%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT026-1 : 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 2.28s 1.75s
% Output : CNFRefutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 97 ( 97 unt; 4 def)
% Number of atoms : 255 ( 96 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 : 4 ( 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 : 92 ( 0 sgn 92 !; 0 ?; 78 :)
% 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',absorbtion) ).
fof(f8,negated_conjecture,
meet(meet(a,b),c) != meet(a,meet(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_meet) ).
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,
meet(meet(a,b),c) != meet(a,meet(b,c)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_92,definition,
iPr_def_10 = meet(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_93,definition,
iPr_def_11 = meet(iPr_def_10,c),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_94,definition,
iPr_def_12 = meet(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_95,definition,
iPr_def_13 = meet(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_165,plain,
meet(c,b) = iPr_def_12,
inference(superposition,[status(thm)],[c_100,c_94]) ).
tcf(c_166,plain,
meet(iPr_def_12,a) = iPr_def_13,
inference(superposition,[status(thm)],[c_100,c_95]) ).
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_179,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_191,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,meet(join(X0,X1),join(X2,X0))) = X0,
inference(superposition,[status(thm)],[c_99,c_153]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i] : join(X0,meet(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_101,c_154]) ).
tcf(c_218,plain,
! [X0: $i] : join(b,join(meet(X0,b),iPr_def_10)) = b,
inference(superposition,[status(thm)],[c_92,c_154]) ).
tcf(c_219,plain,
! [X0: $i] : join(c,join(meet(X0,c),iPr_def_12)) = c,
inference(superposition,[status(thm)],[c_94,c_154]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(meet(X1,X0),meet(X0,X2))) = X0,
inference(superposition,[status(thm)],[c_100,c_154]) ).
tcf(c_224,plain,
! [X0: $i] : join(iPr_def_12,join(meet(X0,iPr_def_12),iPr_def_13)) = iPr_def_12,
inference(superposition,[status(thm)],[c_95,c_154]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i] : meet(X0,join(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_154,c_103]) ).
tcf(c_231,plain,
! [X0: $i] : join(iPr_def_12,join(iPr_def_13,meet(X0,iPr_def_12))) = iPr_def_12,
inference(demodulation,[status(thm)],[c_224,c_99]) ).
tcf(c_234,plain,
! [X0: $i] : join(c,join(iPr_def_12,meet(X0,c))) = c,
inference(demodulation,[status(thm)],[c_219,c_99]) ).
tcf(c_235,plain,
! [X0: $i] : join(b,join(iPr_def_10,meet(X0,b))) = b,
inference(demodulation,[status(thm)],[c_218,c_99]) ).
tcf(c_305,plain,
join(b,iPr_def_10) = b,
inference(superposition,[status(thm)],[c_92,c_205]) ).
tcf(c_306,plain,
join(c,iPr_def_12) = c,
inference(superposition,[status(thm)],[c_94,c_205]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i] : join(X0,meet(X0,X1)) = X0,
inference(superposition,[status(thm)],[c_100,c_205]) ).
tcf(c_311,plain,
join(iPr_def_12,iPr_def_13) = iPr_def_12,
inference(superposition,[status(thm)],[c_95,c_205]) ).
tcf(c_313,plain,
join(b,iPr_def_12) = b,
inference(superposition,[status(thm)],[c_165,c_205]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,join(join(X1,X0),X2)) = X0,
inference(superposition,[status(thm)],[c_99,c_179]) ).
tcf(c_405,plain,
join(c,join(iPr_def_12,iPr_def_11)) = c,
inference(superposition,[status(thm)],[c_93,c_234]) ).
tcf(c_569,plain,
! [X0: $i] : join(a,join(meet(X0,a),iPr_def_10)) = a,
inference(superposition,[status(thm)],[c_92,c_221]) ).
tcf(c_570,plain,
! [X0: $i] : join(b,join(meet(X0,b),iPr_def_12)) = b,
inference(superposition,[status(thm)],[c_94,c_221]) ).
tcf(c_575,plain,
! [X0: $i] : join(a,join(meet(X0,a),iPr_def_13)) = a,
inference(superposition,[status(thm)],[c_95,c_221]) ).
tcf(c_607,plain,
join(iPr_def_12,b) = b,
inference(demodulation,[status(thm)],[c_313,c_99]) ).
tcf(c_608,plain,
join(iPr_def_13,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_311,c_99]) ).
tcf(c_610,plain,
join(iPr_def_12,c) = c,
inference(demodulation,[status(thm)],[c_306,c_99]) ).
tcf(c_611,plain,
join(iPr_def_10,b) = b,
inference(demodulation,[status(thm)],[c_305,c_99]) ).
tcf(c_614,plain,
join(c,join(iPr_def_11,iPr_def_12)) = c,
inference(demodulation,[status(thm)],[c_405,c_99]) ).
tcf(c_623,plain,
! [X0: $i] : join(a,join(iPr_def_13,meet(X0,a))) = a,
inference(demodulation,[status(thm)],[c_575,c_99]) ).
tcf(c_625,plain,
! [X0: $i] : join(b,join(iPr_def_12,meet(X0,b))) = b,
inference(demodulation,[status(thm)],[c_570,c_99]) ).
tcf(c_626,plain,
! [X0: $i] : join(a,join(iPr_def_10,meet(X0,a))) = a,
inference(demodulation,[status(thm)],[c_569,c_99]) ).
tcf(c_1189,plain,
! [X0: $i] : meet(iPr_def_13,join(iPr_def_12,X0)) = iPr_def_13,
inference(superposition,[status(thm)],[c_608,c_176]) ).
tcf(c_1231,plain,
join(a,iPr_def_10) = a,
inference(superposition,[status(thm)],[c_92,c_308]) ).
tcf(c_1236,plain,
join(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(superposition,[status(thm)],[c_93,c_308]) ).
tcf(c_1296,plain,
! [X0: $i] : meet(join(iPr_def_11,iPr_def_12),meet(join(X0,join(iPr_def_11,iPr_def_12)),c)) = join(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_614,c_153]) ).
tcf(c_1366,plain,
join(iPr_def_10,a) = a,
inference(demodulation,[status(thm)],[c_1231,c_99]) ).
tcf(c_1377,plain,
! [X0: $i] : meet(join(iPr_def_11,iPr_def_12),meet(c,join(X0,join(iPr_def_11,iPr_def_12)))) = join(iPr_def_11,iPr_def_12),
inference(demodulation,[status(thm)],[c_1296,c_100]) ).
tcf(c_1426,plain,
! [X0: $i] : meet(iPr_def_11,join(iPr_def_10,X0)) = iPr_def_11,
inference(superposition,[status(thm)],[c_1236,c_343]) ).
tcf(c_1532,plain,
meet(iPr_def_13,c) = iPr_def_13,
inference(superposition,[status(thm)],[c_610,c_1189]) ).
tcf(c_1533,plain,
meet(iPr_def_13,b) = iPr_def_13,
inference(superposition,[status(thm)],[c_607,c_1189]) ).
tcf(c_2215,plain,
join(c,iPr_def_13) = c,
inference(superposition,[status(thm)],[c_1532,c_205]) ).
tcf(c_2232,plain,
join(b,join(iPr_def_10,iPr_def_13)) = b,
inference(superposition,[status(thm)],[c_1533,c_235]) ).
tcf(c_2250,plain,
meet(iPr_def_11,b) = iPr_def_11,
inference(superposition,[status(thm)],[c_611,c_1426]) ).
tcf(c_2253,plain,
meet(iPr_def_11,a) = iPr_def_11,
inference(superposition,[status(thm)],[c_1366,c_1426]) ).
tcf(c_2279,plain,
join(a,join(iPr_def_10,iPr_def_13)) = a,
inference(superposition,[status(thm)],[c_166,c_626]) ).
tcf(c_2395,plain,
join(iPr_def_13,c) = c,
inference(demodulation,[status(thm)],[c_2215,c_99]) ).
tcf(c_2489,plain,
join(b,join(iPr_def_12,iPr_def_11)) = b,
inference(superposition,[status(thm)],[c_2250,c_625]) ).
tcf(c_2501,plain,
join(a,join(iPr_def_13,iPr_def_11)) = a,
inference(superposition,[status(thm)],[c_2253,c_623]) ).
tcf(c_2522,plain,
! [X0: $i] : meet(iPr_def_13,meet(c,join(X0,iPr_def_13))) = iPr_def_13,
inference(superposition,[status(thm)],[c_2395,c_191]) ).
tcf(c_2716,plain,
! [X0: $i] : meet(join(iPr_def_10,iPr_def_13),meet(join(X0,join(iPr_def_10,iPr_def_13)),b)) = join(iPr_def_10,iPr_def_13),
inference(superposition,[status(thm)],[c_2232,c_153]) ).
tcf(c_2741,plain,
join(a,join(iPr_def_11,iPr_def_13)) = a,
inference(demodulation,[status(thm)],[c_2501,c_99]) ).
tcf(c_2742,plain,
join(b,join(iPr_def_11,iPr_def_12)) = b,
inference(demodulation,[status(thm)],[c_2489,c_99]) ).
tcf(c_2761,plain,
! [X0: $i] : meet(join(iPr_def_10,iPr_def_13),meet(b,join(X0,join(iPr_def_10,iPr_def_13)))) = join(iPr_def_10,iPr_def_13),
inference(demodulation,[status(thm)],[c_2716,c_100]) ).
tcf(c_3010,plain,
! [X0: $i] : meet(join(iPr_def_11,iPr_def_13),meet(join(X0,join(iPr_def_11,iPr_def_13)),a)) = join(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_2741,c_153]) ).
tcf(c_3186,plain,
! [X0: $i] : meet(join(iPr_def_11,iPr_def_13),meet(a,join(X0,join(iPr_def_11,iPr_def_13)))) = join(iPr_def_11,iPr_def_13),
inference(demodulation,[status(thm)],[c_3010,c_100]) ).
tcf(c_5325,plain,
meet(join(iPr_def_11,iPr_def_12),meet(c,b)) = join(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_2742,c_1377]) ).
tcf(c_5551,plain,
join(iPr_def_11,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_5325,c_100,c_165,c_226]) ).
tcf(c_5971,plain,
meet(iPr_def_11,iPr_def_12) = iPr_def_11,
inference(superposition,[status(thm)],[c_5551,c_175]) ).
tcf(c_6797,plain,
join(iPr_def_12,join(iPr_def_13,iPr_def_11)) = iPr_def_12,
inference(superposition,[status(thm)],[c_5971,c_231]) ).
tcf(c_7090,plain,
join(iPr_def_12,join(iPr_def_11,iPr_def_13)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_6797,c_99]) ).
tcf(c_9973,plain,
meet(join(iPr_def_10,iPr_def_13),meet(b,a)) = join(iPr_def_10,iPr_def_13),
inference(superposition,[status(thm)],[c_2279,c_2761]) ).
tcf(c_10120,plain,
join(iPr_def_10,iPr_def_13) = iPr_def_10,
inference(demodulation,[status(thm)],[c_9973,c_100,c_92,c_175]) ).
tcf(c_10343,plain,
meet(join(iPr_def_11,iPr_def_13),meet(a,iPr_def_12)) = join(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_7090,c_3186]) ).
tcf(c_10495,plain,
join(iPr_def_11,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_10343,c_100,c_95,c_226]) ).
tcf(c_10975,plain,
meet(iPr_def_11,iPr_def_13) = iPr_def_11,
inference(superposition,[status(thm)],[c_10495,c_175]) ).
tcf(c_16505,plain,
meet(iPr_def_13,meet(c,iPr_def_10)) = iPr_def_13,
inference(superposition,[status(thm)],[c_10120,c_2522]) ).
tcf(c_16591,plain,
iPr_def_11 = iPr_def_13,
inference(demodulation,[status(thm)],[c_16505,c_100,c_93,c_10975]) ).
tcf(c_16592,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_16591,c_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT026-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n008.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 20:03:39 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running UEQ theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 2.28/1.75 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.28/1.75 % SZS status Started for theBenchmark.p
% 2.28/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 2.28/1.75
% 2.28/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.28/1.75
% 2.28/1.75 % ------ iProver source info
% 2.28/1.75
% 2.28/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 2.28/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.28/1.75 % git: non_committed_changes: false
% 2.28/1.75
% 2.28/1.75 % ------ Parsing...% successful
% 2.28/1.75
% 2.28/1.75
% 2.28/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.28/1.75
% 2.28/1.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.28/1.75
% 2.28/1.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.28/1.75
% 2.28/1.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.28/1.75 % ------ Proving...
% 2.28/1.75 % ------ Problem Properties
% 2.28/1.75
% 2.28/1.75 %
% 2.28/1.75 % clauses 12
% 2.28/1.75 % conjectures 1
% 2.28/1.75 % EPR 1
% 2.28/1.75 % Horn 12
% 2.28/1.75 % unary 12
% 2.28/1.75 % binary 0
% 2.28/1.75 % lits 12
% 2.28/1.75 % lits eq 12
% 2.28/1.75 % fd_pure 0
% 2.28/1.75 % fd_pseudo 0
% 2.28/1.75 % fd_cond 0
% 2.28/1.75 % fd_pseudo_cond 0
% 2.28/1.75 % AC symbols 0
% 2.28/1.75
% 2.28/1.75 % ------ Input Options Time Limit: Unbounded
% 2.28/1.75
% 2.28/1.75
% 2.28/1.75 % ------
% 2.28/1.75 % Current options:
% 2.28/1.75 % ------
% 2.28/1.75
% 2.28/1.75
% 2.28/1.75 %
% 2.28/1.75
% 2.28/1.75 % ------ Proving...
% 2.28/1.75 %
% 2.28/1.75
% 2.28/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 2.28/1.75
% 2.28/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.28/1.75
% 2.28/1.75
%------------------------------------------------------------------------------