%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL121-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 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 : Thu Sep 24 01:11:50 PM UTC 2026
% Result : Unsatisfiable 12.58s 2.45s
% Output : CNFRefutation 12.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of clauses : 46 ( 19 unt; 0 nHn; 22 RR)
% Number of literals : 81 ( 0 equ; 38 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 142 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X1,X2))
| is_a_theorem(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(lg_2,axiom,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lg_2) ).
cnf(prove_lg_1,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,equivalent(c,c)),b)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lg_1) ).
cnf(c_0_3,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X1,X2))
| is_a_theorem(X2) ),
inference(fof_simplification,[status(thm)],[condensed_detachment]) ).
cnf(c_0_4,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X1,X2))
| is_a_theorem(X2) ),
c_0_3 ).
cnf(c_0_5,axiom,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))),
lg_2 ).
cnf(c_0_6,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4))))) ),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
( ~ is_a_theorem(X4)
| is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3)))) ),
inference(spm,[status(thm)],[c_0_4,c_0_6]) ).
cnf(c_0_8,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3)))),
inference(spm,[status(thm)],[c_0_7,c_0_5]) ).
cnf(c_0_9,plain,
( ~ is_a_theorem(equivalent(X1,X3))
| is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2))) ),
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
cnf(c_0_10,plain,
( ~ is_a_theorem(equivalent(X3,X1))
| ~ is_a_theorem(equivalent(X3,X2))
| is_a_theorem(equivalent(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_9]) ).
cnf(c_0_11,plain,
( ~ is_a_theorem(equivalent(equivalent(X2,X4),X1))
| is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X4,X3)))) ),
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
cnf(c_0_12,plain,
( ~ is_a_theorem(X4)
| ~ is_a_theorem(equivalent(equivalent(X1,X3),X4))
| is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2))) ),
inference(spm,[status(thm)],[c_0_4,c_0_11]) ).
cnf(c_0_13,plain,
( ~ is_a_theorem(equivalent(X4,X2))
| ~ is_a_theorem(equivalent(equivalent(X4,X3),X1))
| is_a_theorem(equivalent(X1,equivalent(X2,X3))) ),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_14,plain,
( ~ is_a_theorem(equivalent(equivalent(X1,X4),equivalent(X3,X4)))
| is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2))) ),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
cnf(c_0_15,plain,
( ~ is_a_theorem(equivalent(X1,X4))
| is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X4,X3))) ),
inference(spm,[status(thm)],[c_0_13,c_0_8]) ).
cnf(c_0_16,plain,
( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X3,X5),equivalent(X4,X5))))
| is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X4),X2))) ),
inference(spm,[status(thm)],[c_0_14,c_0_6]) ).
cnf(c_0_17,plain,
( ~ is_a_theorem(equivalent(X3,X1))
| ~ is_a_theorem(equivalent(equivalent(X3,X4),equivalent(X2,X4)))
| is_a_theorem(equivalent(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_15]) ).
cnf(c_0_18,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_16,c_0_8]) ).
cnf(c_0_19,plain,
( ~ is_a_theorem(equivalent(equivalent(X2,X3),X1))
| is_a_theorem(equivalent(X1,equivalent(X2,X3))) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3))),
inference(spm,[status(thm)],[c_0_19,c_0_8]) ).
cnf(c_0_21,plain,
( ~ is_a_theorem(equivalent(equivalent(X1,X3),equivalent(X2,X3)))
| is_a_theorem(equivalent(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_20]) ).
cnf(c_0_22,plain,
( ~ is_a_theorem(equivalent(X3,X1))
| is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2))) ),
inference(spm,[status(thm)],[c_0_19,c_0_9]) ).
cnf(c_0_23,plain,
( ~ is_a_theorem(equivalent(X2,X1))
| is_a_theorem(equivalent(X1,X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X2,X4),equivalent(X3,X4)),X1))
| is_a_theorem(equivalent(X1,equivalent(X2,X3))) ),
inference(spm,[status(thm)],[c_0_10,c_0_20]) ).
cnf(c_0_25,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))),X1)),
inference(spm,[status(thm)],[c_0_23,c_0_5]) ).
cnf(c_0_26,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X4,X3))),equivalent(X1,equivalent(X2,X4)))),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X4,X2)),equivalent(X1,equivalent(X4,X3)))),
inference(spm,[status(thm)],[c_0_24,c_0_26]) ).
cnf(c_0_28,plain,
( ~ is_a_theorem(equivalent(equivalent(X2,equivalent(X3,X3)),X1))
| is_a_theorem(equivalent(X1,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).
cnf(c_0_29,plain,
( ~ is_a_theorem(equivalent(X1,X3))
| ~ is_a_theorem(equivalent(X3,X2))
| is_a_theorem(equivalent(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_22]) ).
cnf(c_0_30,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X2)),X1)),
inference(spm,[status(thm)],[c_0_21,c_0_27]) ).
cnf(c_0_31,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X3),X2)),X1)),
inference(spm,[status(thm)],[c_0_28,c_0_8]) ).
cnf(c_0_32,plain,
( ~ is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X3,X3))))
| is_a_theorem(equivalent(X1,X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
( ~ is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X3),X2)))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_4,c_0_31]) ).
cnf(c_0_34,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X1)),
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_35,plain,
( ~ is_a_theorem(equivalent(equivalent(X2,X3),equivalent(X1,equivalent(X3,X2))))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_11]) ).
cnf(c_0_36,plain,
( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(X4,X3)),X2))
| is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X3,X4)))) ),
inference(spm,[status(thm)],[c_0_13,c_0_34]) ).
cnf(c_0_37,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(equivalent(X1,equivalent(X4,X3)),equivalent(X2,X4)))),
inference(spm,[status(thm)],[c_0_23,c_0_27]) ).
cnf(c_0_38,plain,
( ~ is_a_theorem(equivalent(equivalent(X2,X3),equivalent(X1,X3)))
| is_a_theorem(equivalent(X1,X2)) ),
inference(spm,[status(thm)],[c_0_35,c_0_6]) ).
cnf(c_0_39,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X4,X2)),equivalent(X3,X4)))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,equivalent(c,c)),b)))),
inference(fof_simplification,[status(thm)],[prove_lg_1]) ).
cnf(c_0_41,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(equivalent(X3,X3),X4)),X4),X1))
| is_a_theorem(equivalent(X1,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_31]) ).
cnf(c_0_42,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X4,X2)),equivalent(X3,X4)),X1)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,equivalent(c,c)),b)))),
c_0_40 ).
cnf(c_0_44,plain,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,equivalent(X3,X3)),X2)))),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL121-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 00:06:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 12.58/2.45 % Version: 3.5.1
% 12.58/2.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 12.58/2.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.58/2.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 12.58/2.45 % Starting new_bool_3 with 300s (1) cores
% 12.58/2.45 % Starting new_bool_1 with 300s (1) cores
% 12.58/2.45 % Starting sh5l with 300s (1) cores
% 12.58/2.45 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1835024 completed with status 0
% 12.58/2.45 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 12.58/2.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 12.58/2.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.58/2.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 12.58/2.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 12.58/2.45 % No SInE strategy applied
% 12.58/2.45 % Search class: FHUNF-FFSF22-MFFFFFNN
% 12.58/2.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 12.58/2.45 % Starting SubtermCWHack with 136s (1) cores
% 12.58/2.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 12.58/2.45 % Starting G-E--_060_C18_F1_PI_AE_CS_SP_S0Y with 136s (1) cores
% 12.58/2.45 % Starting new_bool_3 with 136s (1) cores
% 12.58/2.45 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 12.58/2.45 % G-E--_060_C18_F1_PI_AE_CS_SP_S0Y with pid 1835030 completed with status 0
% 12.58/2.45 % Result found by G-E--_060_C18_F1_PI_AE_CS_SP_S0Y
% 12.58/2.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 12.58/2.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.58/2.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 12.58/2.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 12.58/2.45 % No SInE strategy applied
% 12.58/2.45 % Search class: FHUNF-FFSF22-MFFFFFNN
% 12.58/2.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 12.58/2.45 % Starting SubtermCWHack with 136s (1) cores
% 12.58/2.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 12.58/2.45 % Starting G-E--_060_C18_F1_PI_AE_CS_SP_S0Y with 136s (1) cores
% 12.58/2.45 % Preprocessing time : 0.001 s
% 12.58/2.45
% 12.58/2.45 % Proof found!
% 12.58/2.45 % SZS status Unsatisfiable
% 12.58/2.45 % SZS output start CNFRefutation
% See solution above
% 12.58/2.45 % Parsed axioms : 3
% 12.58/2.45 % Removed by relevancy pruning/SinE : 0
% 12.58/2.45 % Initial clauses : 3
% 12.58/2.45 % Removed in clause preprocessing : 0
% 12.58/2.45 % Initial clauses in saturation : 3
% 12.58/2.45 % Processed clauses : 13706
% 12.58/2.45 % ...of these trivial : 3458
% 12.58/2.45 % ...subsumed : 9515
% 12.58/2.45 % ...remaining for further processing : 733
% 12.58/2.45 % Other redundant clauses eliminated : 0
% 12.58/2.45 % Clauses deleted for lack of memory : 0
% 12.58/2.45 % Backward-subsumed : 1
% 12.58/2.45 % Backward-rewritten : 6
% 12.58/2.45 % Generated clauses : 106341
% 12.58/2.45 % ...of the previous two non-redundant : 71148
% 12.58/2.45 % ...aggressively subsumed : 0
% 12.58/2.45 % Contextual simplify-reflections : 0
% 12.58/2.45 % Paramodulations : 106341
% 12.58/2.45 % Factorizations : 0
% 12.58/2.45 % NegExts : 0
% 12.58/2.45 % Equation resolutions : 0
% 12.58/2.45 % Disequality decompositions : 0
% 12.58/2.45 % Total rewrite steps : 44617
% 12.58/2.45 % ...of those cached : 43950
% 12.58/2.45 % Propositional unsat checks : 0
% 12.58/2.45 % Propositional check models : 0
% 12.58/2.45 % Propositional check unsatisfiable : 0
% 12.58/2.45 % Propositional clauses : 0
% 12.58/2.45 % Propositional clauses after purity: 0
% 12.58/2.45 % Propositional unsat core size : 0
% 12.58/2.45 % Propositional preprocessing time : 0.000
% 12.58/2.45 % Propositional encoding time : 0.000
% 12.58/2.45 % Propositional solver time : 0.000
% 12.58/2.45 % Success case prop preproc time : 0.000
% 12.58/2.45 % Success case prop encoding time : 0.000
% 12.58/2.45 % Success case prop solver time : 0.000
% 12.58/2.45 % Current number of processed clauses : 726
% 12.58/2.45 % Positive orientable unit clauses : 380
% 12.58/2.45 % Positive unorientable unit clauses: 0
% 12.58/2.45 % Negative unit clauses : 1
% 12.58/2.45 % Non-unit-clauses : 345
% 12.58/2.45 % Current number of unprocessed clauses: 57328
% 12.58/2.45 % ...number of literals in the above : 100678
% 12.58/2.45 % Current number of archived formulas : 0
% 12.58/2.45 % Current number of archived clauses : 7
% 12.58/2.45 % Clause-clause subsumption calls (NU) : 213442
% 12.58/2.45 % Rec. Clause-clause subsumption calls : 213284
% 12.58/2.45 % Non-unit clause-clause subsumptions : 9516
% 12.58/2.45 % Unit Clause-clause subsumption calls : 162
% 12.58/2.45 % Rewrite failures with RHS unbound : 0
% 12.58/2.45 % BW rewrite match attempts : 73090
% 12.58/2.45 % BW rewrite match successes : 6
% 12.58/2.45 % Condensation attempts : 0
% 12.58/2.45 % Condensation successes : 0
% 12.58/2.45 % Termbank termtop insertions : 1307308
% 12.58/2.45 % Search garbage collected termcells : 8
% 12.58/2.45
% 12.58/2.45 % -------------------------------------------------
% 12.58/2.45 % User time : 0.938 s
% 12.58/2.45 % System time : 0.029 s
% 12.58/2.45 % Total time : 0.968 s
% 12.58/2.45 % Maximum resident set size: 3636 pages
% 12.58/2.45
% 12.58/2.45 % -------------------------------------------------
% 12.58/2.45 % User time : 7.285 s
% 12.58/2.45 % System time : 0.302 s
% 12.58/2.45 % Total time : 7.587 s
% 12.58/2.45 % Maximum resident set size: 4608 pages
% 12.58/2.45 % E exiting
%------------------------------------------------------------------------------