet(xx,meet(sF0,X0)) = meet(xx,X0),
inference(superposition,[],[f7,f940]) ).
fof(f1088,plain,
sF2 = meet(zz,meet(xx,sF2)),
inference(superposition,[],[f304,f961]) ).
fof(f1200,plain,
meet(xx,sF2) = meet(xx,join(zz,sF2)),
inference(superposition,[],[f901,f2]) ).
fof(f1234,plain,
meet(xx,sF2) = meet(xx,meet(join(zz,xx),join(zz,zz))),
inference(forward_demodulation,[],[f1200,f52]) ).
fof(f1239,plain,
meet(xx,sF2) = meet(xx,meet(join(zz,xx),zz)),
inference(forward_demodulation,[],[f1234,f2]) ).
fof(f1244,plain,
meet(xx,sF2) = meet(xx,meet(zz,join(zz,xx))),
inference(forward_demodulation,[],[f1239,f5]) ).
fof(f1248,plain,
meet(xx,zz) = meet(xx,sF2),
inference(forward_demodulation,[],[f1244,f3]) ).
fof(f1252,plain,
sF3 = meet(xx,sF2),
inference(forward_demodulation,[],[f1248,f22]) ).
fof(f1256,plain,
sF2 = meet(xx,sF2),
inference(forward_demodulation,[],[f1252,f23]) ).
fof(f1279,plain,
sF2 = meet(zz,sF2),
inference(superposition,[],[f1088,f1256]) ).
fof(f1452,plain,
zz = meet(zz,meet(join(xx,zz),zz)),
inference(superposition,[],[f186,f2]) ).
fof(f1485,plain,
zz = meet(zz,meet(zz,join(xx,zz))),
inference(forward_demodulation,[],[f1452,f5]) ).
fof(f1501,plain,
zz = meet(zz,join(xx,zz)),
inference(forward_demodulation,[],[f1485,f934]) ).
fof(f1513,plain,
zz = meet(zz,sF1),
inference(forward_demodulation,[],[f1501,f17]) ).
fof(f1524,plain,
zz = meet(zz,sF0),
inference(forward_demodulation,[],[f1513,f18]) ).
fof(f2291,plain,
! [X0] : meet(join(X0,xx),join(X0,zz)) = meet(join(X0,xx),join(X0,yy)),
inference(forward_demodulation,[],[f25,f52]) ).
fof(f2293,plain,
! [X0] : meet(X0,sF2) = meet(zz,meet(xx,X0)),
inference(forward_demodulation,[],[f305,f961]) ).
fof(f2299,plain,
meet(zz,sF2) = meet(yy,sF2),
inference(superposition,[],[f2293,f20]) ).
fof(f2338,plain,
sF2 = meet(yy,sF2),
inference(forward_demodulation,[],[f2299,f1279]) ).
fof(f2368,plain,
yy = join(yy,sF2),
inference(superposition,[],[f4,f2338]) ).
fof(f2374,plain,
yy = meet(join(yy,xx),join(yy,zz)),
inference(forward_demodulation,[],[f2368,f52]) ).
fof(f2376,plain,
yy = meet(join(xx,yy),join(yy,zz)),
inference(forward_demodulation,[],[f2374,f6]) ).
fof(f2377,plain,
yy = meet(sF0,join(yy,zz)),
inference(forward_demodulation,[],[f2376,f15]) ).
fof(f2616,plain,
meet(join(zz,xx),zz) = meet(join(zz,xx),join(zz,yy)),
inference(superposition,[],[f2291,f2]) ).
fof(f2646,plain,
meet(join(zz,xx),zz) = meet(join(zz,xx),join(yy,zz)),
inference(forward_demodulation,[],[f2616,f6]) ).
fof(f2661,plain,
meet(join(zz,xx),zz) = meet(join(yy,zz),join(zz,xx)),
inference(forward_demodulation,[],[f2646,f5]) ).
fof(f2674,plain,
meet(join(xx,zz),zz) = meet(join(yy,zz),join(xx,zz)),
inference(forward_demodulation,[],[f2661,f6]) ).
fof(f2685,plain,
meet(join(xx,zz),zz) = meet(join(xx,zz),join(yy,zz)),
inference(forward_demodulation,[],[f2674,f5]) ).
fof(f2695,plain,
meet(sF1,zz) = meet(sF1,join(yy,zz)),
inference(forward_demodulation,[],[f2685,f17]) ).
fof(f2705,plain,
meet(sF0,join(yy,zz)) = meet(sF0,zz),
inference(forward_demodulation,[],[f2695,f18]) ).
fof(f2714,plain,
meet(sF0,join(yy,zz)) = meet(zz,sF0),
inference(forward_demodulation,[],[f2705,f5]) ).
fof(f2721,plain,
zz = meet(sF0,join(yy,zz)),
inference(forward_demodulation,[],[f2714,f1524]) ).
fof(f2728,plain,
yy = zz,
inference(forward_demodulation,[],[f2721,f2377]) ).
fof(f2826,plain,
yy != yy,
inference(superposition,[],[f13,f2728]) ).
fof(f2855,plain,
$false,
inference(trivial_inequality_removal,[],[f2826]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT040-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n017.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 13:53:06 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.24/1.14 % (2567924)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.24/1.14 % (2567933)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1377752735:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.24/1.14 % (2567933)First to succeed.
% 2.24/1.14 % (2567933)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2567924"
% 2.24/1.14 % (2567932)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2849268014:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.24/1.14 % (2567929)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=28114213:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.24/1.14 % (2567931)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3915701305:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.24/1.14 % (2567934)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1143830393:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.24/1.14 % (2567930)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=3439637548:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.24/1.14 % (2567935)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4030305787:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.24/1.14 % (2567932)Also succeeded, but the first one will report.
% 2.24/1.14 % (2567933)Refutation found. Thanks to Tanya!
% 2.24/1.14 % SZS status Unsatisfiable for theBenchmark
% 2.24/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.33 % (2567933)------------------------------
% 2.67/1.33 % (2567933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.33 % (2567933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.33 % (2567933)CaDiCaL version: 2.1.3
% 2.67/1.33 % (2567933)Termination reason: Refutation
% 2.67/1.33 % (2567933)Time elapsed: 0.027 s
% 2.67/1.33 % (2567933)Peak memory usage: 89 MB
% 2.67/1.33 % (2567933)Instructions burned: 85 (million)
% 2.67/1.33 % (2567933)------------------------------
% 2.67/1.33 % (2567933)------------------------------
% 2.67/1.33 % (2567924)Success in time 0.289 s
% 2.67/1.33 % Vampire exiting
%------------------------------------------------------------------------------