%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT042-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n004.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 01:58:10 PM UTC 2026
% Result : Unsatisfiable 4.61s 1.32s
% Output : CNFRefutation 4.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 70 ( 70 unt; 5 def)
% Number of atoms : 142 ( 69 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 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 : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 102 !; 0 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : meet(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
fof(f2,axiom,
! [X0] : join(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).
fof(f3,axiom,
! [X0,X1] : meet(X0,join(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
fof(f4,axiom,
! [X0,X1] : join(X0,meet(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
fof(f6,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
fof(f7,axiom,
! [X2,X0,X1] : meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
fof(f8,axiom,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
fof(f9,axiom,
! [X2,X0,X1] : meet(X0,join(X1,X2)) = join(meet(X0,X1),meet(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity) ).
fof(f13,negated_conjecture,
join(a,meet(b,join(a,c))) != meet(join(a,b),join(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_modular_law) ).
tcf(c_62,negated_conjecture,
! [X0: $i] : meet(X0,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_63,negated_conjecture,
! [X0: $i] : join(X0,X0) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_64,negated_conjecture,
! [X0: $i,X1: $i] : meet(X0,join(X0,X1)) = X0,
inference(cnf_transformation,[],[f3]) ).
tcf(c_65,negated_conjecture,
! [X0: $i,X1: $i] : join(X0,meet(X0,X1)) = X0,
inference(cnf_transformation,[],[f4]) ).
tcf(c_66,negated_conjecture,
! [X0: $i,X1: $i] : meet(X0,X1) = meet(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_67,negated_conjecture,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_68,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] : meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
tcf(c_69,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_70,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] : join(meet(X0,X1),meet(X0,X2)) = meet(X0,join(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
tcf(c_74,negated_conjecture,
join(a,meet(b,join(a,c))) != meet(join(a,b),join(a,c)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_118,definition,
iPr_def_10 = join(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_119,definition,
iPr_def_11 = meet(b,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_120,definition,
iPr_def_12 = join(a,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_121,definition,
iPr_def_13 = join(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_122,definition,
iPr_def_14 = meet(iPr_def_13,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_123,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_124,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] : meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_125,negated_conjecture,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_126,negated_conjecture,
! [X0: $i,X1: $i] : meet(X0,X1) = meet(X1,X0),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_127,negated_conjecture,
! [X0: $i,X1: $i] : join(X0,meet(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_128,negated_conjecture,
! [X0: $i,X1: $i] : meet(X0,join(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_129,negated_conjecture,
! [X0: $i] : join(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_130,negated_conjecture,
! [X0: $i] : meet(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_131,negated_conjecture,
iPr_def_12 != iPr_def_14,
inference(demodulation,[status(thm)],[c_74,c_121,c_122,c_118,c_119,c_120]) ).
tcf(c_135,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] : join(meet(X0,X1),meet(X0,X2)) = meet(X0,join(X1,X2)),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(superposition,[status(thm)],[c_123,c_125]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,meet(X1,X2)) = meet(X1,meet(X0,X2)),
inference(superposition,[status(thm)],[c_124,c_126]) ).
tcf(c_229,plain,
meet(iPr_def_10,b) = iPr_def_11,
inference(superposition,[status(thm)],[c_126,c_119]) ).
tcf(c_230,plain,
meet(iPr_def_10,iPr_def_13) = iPr_def_14,
inference(superposition,[status(thm)],[c_126,c_122]) ).
tcf(c_238,plain,
meet(a,iPr_def_10) = a,
inference(superposition,[status(thm)],[c_118,c_128]) ).
tcf(c_270,plain,
! [X0: $i] : meet(iPr_def_13,meet(X0,iPr_def_10)) = meet(X0,iPr_def_14),
inference(superposition,[status(thm)],[c_122,c_204]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,meet(X0,X2))) = join(X1,X0),
inference(superposition,[status(thm)],[c_127,c_203]) ).
tcf(c_312,plain,
! [X0: $i] : join(a,join(X0,iPr_def_11)) = join(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_120,c_203]) ).
tcf(c_337,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_129,c_123]) ).
tcf(c_363,plain,
! [X0: $i,X1: $i] : meet(X0,meet(X0,X1)) = meet(X0,X1),
inference(superposition,[status(thm)],[c_130,c_124]) ).
tcf(c_369,plain,
! [X0: $i] : meet(iPr_def_13,meet(iPr_def_10,X0)) = meet(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_122,c_124]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,meet(X1,join(meet(X0,X1),X2))) = meet(X0,X1),
inference(superposition,[status(thm)],[c_124,c_128]) ).
tcf(c_389,plain,
! [X0: $i] : join(meet(X0,a),meet(X0,b)) = meet(X0,iPr_def_13),
inference(superposition,[status(thm)],[c_121,c_135]) ).
tcf(c_393,plain,
! [X0: $i,X1: $i,X2: $i] : join(meet(X0,X1),meet(X0,X2)) = meet(X0,join(X2,X1)),
inference(superposition,[status(thm)],[c_125,c_135]) ).
tcf(c_399,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(meet(X0,X1),meet(X0,X2))) = X0,
inference(superposition,[status(thm)],[c_135,c_127]) ).
tcf(c_408,plain,
! [X0: $i] : meet(X0,iPr_def_14) = meet(iPr_def_14,X0),
inference(ac_demodulation,[status(thm)],[c_369,c_230,c_123,c_125,c_124,c_126]) ).
tcf(c_415,plain,
! [X0: $i,X1: $i,X2: $i] : join(meet(X0,meet(X1,meet(X0,X1))),meet(X0,meet(X1,X2))) = meet(X0,X1),
inference(demodulation,[status(thm)],[c_376,c_393]) ).
tcf(c_416,plain,
! [X0: $i,X1: $i,X2: $i] : join(meet(X0,X1),meet(X1,meet(X0,X2))) = meet(X1,X0),
inference(ac_demodulation,[status(thm)],[c_415,c_363,c_123,c_125,c_124,c_126]) ).
tcf(c_728,plain,
meet(iPr_def_10,a) = a,
inference(superposition,[status(thm)],[c_238,c_126]) ).
tcf(c_909,plain,
join(a,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_120,c_337]) ).
tcf(c_975,plain,
join(a,iPr_def_11) = join(a,iPr_def_12),
inference(superposition,[status(thm)],[c_312,c_337]) ).
tcf(c_1082,plain,
! [X0: $i] : meet(iPr_def_13,meet(iPr_def_10,X0)) = meet(X0,iPr_def_14),
inference(superposition,[status(thm)],[c_126,c_270]) ).
tcf(c_1537,plain,
! [X0: $i,X1: $i] : join(iPr_def_14,join(meet(iPr_def_14,X0),meet(X1,iPr_def_14))) = iPr_def_14,
inference(superposition,[status(thm)],[c_408,c_399]) ).
tcf(c_1587,plain,
join(meet(iPr_def_10,a),iPr_def_11) = meet(iPr_def_10,iPr_def_13),
inference(superposition,[status(thm)],[c_229,c_389]) ).
tcf(c_1831,plain,
! [X0: $i,X1: $i] : join(meet(X0,X1),X0) = X0,
inference(superposition,[status(thm)],[c_309,c_399]) ).
tcf(c_1976,plain,
! [X0: $i] : join(iPr_def_14,meet(iPr_def_10,meet(iPr_def_13,X0))) = meet(iPr_def_10,iPr_def_13),
inference(superposition,[status(thm)],[c_122,c_416]) ).
tcf(c_2836,plain,
join(a,iPr_def_11) = iPr_def_12,
inference(demodulation,[status(thm)],[c_975,c_909]) ).
tcf(c_2919,plain,
meet(iPr_def_10,iPr_def_13) = iPr_def_12,
inference(demodulation,[status(thm)],[c_1587,c_728,c_2836]) ).
tcf(c_2946,plain,
! [X0: $i] : meet(X0,iPr_def_12) = meet(X0,iPr_def_14),
inference(ac_demodulation,[status(thm)],[c_1082,c_2919,c_123,c_125,c_124,c_126]) ).
tcf(c_3038,plain,
! [X0: $i] : join(iPr_def_14,meet(iPr_def_10,meet(iPr_def_13,X0))) = iPr_def_12,
inference(demodulation,[status(thm)],[c_1976,c_2919]) ).
tcf(c_3039,plain,
! [X0: $i] : join(iPr_def_14,meet(X0,iPr_def_12)) = iPr_def_12,
inference(ac_demodulation,[status(thm)],[c_3038,c_2919,c_123,c_125,c_124,c_126]) ).
tcf(c_3075,plain,
! [X0: $i,X1: $i] : join(iPr_def_14,join(meet(iPr_def_14,X0),meet(X1,iPr_def_12))) = iPr_def_14,
inference(demodulation,[status(thm)],[c_1537,c_2946]) ).
tcf(c_3076,plain,
! [X0: $i] : join(meet(X0,iPr_def_12),iPr_def_14) = iPr_def_14,
inference(ac_demodulation,[status(thm)],[c_3075,c_1831,c_123,c_125,c_124,c_126]) ).
tcf(c_3077,plain,
iPr_def_12 = iPr_def_14,
inference(ac_demodulation,[status(thm)],[c_3076,c_3039,c_123,c_125,c_124,c_126]) ).
tcf(c_3687,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3077,c_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT042-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 20:05:36 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running UEQ theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 4.61/1.32 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 4.61/1.32 % SZS status Started for theBenchmark.p
% 4.61/1.32 % SZS status Unsatisfiable for theBenchmark.p
% 4.61/1.32
% 4.61/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.61/1.32
% 4.61/1.32 % ------ iProver source info
% 4.61/1.32
% 4.61/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 4.61/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.61/1.32 % git: non_committed_changes: false
% 4.61/1.32
% 4.61/1.32 % ------ Parsing...% successful
% 4.61/1.32
% 4.61/1.32
% 4.61/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.61/1.32
% 4.61/1.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.61/1.32
% 4.61/1.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.61/1.32
% 4.61/1.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.61/1.32 % ------ Proving...
% 4.61/1.32 % ------ Problem Properties
% 4.61/1.32
% 4.61/1.32 %
% 4.61/1.32 % clauses 18
% 4.61/1.32 % conjectures 13
% 4.61/1.32 % EPR 1
% 4.61/1.32 % Horn 18
% 4.61/1.32 % unary 18
% 4.61/1.32 % binary 0
% 4.61/1.32 % lits 18
% 4.61/1.32 % lits eq 18
% 4.61/1.32 % fd_pure 0
% 4.61/1.32 % fd_pseudo 0
% 4.61/1.32 % fd_cond 0
% 4.61/1.32 % fd_pseudo_cond 0
% 4.61/1.32 % AC symbols 2
% 4.61/1.32
% 4.61/1.32 % ------ Input Options Time Limit: Unbounded
% 4.61/1.32
% 4.61/1.32
% 4.61/1.32 % ------
% 4.61/1.32 % Current options:
% 4.61/1.32 % ------
% 4.61/1.32
% 4.61/1.32
% 4.61/1.32 %
% 4.61/1.32
% 4.61/1.32 % ------ Proving...
% 4.61/1.32 %
% 4.61/1.32
% 4.61/1.32 % SZS status Unsatisfiable for theBenchmark.p
% 4.61/1.32
% 4.61/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.61/1.32
% 4.61/1.32
%------------------------------------------------------------------------------