%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT225-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 : Thu Sep 24 01:04:29 PM UTC 2026
% Result : Unsatisfiable 106.41s 14.00s
% Output : CNFRefutation 106.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 69 ( 60 unt; 0 nHn; 28 RR)
% Number of literals : 83 ( 82 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 98 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(equation_H10,axiom,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X1,meet(X2,X3))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H10) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_join) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
cnf(prove_distributivity_hypothesis,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).
cnf(meet_join_complement,axiom,
( join(X1,X2) != one
| meet(X1,X2) != zero
| complement(X1) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',meet_join_complement) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
cnf(prove_distributivity,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c_0_13,axiom,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X1,meet(X2,X3))))),
equation_H10 ).
cnf(c_0_14,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_15,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_16,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_17,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_18,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_19,hypothesis,
meet(b,a) = a,
prove_distributivity_hypothesis ).
cnf(c_0_20,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_21,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_22,plain,
meet(X1,join(X2,meet(X3,join(meet(X2,X3),X1)))) = meet(X1,join(X2,meet(X1,X3))),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_23,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_24,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_26,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( join(X1,X2) != one
| meet(X1,X2) != zero
| complement(X1) = X2 ),
inference(fof_simplification,[status(thm)],[meet_join_complement]) ).
cnf(c_0_28,plain,
meet(complement(meet(X1,X2)),join(X1,meet(X2,complement(meet(X1,X2))))) = meet(join(X1,X2),complement(meet(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_16]),c_0_23]),c_0_18]),c_0_18]) ).
cnf(c_0_29,hypothesis,
join(a,b) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_14]) ).
cnf(c_0_30,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_14]),c_0_20]) ).
cnf(c_0_31,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_32,plain,
( join(X1,X2) != one
| meet(X1,X2) != zero
| complement(X1) = X2 ),
c_0_27 ).
cnf(c_0_33,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_34,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_35,hypothesis,
meet(complement(a),join(a,meet(b,complement(a)))) = meet(b,complement(a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_25]),c_0_29]) ).
cnf(c_0_36,plain,
join(X1,join(X2,meet(X3,X1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_37,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_38,plain,
join(X1,join(complement(X1),X2)) = join(one,X2),
inference(spm,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_39,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_14,c_0_31]) ).
cnf(c_0_40,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_26,c_0_14]) ).
cnf(c_0_41,plain,
( join(X1,X2) != one
| meet(X2,X1) != zero
| complement(X1) = X2 ),
inference(spm,[status(thm)],[c_0_32,c_0_18]) ).
cnf(c_0_42,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_33]) ).
cnf(c_0_43,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_44,hypothesis,
meet(complement(meet(b,complement(a))),join(complement(a),meet(join(a,meet(b,complement(a))),complement(meet(b,complement(a)))))) = complement(meet(b,complement(a))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_35]),c_0_36]),c_0_16]),c_0_37]) ).
cnf(c_0_45,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
join(X1,join(X2,join(X3,X1))) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_40,c_0_20]) ).
cnf(c_0_47,plain,
( join(meet(X1,X2),X3) != one
| meet(X2,meet(X3,X1)) != zero
| complement(meet(X1,X2)) = X3 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,hypothesis,
meet(complement(a),meet(join(a,meet(b,complement(a))),complement(meet(b,complement(a))))) = zero,
inference(spm,[status(thm)],[c_0_43,c_0_35]) ).
cnf(c_0_49,hypothesis,
meet(complement(a),join(a,join(meet(b,complement(a)),meet(complement(a),complement(meet(b,complement(a))))))) = complement(a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_44]),c_0_20]),c_0_16]),c_0_31]),c_0_23]),c_0_20]) ).
cnf(c_0_50,plain,
join(X1,join(X2,join(X3,complement(X1)))) = one,
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,hypothesis,
( join(a,join(meet(b,complement(a)),meet(complement(a),complement(meet(b,complement(a)))))) != one
| complement(meet(complement(a),complement(meet(b,complement(a))))) = join(a,meet(b,complement(a))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_18]),c_0_18]),c_0_14]),c_0_20]) ).
cnf(c_0_52,hypothesis,
join(a,join(meet(b,complement(a)),meet(complement(a),complement(meet(b,complement(a)))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_49]),c_0_20]),c_0_20]),c_0_50]) ).
cnf(c_0_53,plain,
( join(X2,meet(X1,complement(meet(X2,X1)))) != one
| complement(meet(X1,complement(meet(X2,X1)))) = X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_43]),c_0_14]) ).
cnf(c_0_54,hypothesis,
complement(meet(complement(a),complement(meet(b,complement(a))))) = join(a,meet(b,complement(a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
cnf(c_0_55,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_34]),c_0_14]),c_0_16])]) ).
cnf(c_0_56,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_57,hypothesis,
( join(b,meet(complement(a),complement(meet(b,complement(a))))) != one
| join(a,meet(b,complement(a))) = b ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,hypothesis,
meet(complement(a),complement(meet(b,complement(a)))) = complement(join(a,meet(b,complement(a)))),
inference(spm,[status(thm)],[c_0_55,c_0_54]) ).
cnf(c_0_59,plain,
join(X1,join(X2,join(meet(X1,X3),X4))) = join(X2,join(X1,X4)),
inference(spm,[status(thm)],[c_0_30,c_0_56]) ).
cnf(c_0_60,hypothesis,
join(a,join(b,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_20,c_0_29]) ).
cnf(c_0_61,hypothesis,
( join(b,complement(join(a,meet(b,complement(a))))) != one
| join(a,meet(b,complement(a))) = b ),
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,hypothesis,
join(b,complement(join(a,meet(b,complement(a))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_52]),c_0_31]),c_0_60]),c_0_58]) ).
cnf(c_0_63,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
inference(fof_simplification,[status(thm)],[prove_distributivity]) ).
cnf(c_0_64,hypothesis,
join(a,meet(b,complement(a))) = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]) ).
cnf(c_0_65,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
c_0_63 ).
cnf(c_0_66,hypothesis,
meet(complement(a),complement(meet(b,complement(a)))) = complement(b),
inference(rw,[status(thm)],[c_0_58,c_0_64]) ).
cnf(c_0_67,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_65,c_0_14]) ).
cnf(c_0_68,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_66]),c_0_67]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT225-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 23:21:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 106.41/14.00 % Version: 3.5.1
% 106.41/14.00 % Preprocessing class: FSSSSMSSSSSNFFN.
% 106.41/14.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 106.41/14.00 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 106.41/14.00 % Starting new_bool_3 with 300s (1) cores
% 106.41/14.00 % Starting new_bool_1 with 300s (1) cores
% 106.41/14.00 % Starting sh5l with 300s (1) cores
% 106.41/14.00 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2576785 completed with status 0
% 106.41/14.00 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 106.41/14.00 % Preprocessing class: FSSSSMSSSSSNFFN.
% 106.41/14.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 106.41/14.00 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 106.41/14.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 106.41/14.00 % No SInE strategy applied
% 106.41/14.00 % Search class: FHUPM-FFSF21-MFFFFFNN
% 106.41/14.00 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 106.41/14.00 % Starting SubtermCWHack with 136s (1) cores
% 106.41/14.00 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 106.41/14.00 % Starting G-E--_303_C18_F1_URBAN_S0Y with 136s (1) cores
% 106.41/14.00 % Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 106.41/14.00 % Starting new_bool_3 with 136s (1) cores
% 106.41/14.00 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2576790 completed with status 0
% 106.41/14.00 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 106.41/14.00 % Preprocessing class: FSSSSMSSSSSNFFN.
% 106.41/14.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 106.41/14.00 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 106.41/14.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 106.41/14.00 % No SInE strategy applied
% 106.41/14.00 % Search class: FHUPM-FFSF21-MFFFFFNN
% 106.41/14.00 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 106.41/14.00 % Starting SubtermCWHack with 136s (1) cores
% 106.41/14.00 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 106.41/14.00 % Preprocessing time : 0.002 s
% 106.41/14.00
% 106.41/14.00 % Proof found!
% 106.41/14.00 % SZS status Unsatisfiable
% 106.41/14.00 % SZS output start CNFRefutation
% See solution above
% 106.41/14.01 % Parsed axioms : 14
% 106.41/14.01 % Removed by relevancy pruning/SinE : 0
% 106.41/14.01 % Initial clauses : 14
% 106.41/14.01 % Removed in clause preprocessing : 0
% 106.41/14.01 % Initial clauses in saturation : 14
% 106.41/14.01 % Processed clauses : 7960
% 106.41/14.01 % ...of these trivial : 1073
% 106.41/14.01 % ...subsumed : 6147
% 106.41/14.01 % ...remaining for further processing : 740
% 106.41/14.01 % Other redundant clauses eliminated : 0
% 106.41/14.01 % Clauses deleted for lack of memory : 0
% 106.41/14.01 % Backward-subsumed : 75
% 106.41/14.01 % Backward-rewritten : 65
% 106.41/14.01 % Generated clauses : 243320
% 106.41/14.01 % ...of the previous two non-redundant : 188400
% 106.41/14.01 % ...aggressively subsumed : 0
% 106.41/14.01 % Contextual simplify-reflections : 5
% 106.41/14.01 % Paramodulations : 243318
% 106.41/14.01 % Factorizations : 0
% 106.41/14.01 % NegExts : 0
% 106.41/14.01 % Equation resolutions : 2
% 106.41/14.01 % Disequality decompositions : 0
% 106.41/14.01 % Total rewrite steps : 457465
% 106.41/14.01 % ...of those cached : 339405
% 106.41/14.01 % Propositional unsat checks : 0
% 106.41/14.01 % Propositional check models : 0
% 106.41/14.01 % Propositional check unsatisfiable : 0
% 106.41/14.01 % Propositional clauses : 0
% 106.41/14.01 % Propositional clauses after purity: 0
% 106.41/14.01 % Propositional unsat core size : 0
% 106.41/14.01 % Propositional preprocessing time : 0.000
% 106.41/14.01 % Propositional encoding time : 0.000
% 106.41/14.01 % Propositional solver time : 0.000
% 106.41/14.01 % Success case prop preproc time : 0.000
% 106.41/14.01 % Success case prop encoding time : 0.000
% 106.41/14.01 % Success case prop solver time : 0.000
% 106.41/14.01 % Current number of processed clauses : 600
% 106.41/14.01 % Positive orientable unit clauses : 401
% 106.41/14.01 % Positive unorientable unit clauses: 8
% 106.41/14.01 % Negative unit clauses : 51
% 106.41/14.01 % Non-unit-clauses : 140
% 106.41/14.01 % Current number of unprocessed clauses: 179857
% 106.41/14.01 % ...number of literals in the above : 262107
% 106.41/14.01 % Current number of archived formulas : 0
% 106.41/14.01 % Current number of archived clauses : 140
% 106.41/14.01 % Clause-clause subsumption calls (NU) : 8571
% 106.41/14.01 % Rec. Clause-clause subsumption calls : 7342
% 106.41/14.01 % Non-unit clause-clause subsumptions : 671
% 106.41/14.01 % Unit Clause-clause subsumption calls : 541
% 106.41/14.01 % Rewrite failures with RHS unbound : 0
% 106.41/14.01 % BW rewrite match attempts : 9386
% 106.41/14.01 % BW rewrite match successes : 278
% 106.41/14.01 % Condensation attempts : 0
% 106.41/14.01 % Condensation successes : 0
% 106.41/14.01 % Termbank termtop insertions : 5554176
% 106.41/14.01 % Search garbage collected termcells : 8
% 106.41/14.01
% 106.41/14.01 % -------------------------------------------------
% 106.41/14.01 % User time : 11.781 s
% 106.41/14.01 % System time : 0.430 s
% 106.41/14.01 % Total time : 12.211 s
% 106.41/14.01 % Maximum resident set size: 3640 pages
% 106.41/14.01
% 106.41/14.01 % -------------------------------------------------
% 106.41/14.01 % User time : 63.446 s
% 106.41/14.01 % System time : 2.230 s
% 106.41/14.01 % Total time : 65.676 s
% 106.41/14.01 % Maximum resident set size: 4608 pages
% 106.41/14.01 % E exiting
%------------------------------------------------------------------------------