%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT027-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 : Fri Sep 25 01:58:07 PM UTC 2026
% Result : Unsatisfiable 5.05s 2.72s
% Output : CNFRefutation 5.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 84 ( 84 unt; 4 def)
% Number of atoms : 216 ( 83 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 95 !; 0 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : join(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT005-0.ax',idempotence_of_join) ).
fof(f3,axiom,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT005-0.ax',commutativity_of_meet) ).
fof(f4,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT005-0.ax',commutativity_of_join) ).
fof(f5,axiom,
! [X2,X0,X1] : meet(meet(join(X0,X1),join(X2,X1)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT005-0.ax',wal_1) ).
fof(f6,axiom,
! [X2,X0,X1] : join(join(meet(X0,X1),meet(X2,X1)),X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT005-0.ax',wal_2) ).
fof(f7,axiom,
! [X2,X0,X1] : meet(X0,join(X1,join(X0,X2))) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption) ).
fof(f8,negated_conjecture,
join(join(a,b),c) != join(a,join(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_join) ).
tcf(c_58,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : meet(X0,X1) = meet(X1,X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f4]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] : meet(meet(join(X0,X1),join(X2,X1)),X1) = X1,
inference(cnf_transformation,[],[f5]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(meet(X0,X1),meet(X2,X1)),X1) = X1,
inference(cnf_transformation,[],[f6]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,join(X1,join(X0,X2))) = X0,
inference(cnf_transformation,[],[f7]) ).
tcf(c_64,negated_conjecture,
join(join(a,b),c) != join(a,join(b,c)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_92,definition,
iPr_def_10 = join(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_93,definition,
iPr_def_11 = join(iPr_def_10,c),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_94,definition,
iPr_def_12 = join(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_95,definition,
iPr_def_13 = join(a,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_96,negated_conjecture,
iPr_def_11 != iPr_def_13,
inference(demodulation,[status(thm)],[c_64,c_94,c_95,c_92,c_93]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(meet(X0,X1),meet(X2,X1)),X1) = X1,
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i] : meet(meet(join(X0,X1),join(X2,X1)),X1) = X1,
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] : meet(X0,X1) = meet(X1,X0),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_101,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,join(X1,join(X0,X2))) = X0,
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,meet(join(X1,X0),join(X2,X0))) = X0,
inference(demodulation,[status(thm)],[c_98,c_100]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(meet(X1,X0),meet(X2,X0))) = X0,
inference(demodulation,[status(thm)],[c_97,c_99]) ).
tcf(c_173,plain,
join(c,b) = iPr_def_12,
inference(superposition,[status(thm)],[c_99,c_94]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] : meet(X0,join(X0,X1)) = X0,
inference(superposition,[status(thm)],[c_101,c_103]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,join(join(X0,X1),X2)) = X0,
inference(superposition,[status(thm)],[c_99,c_103]) ).
tcf(c_178,plain,
! [X0: $i] : meet(a,join(X0,iPr_def_10)) = a,
inference(superposition,[status(thm)],[c_92,c_103]) ).
tcf(c_179,plain,
! [X0: $i] : meet(b,join(X0,iPr_def_12)) = b,
inference(superposition,[status(thm)],[c_94,c_103]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,join(X1,join(X2,X0))) = X0,
inference(superposition,[status(thm)],[c_99,c_103]) ).
tcf(c_183,plain,
! [X0: $i] : meet(iPr_def_10,join(X0,iPr_def_11)) = iPr_def_10,
inference(superposition,[status(thm)],[c_93,c_103]) ).
tcf(c_184,plain,
! [X0: $i] : meet(a,join(X0,iPr_def_13)) = a,
inference(superposition,[status(thm)],[c_95,c_103]) ).
tcf(c_206,plain,
! [X0: $i] : meet(c,meet(join(X0,c),iPr_def_12)) = c,
inference(superposition,[status(thm)],[c_94,c_153]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,meet(join(X1,X0),join(X0,X2))) = X0,
inference(superposition,[status(thm)],[c_99,c_153]) ).
tcf(c_211,plain,
! [X0: $i] : meet(iPr_def_12,meet(join(X0,iPr_def_12),iPr_def_13)) = iPr_def_12,
inference(superposition,[status(thm)],[c_95,c_153]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i] : join(X0,meet(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_101,c_154]) ).
tcf(c_248,plain,
! [X0: $i] : meet(iPr_def_12,meet(iPr_def_13,join(X0,iPr_def_12))) = iPr_def_12,
inference(demodulation,[status(thm)],[c_211,c_100]) ).
tcf(c_252,plain,
! [X0: $i] : meet(c,meet(iPr_def_12,join(X0,c))) = c,
inference(demodulation,[status(thm)],[c_206,c_100]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i] : join(join(X0,iPr_def_10),join(meet(X1,join(X0,iPr_def_10)),a)) = join(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_178,c_154]) ).
tcf(c_333,plain,
meet(b,iPr_def_13) = b,
inference(superposition,[status(thm)],[c_95,c_179]) ).
tcf(c_336,plain,
meet(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(superposition,[status(thm)],[c_101,c_183]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i] : join(join(X0,iPr_def_13),join(meet(X1,join(X0,iPr_def_13)),a)) = join(X0,iPr_def_13),
inference(superposition,[status(thm)],[c_184,c_154]) ).
tcf(c_348,plain,
! [X0: $i,X1: $i] : join(X0,meet(X0,X1)) = X0,
inference(superposition,[status(thm)],[c_100,c_229]) ).
tcf(c_387,plain,
! [X0: $i] : meet(c,join(iPr_def_12,X0)) = c,
inference(superposition,[status(thm)],[c_173,c_176]) ).
tcf(c_395,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,join(join(X1,X0),X2)) = X0,
inference(superposition,[status(thm)],[c_99,c_181]) ).
tcf(c_398,plain,
! [X0: $i] : meet(b,join(X0,iPr_def_10)) = b,
inference(superposition,[status(thm)],[c_92,c_181]) ).
tcf(c_430,plain,
meet(iPr_def_12,iPr_def_13) = iPr_def_12,
inference(superposition,[status(thm)],[c_175,c_248]) ).
tcf(c_457,plain,
meet(c,meet(iPr_def_12,iPr_def_11)) = c,
inference(superposition,[status(thm)],[c_93,c_252]) ).
tcf(c_538,plain,
! [X0: $i] : meet(b,meet(join(X0,b),iPr_def_12)) = b,
inference(superposition,[status(thm)],[c_94,c_208]) ).
tcf(c_617,plain,
meet(iPr_def_13,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_430,c_100]) ).
tcf(c_620,plain,
meet(iPr_def_11,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_336,c_100]) ).
tcf(c_621,plain,
meet(iPr_def_13,b) = b,
inference(demodulation,[status(thm)],[c_333,c_100]) ).
tcf(c_626,plain,
meet(c,meet(iPr_def_11,iPr_def_12)) = c,
inference(demodulation,[status(thm)],[c_457,c_100]) ).
tcf(c_637,plain,
! [X0: $i] : meet(b,meet(iPr_def_12,join(X0,b))) = b,
inference(demodulation,[status(thm)],[c_538,c_100]) ).
tcf(c_668,plain,
! [X0: $i,X1: $i] : join(join(X0,iPr_def_13),join(a,meet(X1,join(X0,iPr_def_13)))) = join(X0,iPr_def_13),
inference(demodulation,[status(thm)],[c_345,c_99]) ).
tcf(c_671,plain,
! [X0: $i,X1: $i] : join(join(X0,iPr_def_10),join(a,meet(X1,join(X0,iPr_def_10)))) = join(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_329,c_99]) ).
tcf(c_1183,plain,
join(iPr_def_13,iPr_def_12) = iPr_def_13,
inference(superposition,[status(thm)],[c_617,c_348]) ).
tcf(c_1188,plain,
join(iPr_def_11,iPr_def_10) = iPr_def_11,
inference(superposition,[status(thm)],[c_620,c_348]) ).
tcf(c_1189,plain,
join(iPr_def_13,b) = iPr_def_13,
inference(superposition,[status(thm)],[c_621,c_348]) ).
tcf(c_1326,plain,
! [X0: $i,X1: $i] : join(join(iPr_def_12,X0),join(meet(X1,join(iPr_def_12,X0)),c)) = join(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_387,c_154]) ).
tcf(c_1355,plain,
! [X0: $i] : join(meet(iPr_def_11,iPr_def_12),join(meet(X0,meet(iPr_def_11,iPr_def_12)),c)) = meet(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_626,c_154]) ).
tcf(c_1404,plain,
! [X0: $i] : join(meet(iPr_def_11,iPr_def_12),join(c,meet(X0,meet(iPr_def_11,iPr_def_12)))) = meet(iPr_def_11,iPr_def_12),
inference(demodulation,[status(thm)],[c_1355,c_99]) ).
tcf(c_1410,plain,
! [X0: $i,X1: $i] : join(join(iPr_def_12,X0),join(c,meet(X1,join(iPr_def_12,X0)))) = join(iPr_def_12,X0),
inference(demodulation,[status(thm)],[c_1326,c_99]) ).
tcf(c_1722,plain,
meet(b,iPr_def_11) = b,
inference(superposition,[status(thm)],[c_1188,c_398]) ).
tcf(c_1731,plain,
! [X0: $i] : meet(b,join(iPr_def_13,X0)) = b,
inference(superposition,[status(thm)],[c_1189,c_395]) ).
tcf(c_1761,plain,
meet(iPr_def_11,b) = b,
inference(demodulation,[status(thm)],[c_1722,c_100]) ).
tcf(c_2211,plain,
join(iPr_def_11,b) = iPr_def_11,
inference(superposition,[status(thm)],[c_1761,c_348]) ).
tcf(c_2556,plain,
meet(b,meet(iPr_def_12,iPr_def_11)) = b,
inference(superposition,[status(thm)],[c_2211,c_637]) ).
tcf(c_2839,plain,
meet(b,meet(iPr_def_11,iPr_def_12)) = b,
inference(demodulation,[status(thm)],[c_2556,c_100]) ).
tcf(c_5484,plain,
join(join(iPr_def_13,iPr_def_13),join(a,b)) = join(iPr_def_13,iPr_def_13),
inference(superposition,[status(thm)],[c_1731,c_668]) ).
tcf(c_5688,plain,
join(iPr_def_13,iPr_def_10) = iPr_def_13,
inference(demodulation,[status(thm)],[c_5484,c_101,c_92]) ).
tcf(c_5779,plain,
! [X0: $i] : meet(iPr_def_10,join(X0,iPr_def_13)) = iPr_def_10,
inference(superposition,[status(thm)],[c_5688,c_181]) ).
tcf(c_8013,plain,
join(meet(iPr_def_11,iPr_def_12),join(c,b)) = meet(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_2839,c_1404]) ).
tcf(c_8082,plain,
meet(iPr_def_11,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_8013,c_99,c_173,c_229]) ).
tcf(c_8500,plain,
join(join(iPr_def_12,iPr_def_13),join(c,iPr_def_10)) = join(iPr_def_12,iPr_def_13),
inference(superposition,[status(thm)],[c_5779,c_1410]) ).
tcf(c_8637,plain,
join(iPr_def_11,iPr_def_12) = iPr_def_11,
inference(superposition,[status(thm)],[c_8082,c_348]) ).
tcf(c_8713,plain,
join(iPr_def_13,iPr_def_11) = iPr_def_13,
inference(demodulation,[status(thm)],[c_8500,c_99,c_93,c_1183]) ).
tcf(c_8848,plain,
! [X0: $i] : meet(iPr_def_12,join(iPr_def_11,X0)) = iPr_def_12,
inference(superposition,[status(thm)],[c_8637,c_395]) ).
tcf(c_9505,plain,
join(join(iPr_def_11,iPr_def_10),join(a,iPr_def_12)) = join(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_8848,c_671]) ).
tcf(c_9815,plain,
iPr_def_11 = iPr_def_13,
inference(demodulation,[status(thm)],[c_9505,c_99,c_95,c_1188,c_8713]) ).
tcf(c_9816,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9815,c_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT027-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 20:03:54 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running UEQ theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 5.05/2.72 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 5.05/2.72 % SZS status Started for theBenchmark.p
% 5.05/2.72 % SZS status Unsatisfiable for theBenchmark.p
% 5.05/2.72
% 5.05/2.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.05/2.72
% 5.05/2.72 % ------ iProver source info
% 5.05/2.72
% 5.05/2.72 % git: date: 2026-07-19 20:42:38 +0200
% 5.05/2.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.05/2.72 % git: non_committed_changes: false
% 5.05/2.72
% 5.05/2.72 % ------ Parsing...% successful
% 5.05/2.72
% 5.05/2.72
% 5.05/2.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.05/2.72
% 5.05/2.72 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 5.05/2.72
% 5.05/2.72 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.05/2.72
% 5.05/2.72 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 5.05/2.72 % ------ Proving...
% 5.05/2.72 % ------ Problem Properties
% 5.05/2.72
% 5.05/2.72 %
% 5.05/2.72 % clauses 12
% 5.05/2.72 % conjectures 1
% 5.05/2.72 % EPR 1
% 5.05/2.72 % Horn 12
% 5.05/2.72 % unary 12
% 5.05/2.72 % binary 0
% 5.05/2.72 % lits 12
% 5.05/2.72 % lits eq 12
% 5.05/2.72 % fd_pure 0
% 5.05/2.72 % fd_pseudo 0
% 5.05/2.72 % fd_cond 0
% 5.05/2.72 % fd_pseudo_cond 0
% 5.05/2.72 % AC symbols 0
% 5.05/2.72
% 5.05/2.72 % ------ Input Options Time Limit: Unbounded
% 5.05/2.72
% 5.05/2.72
% 5.05/2.72 % ------
% 5.05/2.72 % Current options:
% 5.05/2.72 % ------
% 5.05/2.72
% 5.05/2.72
% 5.05/2.72 %
% 5.05/2.72
% 5.05/2.72 % ------ Proving...
% 5.05/2.72 %
% 5.05/2.72
% 5.05/2.72 % SZS status Unsatisfiable for theBenchmark.p
% 5.05/2.72
% 5.05/2.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.05/2.72
% 5.05/2.72
%------------------------------------------------------------------------------