%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT223-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 85.13s 13.07s
% Output : CNFRefutation 85.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 65 ( 57 unt; 0 nHn; 25 RR)
% Number of literals : 80 ( 79 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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 : 89 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_join) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
cnf(prove_distributivity_hypothesis,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(meet_join_complement,axiom,
( join(X1,X2) != one
| meet(X1,X2) != zero
| complement(X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',meet_join_complement) ).
cnf(equation_H7,axiom,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X1,join(meet(X1,X2),meet(X3,join(X1,X2)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H7) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
cnf(prove_distributivity,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c_0_13,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_14,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_15,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
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(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_21,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_24,plain,
join(X1,join(complement(X1),X2)) = join(one,X2),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_25,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_20]),c_0_13]) ).
cnf(c_0_27,hypothesis,
join(a,b) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_20]) ).
cnf(c_0_28,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,hypothesis,
join(a,join(X1,b)) = join(X1,b),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_31,plain,
( join(X1,X2) != one
| meet(X1,X2) != zero
| complement(X1) = X2 ),
inference(fof_simplification,[status(thm)],[meet_join_complement]) ).
cnf(c_0_32,axiom,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X1,join(meet(X1,X2),meet(X3,join(X1,X2)))))),
equation_H7 ).
cnf(c_0_33,hypothesis,
join(b,complement(a)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_20]) ).
cnf(c_0_34,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_16]) ).
cnf(c_0_35,plain,
( join(X1,X2) != one
| meet(X1,X2) != zero
| complement(X1) = X2 ),
c_0_31 ).
cnf(c_0_36,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_37,hypothesis,
meet(b,join(complement(a),meet(b,join(meet(b,complement(a)),X1)))) = meet(b,join(complement(a),meet(b,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_38,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_39,plain,
meet(X1,join(X2,meet(X1,join(meet(X1,X2),meet(X3,join(X2,X1)))))) = meet(X1,join(X2,meet(X1,X3))),
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_40,plain,
( meet(X2,join(X1,meet(X2,X3))) != zero
| join(X2,join(X1,meet(X2,join(meet(X2,X1),meet(X3,join(X2,X1)))))) != one
| join(X1,meet(X2,join(meet(X2,X1),meet(X3,join(X2,X1))))) = complement(X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_41,plain,
join(X1,join(X2,meet(X1,X3))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_42,hypothesis,
meet(a,meet(b,X1)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_36,c_0_23]) ).
cnf(c_0_43,hypothesis,
meet(b,join(complement(a),meet(b,complement(meet(b,complement(a)))))) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_16]),c_0_34]),c_0_20]),c_0_33]),c_0_34]) ).
cnf(c_0_44,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_45,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_38]) ).
cnf(c_0_46,plain,
( join(X1,X2) != one
| meet(X2,X1) != zero
| complement(X1) = X2 ),
inference(spm,[status(thm)],[c_0_35,c_0_18]) ).
cnf(c_0_47,hypothesis,
meet(complement(a),join(b,meet(complement(a),join(meet(b,complement(a)),X1)))) = meet(complement(a),join(b,meet(complement(a),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_33]),c_0_34]),c_0_18]) ).
cnf(c_0_48,plain,
( join(X1,X2) != one
| meet(X2,join(X1,meet(X2,X3))) != zero
| join(X1,meet(X2,join(meet(X2,X1),meet(X3,join(X2,X1))))) = complement(X2) ),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,hypothesis,
meet(a,join(complement(a),meet(b,complement(meet(b,complement(a)))))) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_23]) ).
cnf(c_0_50,plain,
meet(X1,meet(X2,complement(meet(X2,X1)))) = zero,
inference(spm,[status(thm)],[c_0_44,c_0_18]) ).
cnf(c_0_51,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_45]) ).
cnf(c_0_52,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_38]),c_0_20]),c_0_16])]) ).
cnf(c_0_53,hypothesis,
meet(complement(a),join(b,meet(complement(a),complement(meet(b,complement(a)))))) = complement(a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_16]),c_0_34]),c_0_33]),c_0_34]) ).
cnf(c_0_54,hypothesis,
join(b,join(X1,complement(a))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_33]),c_0_21]) ).
cnf(c_0_55,hypothesis,
( join(complement(a),meet(b,complement(meet(b,complement(a))))) != one
| meet(b,complement(meet(b,complement(a)))) = a ),
inference(rw,[status(thm)],[inference(cn,[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_51]),c_0_18]),c_0_38]),c_0_45]),c_0_52]),c_0_18]),c_0_38]),c_0_45]),c_0_50])]),c_0_20]) ).
cnf(c_0_56,hypothesis,
join(complement(a),meet(b,complement(meet(b,complement(a))))) = one,
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_22,c_0_43]),c_0_13]),c_0_20]),c_0_17]),c_0_20]),c_0_33]) ).
cnf(c_0_57,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
inference(fof_simplification,[status(thm)],[prove_distributivity]) ).
cnf(c_0_58,plain,
( join(X1,meet(X2,X3)) != one
| meet(X2,meet(X3,X1)) != zero
| complement(X1) = meet(X2,X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_36]) ).
cnf(c_0_59,hypothesis,
join(b,meet(complement(a),complement(meet(b,complement(a))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_53]),c_0_13]),c_0_54]) ).
cnf(c_0_60,hypothesis,
meet(b,complement(meet(b,complement(a)))) = a,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]) ).
cnf(c_0_61,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
c_0_57 ).
cnf(c_0_62,hypothesis,
meet(complement(a),complement(meet(b,complement(a)))) = complement(b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_18]),c_0_60]),c_0_18]),c_0_38])]) ).
cnf(c_0_63,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_61,c_0_20]) ).
cnf(c_0_64,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_62]),c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT223-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n005.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 20 23:21:18 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.28/0.53 Running first-order theorem proving
% 0.28/0.54 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 85.13/13.07 % Version: 3.5.1
% 85.13/13.07 % Preprocessing class: FSSSSMSSSSSNFFN.
% 85.13/13.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 85.13/13.07 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 85.13/13.07 % Starting new_bool_3 with 300s (1) cores
% 85.13/13.07 % Starting new_bool_1 with 300s (1) cores
% 85.13/13.07 % Starting sh5l with 300s (1) cores
% 85.13/13.07 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1972744 completed with status 0
% 85.13/13.07 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 85.13/13.07 % Preprocessing class: FSSSSMSSSSSNFFN.
% 85.13/13.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 85.13/13.07 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 85.13/13.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 85.13/13.07 % No SInE strategy applied
% 85.13/13.07 % Search class: FHUPM-FFSF21-DFFFFFNN
% 85.13/13.07 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 85.13/13.07 % Starting SubtermCWHack with 136s (1) cores
% 85.13/13.07 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 85.13/13.07 % Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 85.13/13.07 % Starting new_bool_3 with 136s (1) cores
% 85.13/13.07 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 85.13/13.07 % G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with pid 1972755 completed with status 0
% 85.13/13.07 % Result found by G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN
% 85.13/13.07 % Preprocessing class: FSSSSMSSSSSNFFN.
% 85.13/13.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 85.13/13.07 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 85.13/13.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 85.13/13.07 % No SInE strategy applied
% 85.13/13.07 % Search class: FHUPM-FFSF21-DFFFFFNN
% 85.13/13.07 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 85.13/13.07 % Starting SubtermCWHack with 136s (1) cores
% 85.13/13.07 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 85.13/13.07 % Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 85.13/13.07 % Starting new_bool_3 with 136s (1) cores
% 85.13/13.07 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 85.13/13.07 % Preprocessing time : 0.002 s
% 85.13/13.07
% 85.13/13.07 % Proof found!
% 85.13/13.07 % SZS status Unsatisfiable
% 85.13/13.07 % SZS output start CNFRefutation
% See solution above
% 85.13/13.07 % Parsed axioms : 14
% 85.13/13.07 % Removed by relevancy pruning/SinE : 0
% 85.13/13.07 % Initial clauses : 14
% 85.13/13.07 % Removed in clause preprocessing : 0
% 85.13/13.07 % Initial clauses in saturation : 14
% 85.13/13.07 % Processed clauses : 5883
% 85.13/13.07 % ...of these trivial : 829
% 85.13/13.07 % ...subsumed : 4459
% 85.13/13.07 % ...remaining for further processing : 595
% 85.13/13.07 % Other redundant clauses eliminated : 0
% 85.13/13.07 % Clauses deleted for lack of memory : 0
% 85.13/13.07 % Backward-subsumed : 61
% 85.13/13.07 % Backward-rewritten : 36
% 85.13/13.07 % Generated clauses : 224273
% 85.13/13.07 % ...of the previous two non-redundant : 161710
% 85.13/13.07 % ...aggressively subsumed : 0
% 85.13/13.07 % Contextual simplify-reflections : 9
% 85.13/13.07 % Paramodulations : 224267
% 85.13/13.07 % Factorizations : 0
% 85.13/13.07 % NegExts : 0
% 85.13/13.07 % Equation resolutions : 6
% 85.13/13.07 % Disequality decompositions : 0
% 85.13/13.07 % Total rewrite steps : 544182
% 85.13/13.07 % ...of those cached : 429981
% 85.13/13.07 % Propositional unsat checks : 0
% 85.13/13.07 % Propositional check models : 0
% 85.13/13.07 % Propositional check unsatisfiable : 0
% 85.13/13.07 % Propositional clauses : 0
% 85.13/13.07 % Propositional clauses after purity: 0
% 85.13/13.07 % Propositional unsat core size : 0
% 85.13/13.07 % Propositional preprocessing time : 0.000
% 85.13/13.07 % Propositional encoding time : 0.000
% 85.13/13.07 % Propositional solver time : 0.000
% 85.13/13.07 % Success case prop preproc time : 0.000
% 85.13/13.07 % Success case prop encoding time : 0.000
% 85.13/13.07 % Success case prop solver time : 0.000
% 85.13/13.07 % Current number of processed clauses : 498
% 85.13/13.07 % Positive orientable unit clauses : 356
% 85.13/13.07 % Positive unorientable unit clauses: 8
% 85.13/13.07 % Negative unit clauses : 44
% 85.13/13.07 % Non-unit-clauses : 90
% 85.13/13.07 % Current number of unprocessed clauses: 155155
% 85.13/13.07 % ...number of literals in the above : 207739
% 85.13/13.07 % Current number of archived formulas : 0
% 85.13/13.07 % Current number of archived clauses : 97
% 85.13/13.07 % Clause-clause subsumption calls (NU) : 2344
% 85.13/13.07 % Rec. Clause-clause subsumption calls : 2191
% 85.13/13.07 % Non-unit clause-clause subsumptions : 557
% 85.13/13.07 % Unit Clause-clause subsumption calls : 321
% 85.13/13.07 % Rewrite failures with RHS unbound : 0
% 85.13/13.07 % BW rewrite match attempts : 5682
% 85.13/13.07 % BW rewrite match successes : 274
% 85.13/13.07 % Condensation attempts : 0
% 85.13/13.07 % Condensation successes : 0
% 85.13/13.07 % Termbank termtop insertions : 6835533
% 85.13/13.07 % Search garbage collected termcells : 8
% 85.13/13.07
% 85.13/13.07 % -------------------------------------------------
% 85.13/13.07 % User time : 11.684 s
% 85.13/13.07 % System time : 0.403 s
% 85.13/13.07 % Total time : 12.087 s
% 85.13/13.07 % Maximum resident set size: 3640 pages
% 85.13/13.07
% 85.13/13.07 % -------------------------------------------------
% 85.13/13.07 % User time : 57.959 s
% 85.13/13.07 % System time : 2.104 s
% 85.13/13.07 % Total time : 60.063 s
% 85.13/13.07 % Maximum resident set size: 4864 pages
% 85.13/13.07 % E exiting
%------------------------------------------------------------------------------