%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LAT028-1 : 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 : n014.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 11:45:52 AM UTC 2026
% Result : Unsatisfiable 1.74s 1.86s
% Output : Refutation 6.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 76 ( 76 unt; 11 def)
% Number of atoms : 76 ( 75 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 : 16 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 136 ( 136 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [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,negated_conjecture,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
fof(f4,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
fof(f5,negated_conjecture,
! [X2,X0,X1] : meet(meet(join(X0,X1),join(X2,X1)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wal_1) ).
fof(f6,negated_conjecture,
! [X2,X0,X1] : join(join(meet(X0,X1),meet(X2,X1)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wal_2) ).
fof(f8,negated_conjecture,
! [X0,X1] : meet2(X0,X1) = meet2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet2) ).
fof(f9,negated_conjecture,
! [X2,X0,X1] : meet2(meet2(join(X0,X1),join(X2,X1)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wal_1_2) ).
fof(f10,negated_conjecture,
! [X2,X0,X1] : join(join(meet2(X0,X1),meet2(X2,X1)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wal_2_2) ).
fof(f11,negated_conjecture,
meet(a,b) != meet2(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',name) ).
fof(f12,definition,
! [X0] : sF0(X0) = meet(X0,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f13,plain,
! [X0] : meet(X0,X0) = sF0(X0),
inference(reorient_equations,[],[f12]) ).
fof(f14,plain,
! [X0] : sF0(X0) = X0,
inference(definition_folding,[],[f1,f13]) ).
fof(f15,definition,
! [X2,X0,X1] : sF1(X0,X1,X2) = meet(join(X0,X1),join(X2,X1)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f16,plain,
! [X2,X0,X1] : meet(join(X0,X1),join(X2,X1)) = sF1(X0,X1,X2),
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = meet(sF1(X0,X1,X2),X1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f18,plain,
! [X2,X0,X1] : meet(sF1(X0,X1,X2),X1) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
! [X2,X0,X1] : sF2(X0,X1,X2) = X1,
inference(definition_folding,[],[f5,f18,f16]) ).
fof(f20,definition,
! [X2,X0,X1] : sF3(X0,X1,X2) = join(meet(X0,X1),meet(X2,X1)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f21,plain,
! [X2,X0,X1] : join(meet(X0,X1),meet(X2,X1)) = sF3(X0,X1,X2),
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
! [X2,X0,X1] : sF4(X0,X1,X2) = join(sF3(X0,X1,X2),X1),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f23,plain,
! [X2,X0,X1] : join(sF3(X0,X1,X2),X1) = sF4(X0,X1,X2),
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
! [X2,X0,X1] : sF4(X0,X1,X2) = X1,
inference(definition_folding,[],[f6,f23,f21]) ).
fof(f28,definition,
! [X2,X0,X1] : sF6(X0,X1,X2) = meet2(join(X0,X1),join(X2,X1)),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f29,plain,
! [X2,X0,X1] : meet2(join(X0,X1),join(X2,X1)) = sF6(X0,X1,X2),
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
! [X2,X0,X1] : sF7(X0,X1,X2) = meet2(sF6(X0,X1,X2),X1),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f31,plain,
! [X2,X0,X1] : meet2(sF6(X0,X1,X2),X1) = sF7(X0,X1,X2),
inference(reorient_equations,[],[f30]) ).
fof(f32,plain,
! [X2,X0,X1] : sF7(X0,X1,X2) = X1,
inference(definition_folding,[],[f9,f31,f29]) ).
fof(f33,definition,
! [X2,X0,X1] : sF8(X0,X1,X2) = join(meet2(X0,X1),meet2(X2,X1)),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f34,plain,
! [X2,X0,X1] : join(meet2(X0,X1),meet2(X2,X1)) = sF8(X0,X1,X2),
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
! [X2,X0,X1] : sF9(X0,X1,X2) = join(sF8(X0,X1,X2),X1),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f36,plain,
! [X2,X0,X1] : join(sF8(X0,X1,X2),X1) = sF9(X0,X1,X2),
inference(reorient_equations,[],[f35]) ).
fof(f37,plain,
! [X2,X0,X1] : sF9(X0,X1,X2) = X1,
inference(definition_folding,[],[f10,f36,f34]) ).
fof(f38,definition,
sF10 = meet(a,b),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f39,plain,
meet(a,b) = sF10,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF11 = meet2(a,b),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f41,plain,
meet2(a,b) = sF11,
inference(reorient_equations,[],[f40]) ).
fof(f42,plain,
sF10 != sF11,
inference(definition_folding,[],[f11,f41,f39]) ).
fof(f43,plain,
! [X2,X0,X1] : join(sF8(X0,X1,X2),X1) = X1,
inference(forward_demodulation,[],[f37,f36]) ).
fof(f44,plain,
! [X2,X0,X1] : meet2(sF6(X0,X1,X2),X1) = X1,
inference(forward_demodulation,[],[f32,f31]) ).
fof(f46,plain,
! [X2,X0,X1] : join(sF3(X0,X1,X2),X1) = X1,
inference(forward_demodulation,[],[f24,f23]) ).
fof(f47,plain,
! [X2,X0,X1] : meet(sF1(X0,X1,X2),X1) = X1,
inference(forward_demodulation,[],[f19,f18]) ).
fof(f48,plain,
! [X0] : meet(X0,X0) = X0,
inference(forward_demodulation,[],[f14,f13]) ).
fof(f49,plain,
! [X2,X0,X1] : join(X1,sF8(X0,X1,X2)) = X1,
inference(forward_demodulation,[],[f43,f4]) ).
fof(f50,plain,
! [X2,X0,X1] : meet2(meet2(join(X0,X1),join(X2,X1)),X1) = X1,
inference(forward_demodulation,[],[f44,f29]) ).
fof(f51,plain,
! [X2,X0,X1] : join(X1,sF3(X0,X1,X2)) = X1,
inference(forward_demodulation,[],[f46,f4]) ).
fof(f52,plain,
! [X2,X0,X1] : meet(meet(join(X0,X1),join(X2,X1)),X1) = X1,
inference(forward_demodulation,[],[f47,f16]) ).
fof(f53,plain,
! [X2,X0,X1] : join(X1,join(meet2(X0,X1),meet2(X2,X1))) = X1,
inference(forward_demodulation,[],[f49,f34]) ).
fof(f54,plain,
! [X2,X0,X1] : join(X1,join(meet(X0,X1),meet(X2,X1))) = X1,
inference(forward_demodulation,[],[f51,f21]) ).
fof(f55,plain,
! [X2,X0,X1] : meet2(X1,meet2(join(X0,X1),join(X2,X1))) = X1,
inference(forward_demodulation,[],[f50,f8]) ).
fof(f56,plain,
! [X2,X0,X1] : meet(X1,meet(join(X0,X1),join(X2,X1))) = X1,
inference(forward_demodulation,[],[f52,f3]) ).
fof(f65,plain,
! [X0,X1] : join(X1,meet2(X0,X1)) = X1,
inference(superposition,[],[f53,f2]) ).
fof(f70,plain,
b = join(b,sF11),
inference(superposition,[],[f65,f41]) ).
fof(f72,plain,
! [X0,X1] : join(X0,meet2(X0,X1)) = X0,
inference(superposition,[],[f65,f8]) ).
fof(f74,plain,
a = join(a,sF11),
inference(superposition,[],[f72,f41]) ).
fof(f97,plain,
! [X0,X1] : join(X1,meet(X0,X1)) = X1,
inference(superposition,[],[f54,f2]) ).
fof(f102,plain,
b = join(b,sF10),
inference(superposition,[],[f97,f39]) ).
fof(f104,plain,
! [X0,X1] : join(X0,meet(X0,X1)) = X0,
inference(superposition,[],[f97,f3]) ).
fof(f106,plain,
a = join(a,sF10),
inference(superposition,[],[f104,f39]) ).
fof(f147,plain,
! [X0] : sF10 = meet2(sF10,meet2(b,join(X0,sF10))),
inference(superposition,[],[f55,f102]) ).
fof(f408,plain,
! [X0] : sF11 = meet(sF11,meet(b,join(X0,sF11))),
inference(superposition,[],[f56,f70]) ).
fof(f436,plain,
! [X0,X1] : meet(X1,join(X0,X1)) = X1,
inference(superposition,[],[f56,f48]) ).
fof(f475,plain,
! [X0,X1] : meet2(X1,X0) = meet(meet2(X1,X0),X0),
inference(superposition,[],[f436,f65]) ).
fof(f506,plain,
! [X0,X1] : meet2(X1,X0) = meet(X0,meet2(X1,X0)),
inference(forward_demodulation,[],[f475,f3]) ).
fof(f636,plain,
sF10 = meet2(sF10,meet2(b,a)),
inference(superposition,[],[f147,f106]) ).
fof(f649,plain,
sF10 = meet2(sF10,meet2(a,b)),
inference(forward_demodulation,[],[f636,f8]) ).
fof(f652,plain,
sF10 = meet2(sF10,sF11),
inference(forward_demodulation,[],[f649,f41]) ).
fof(f659,plain,
sF10 = meet(sF11,sF10),
inference(superposition,[],[f506,f652]) ).
fof(f660,plain,
sF10 = meet(sF10,sF11),
inference(forward_demodulation,[],[f659,f3]) ).
fof(f914,plain,
sF11 = meet(sF11,meet(b,a)),
inference(superposition,[],[f408,f74]) ).
fof(f932,plain,
sF11 = meet(sF11,meet(a,b)),
inference(forward_demodulation,[],[f914,f3]) ).
fof(f935,plain,
sF11 = meet(sF11,sF10),
inference(forward_demodulation,[],[f932,f39]) ).
fof(f936,plain,
sF11 = meet(sF10,sF11),
inference(forward_demodulation,[],[f935,f3]) ).
fof(f937,plain,
sF10 = sF11,
inference(forward_demodulation,[],[f936,f660]) ).
fof(f938,plain,
sF10 != sF10,
inference(superposition,[],[f42,f937]) ).
fof(f955,plain,
$false,
inference(trivial_inequality_removal,[],[f938]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT028-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 % Computer : n014.cluster.edu
% 0.15/0.44 % Model : x86_64 x86_64
% 0.15/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.44 % Memory : 8046.5625MB
% 0.15/0.44 % OS : Linux 6.8.0-71-generic
% 0.15/0.44 % CPULimit : 300
% 0.15/0.44 % WCLimit : 300
% 0.15/0.44 % DateTime : Sun Sep 27 13:57:16 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.49 Running first-order theorem proving
% 0.23/0.50 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
% 1.74/1.86 % (833030)Detected a unit-equality problem, will run specialized UEQ schedule.
% 1.74/1.86 % (833037)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=591604001:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 1.74/1.86 % (833040)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4005147255:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 1.74/1.86 % (833035)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=2278552161:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 1.74/1.86 % (833036)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=264069205:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 1.74/1.86 % (833038)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3377430607:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 1.74/1.86 % (833039)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3833168329:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 1.74/1.86 % (833041)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3770324624:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 1.74/1.86 % (833039)First to succeed.
% 1.74/1.86 % (833039)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-833030"
% 1.74/1.86 % (833038)Instruction limit reached!
% 1.74/1.86 % (833038)------------------------------
% 1.74/1.86 % (833038)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.74/1.86 % (833038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.74/1.86 % (833038)CaDiCaL version: 2.1.3
% 1.74/1.86 % (833038)Termination reason: Instruction limit
% 1.74/1.86 % (833038)Termination phase: Saturation
% 1.74/1.86 % (833038)Time elapsed: 0.129 s
% 1.74/1.86 % (833038)Peak memory usage: 88 MB
% 1.74/1.86 % (833038)Instructions burned: 137 (million)
% 1.74/1.86 % (833041)Also succeeded, but the first one will report.
% 1.74/1.86 % (833040)Instruction limit reached!
% 1.74/1.86 % (833040)------------------------------
% 1.74/1.86 % (833040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.74/1.86 % (833040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.74/1.86 % (833040)CaDiCaL version: 2.1.3
% 1.74/1.86 % (833040)Termination reason: Instruction limit
% 1.74/1.86 % (833040)Termination phase: Saturation
% 1.74/1.86 % (833040)Time elapsed: 0.255 s
% 1.74/1.86 % (833040)Peak memory usage: 91 MB
% 1.74/1.86 % (833040)Instructions burned: 257 (million)
% 1.74/1.86 % (833049)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2278056686:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 1.74/1.86 % (833039)Refutation found. Thanks to Tanya!
% 1.74/1.86 % SZS status Unsatisfiable for theBenchmark
% 1.74/1.86 % SZS output start Proof for theBenchmark
% See solution above
% 6.14/2.16 % (833039)------------------------------
% 6.14/2.16 % (833039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.14/2.16 % (833039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.14/2.16 % (833039)CaDiCaL version: 2.1.3
% 6.14/2.16 % (833039)Termination reason: Refutation
% 6.14/2.16 % (833039)Time elapsed: 0.033 s
% 6.14/2.16 % (833039)Peak memory usage: 88 MB
% 6.14/2.16 % (833039)Instructions burned: 30 (million)
% 6.14/2.16 % (833039)------------------------------
% 6.14/2.16 % (833039)------------------------------
% 6.14/2.16 % (833030)Success in time 0.729 s
% 6.14/2.16 % Vampire exiting
%------------------------------------------------------------------------------