%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT009-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 01:04:01 PM UTC 2026
% Result : Unsatisfiable 2.86s 0.85s
% Output : CNFRefutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 6 RR)
% Number of literals : 52 ( 51 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 120 ( 18 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
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(distributivity_dual,axiom,
join(meet(join(meet(X1,X2),X3),X2),meet(X3,X1)) = meet(join(meet(join(X1,X2),X3),X2),join(X3,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_dual) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
cnf(prove_distributivity,negated_conjecture,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c_0_9,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_10,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_11,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_12,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_13,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_14,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_15,axiom,
join(meet(join(meet(X1,X2),X3),X2),meet(X3,X1)) = meet(join(meet(join(X1,X2),X3),X2),join(X3,X1)),
distributivity_dual ).
cnf(c_0_16,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_17,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_21,plain,
meet(join(X1,X2),join(X3,meet(join(X2,X3),X1))) = join(meet(X1,X2),meet(X3,join(meet(X2,X3),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_13]),c_0_10]),c_0_10]),c_0_13]) ).
cnf(c_0_22,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_12]),c_0_14]) ).
cnf(c_0_23,plain,
meet(X1,join(X2,join(X1,X3))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_12]) ).
cnf(c_0_24,plain,
join(X1,join(X2,meet(join(X2,X1),X3))) = join(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_13]) ).
cnf(c_0_25,plain,
join(X1,meet(X2,join(X1,meet(join(X3,X1),X2)))) = meet(join(X1,X3),join(X2,X1)),
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_21,c_0_22]),c_0_14]),c_0_18]),c_0_10]),c_0_23]),c_0_13]) ).
cnf(c_0_26,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_27,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_28,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_29,plain,
meet(join(X1,X2),join(X3,meet(X1,join(X2,X3)))) = join(meet(X1,X2),meet(X3,join(meet(X2,X3),X1))),
inference(spm,[status(thm)],[c_0_21,c_0_10]) ).
cnf(c_0_30,plain,
join(X1,meet(join(X2,X3),join(X2,X1))) = join(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_14]),c_0_22]) ).
cnf(c_0_31,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_14]) ).
cnf(c_0_32,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_33,plain,
join(X1,meet(X2,meet(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_10]) ).
cnf(c_0_34,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X2,X1)),
inference(spm,[status(thm)],[c_0_27,c_0_10]) ).
cnf(c_0_35,plain,
meet(join(X1,X2),meet(join(X2,X1),X3)) = meet(join(X1,X2),X3),
inference(spm,[status(thm)],[c_0_11,c_0_28]) ).
cnf(c_0_36,plain,
meet(join(X1,X2),join(X1,X3)) = join(X1,meet(X3,join(X1,X2))),
inference(rw,[status(thm)],[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_29,c_0_30]),c_0_14]),c_0_22]),c_0_10]),c_0_12]),c_0_31]),c_0_32]) ).
cnf(c_0_37,plain,
join(X1,join(X2,meet(X1,X3))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_17]),c_0_14]) ).
cnf(c_0_38,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_39,negated_conjecture,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
inference(fof_simplification,[status(thm)],[prove_distributivity]) ).
cnf(c_0_40,plain,
meet(join(X1,X2),X3) = meet(X3,join(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_28]) ).
cnf(c_0_41,plain,
meet(join(X1,X2),join(X3,X1)) = join(X1,meet(X3,join(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_29,c_0_36]),c_0_14]),c_0_22]),c_0_37]),c_0_10]),c_0_12]),c_0_31]),c_0_32]) ).
cnf(c_0_42,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_11,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
c_0_39 ).
cnf(c_0_44,plain,
join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X3,join(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_36]),c_0_41]) ).
cnf(c_0_45,plain,
meet(join(X1,meet(join(X1,X2),X3)),join(X2,meet(join(X1,X2),X3))) = join(meet(X1,X3),meet(X2,join(meet(X1,X2),meet(join(X1,X2),X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_42]),c_0_11]),c_0_27]),c_0_17]),c_0_13]) ).
cnf(c_0_46,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_9]),c_0_11]) ).
cnf(c_0_47,negated_conjecture,
join(a,meet(c,join(a,b))) != join(a,meet(b,c)),
inference(rw,[status(thm)],[c_0_43,c_0_36]) ).
cnf(c_0_48,plain,
join(X1,meet(join(X2,X1),X3)) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_24]),c_0_11]),c_0_46]),c_0_37]) ).
cnf(c_0_49,negated_conjecture,
join(a,meet(b,join(a,c))) != join(a,meet(b,c)),
inference(rw,[status(thm)],[c_0_47,c_0_44]) ).
cnf(c_0_50,plain,
join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_48,c_0_40]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT009-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n010.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 23:06:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.86/0.85 % Version: 3.5.1
% 2.86/0.85 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.86/0.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.86/0.85 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.86/0.85 % Starting new_bool_3 with 300s (1) cores
% 2.86/0.85 % Starting new_bool_1 with 300s (1) cores
% 2.86/0.85 % Starting sh5l with 300s (1) cores
% 2.86/0.85 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3704383 completed with status 0
% 2.86/0.85 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 2.86/0.85 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.86/0.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.86/0.85 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.86/0.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.86/0.85 % No SInE strategy applied
% 2.86/0.85 % Search class: FUUPM-FFSF22-MFFFFFNN
% 2.86/0.85 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 2.86/0.85 % Starting SubtermCWHack with 136s (1) cores
% 2.86/0.85 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.86/0.85 % Starting E---G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 2.86/0.85 % Starting U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.86/0.85 % Starting U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.86/0.85 % E---G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with pid 3704390 completed with status 0
% 2.86/0.85 % Result found by E---G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S
% 2.86/0.85 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.86/0.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.86/0.85 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.86/0.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.86/0.85 % No SInE strategy applied
% 2.86/0.85 % Search class: FUUPM-FFSF22-MFFFFFNN
% 2.86/0.85 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 2.86/0.85 % Starting SubtermCWHack with 136s (1) cores
% 2.86/0.85 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.86/0.85 % Starting E---G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 2.86/0.85 % Preprocessing time : 0.001 s
% 2.86/0.85 % Presaturation interreduction done
% 2.86/0.85
% 2.86/0.85 % Proof found!
% 2.86/0.85 % SZS status Unsatisfiable
% 2.86/0.85 % SZS output start CNFRefutation
% See solution above
% 2.86/0.85 % Parsed axioms : 10
% 2.86/0.85 % Removed by relevancy pruning/SinE : 0
% 2.86/0.85 % Initial clauses : 10
% 2.86/0.85 % Removed in clause preprocessing : 0
% 2.86/0.85 % Initial clauses in saturation : 10
% 2.86/0.85 % Processed clauses : 1395
% 2.86/0.85 % ...of these trivial : 320
% 2.86/0.85 % ...subsumed : 915
% 2.86/0.85 % ...remaining for further processing : 160
% 2.86/0.85 % Other redundant clauses eliminated : 0
% 2.86/0.85 % Clauses deleted for lack of memory : 0
% 2.86/0.85 % Backward-subsumed : 0
% 2.86/0.85 % Backward-rewritten : 39
% 2.86/0.85 % Generated clauses : 26377
% 2.86/0.85 % ...of the previous two non-redundant : 18957
% 2.86/0.85 % ...aggressively subsumed : 0
% 2.86/0.85 % Contextual simplify-reflections : 0
% 2.86/0.85 % Paramodulations : 26377
% 2.86/0.85 % Factorizations : 0
% 2.86/0.85 % NegExts : 0
% 2.86/0.85 % Equation resolutions : 0
% 2.86/0.85 % Disequality decompositions : 0
% 2.86/0.85 % Total rewrite steps : 52771
% 2.86/0.85 % ...of those cached : 39286
% 2.86/0.85 % Propositional unsat checks : 0
% 2.86/0.85 % Propositional check models : 0
% 2.86/0.85 % Propositional check unsatisfiable : 0
% 2.86/0.85 % Propositional clauses : 0
% 2.86/0.85 % Propositional clauses after purity: 0
% 2.86/0.85 % Propositional unsat core size : 0
% 2.86/0.85 % Propositional preprocessing time : 0.000
% 2.86/0.85 % Propositional encoding time : 0.000
% 2.86/0.85 % Propositional solver time : 0.000
% 2.86/0.85 % Success case prop preproc time : 0.000
% 2.86/0.85 % Success case prop encoding time : 0.000
% 2.86/0.85 % Success case prop solver time : 0.000
% 2.86/0.85 % Current number of processed clauses : 111
% 2.86/0.85 % Positive orientable unit clauses : 101
% 2.86/0.85 % Positive unorientable unit clauses: 10
% 2.86/0.85 % Negative unit clauses : 0
% 2.86/0.85 % Non-unit-clauses : 0
% 2.86/0.85 % Current number of unprocessed clauses: 17557
% 2.86/0.85 % ...number of literals in the above : 17557
% 2.86/0.85 % Current number of archived formulas : 0
% 2.86/0.85 % Current number of archived clauses : 49
% 2.86/0.85 % Clause-clause subsumption calls (NU) : 0
% 2.86/0.85 % Rec. Clause-clause subsumption calls : 0
% 2.86/0.85 % Non-unit clause-clause subsumptions : 0
% 2.86/0.85 % Unit Clause-clause subsumption calls : 96
% 2.86/0.85 % Rewrite failures with RHS unbound : 0
% 2.86/0.85 % BW rewrite match attempts : 1014
% 2.86/0.85 % BW rewrite match successes : 333
% 2.86/0.85 % Condensation attempts : 0
% 2.86/0.85 % Condensation successes : 0
% 2.86/0.85 % Termbank termtop insertions : 384462
% 2.86/0.85 % Search garbage collected termcells : 2
% 2.86/0.85
% 2.86/0.85 % -------------------------------------------------
% 2.86/0.85 % User time : 0.378 s
% 2.86/0.85 % System time : 0.033 s
% 2.86/0.85 % Total time : 0.410 s
% 2.86/0.85 % Maximum resident set size: 3380 pages
% 2.86/0.85
% 2.86/0.85 % -------------------------------------------------
% 2.86/0.85 % User time : 1.729 s
% 2.86/0.85 % System time : 0.122 s
% 2.86/0.85 % Total time : 1.850 s
% 2.86/0.85 % Maximum resident set size: 4608 pages
% 2.86/0.85 % E exiting
%------------------------------------------------------------------------------