%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL131-1 : 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 : n019.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 01:11:51 PM UTC 2026
% Result : Unsatisfiable 4.98s 1.18s
% Output : CNFRefutation 4.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of clauses : 33 ( 21 unt; 0 nHn; 14 RR)
% Number of literals : 49 ( 0 equ; 19 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 94 ( 0 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(s_6,axiom,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4))),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_6) ).
cnf(prove_lg_2,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lg_2) ).
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(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4))),X1)),
s_6 ).
cnf(c_0_6,plain,
( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),equivalent(X2,X4))))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3)),equivalent(equivalent(equivalent(X4,X5),equivalent(X6,X5)),equivalent(X4,X6)))),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3))),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,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_8]) ).
cnf(c_0_10,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(equivalent(X1,X4),equivalent(X3,X4)))),
inference(spm,[status(thm)],[c_0_9,c_0_7]) ).
cnf(c_0_11,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X4),equivalent(equivalent(X1,X3),X4))),
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_12,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X2))),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,X4),equivalent(X2,X4)),X3))
| is_a_theorem(equivalent(equivalent(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_4,c_0_11]) ).
cnf(c_0_14,plain,
is_a_theorem(equivalent(X1,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_15,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3)))),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,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_15]) ).
cnf(c_0_17,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_13,c_0_5]) ).
cnf(c_0_18,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_16]) ).
cnf(c_0_19,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_13,c_0_17]) ).
cnf(c_0_20,plain,
( ~ is_a_theorem(equivalent(X2,X1))
| is_a_theorem(equivalent(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_21,plain,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(X2,X2)))),
inference(spm,[status(thm)],[c_0_9,c_0_19]) ).
cnf(c_0_22,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X2)),X1)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
( ~ is_a_theorem(equivalent(equivalent(X2,equivalent(X3,X3)),X1))
| is_a_theorem(equivalent(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_24,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_4,c_0_10]) ).
cnf(c_0_25,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X1)),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_26,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X4),equivalent(X1,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)),X4),equivalent(X1,equivalent(X4,equivalent(X3,X2))))),
inference(spm,[status(thm)],[c_0_13,c_0_26]) ).
cnf(c_0_28,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
inference(fof_simplification,[status(thm)],[prove_lg_2]) ).
cnf(c_0_29,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_4,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
c_0_28 ).
cnf(c_0_31,plain,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))),
inference(spm,[status(thm)],[c_0_29,c_0_5]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL131-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 00:07:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 4.98/1.18 % Version: 3.5.1
% 4.98/1.18 % Preprocessing class: FSSSSMSSSSSNFFN.
% 4.98/1.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.98/1.18 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 4.98/1.18 % Starting new_bool_3 with 300s (1) cores
% 4.98/1.18 % Starting new_bool_1 with 300s (1) cores
% 4.98/1.18 % Starting sh5l with 300s (1) cores
% 4.98/1.18 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1273441 completed with status 0
% 4.98/1.18 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 4.98/1.18 % Preprocessing class: FSSSSMSSSSSNFFN.
% 4.98/1.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.98/1.18 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 4.98/1.18 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.98/1.18 % No SInE strategy applied
% 4.98/1.18 % Search class: FHUNF-FFSF22-MFFFFFNN
% 4.98/1.18 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.98/1.18 % Starting SubtermCWHack with 136s (1) cores
% 4.98/1.18 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 4.98/1.18 % Starting G-E--_060_C18_F1_PI_AE_CS_SP_S0Y with 136s (1) cores
% 4.98/1.18 % Starting new_bool_3 with 136s (1) cores
% 4.98/1.18 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 4.98/1.18 % G-E--_060_C18_F1_PI_AE_CS_SP_S0Y with pid 1273445 completed with status 0
% 4.98/1.18 % Result found by G-E--_060_C18_F1_PI_AE_CS_SP_S0Y
% 4.98/1.18 % Preprocessing class: FSSSSMSSSSSNFFN.
% 4.98/1.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.98/1.18 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 4.98/1.18 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.98/1.18 % No SInE strategy applied
% 4.98/1.18 % Search class: FHUNF-FFSF22-MFFFFFNN
% 4.98/1.18 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.98/1.18 % Starting SubtermCWHack with 136s (1) cores
% 4.98/1.18 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 4.98/1.18 % Starting G-E--_060_C18_F1_PI_AE_CS_SP_S0Y with 136s (1) cores
% 4.98/1.18 % Preprocessing time : 0.002 s
% 4.98/1.18
% 4.98/1.18 % Proof found!
% 4.98/1.18 % SZS status Unsatisfiable
% 4.98/1.18 % SZS output start CNFRefutation
% See solution above
% 4.98/1.18 % Parsed axioms : 3
% 4.98/1.18 % Removed by relevancy pruning/SinE : 0
% 4.98/1.18 % Initial clauses : 3
% 4.98/1.18 % Removed in clause preprocessing : 0
% 4.98/1.18 % Initial clauses in saturation : 3
% 4.98/1.18 % Processed clauses : 7717
% 4.98/1.18 % ...of these trivial : 3041
% 4.98/1.18 % ...subsumed : 4187
% 4.98/1.18 % ...remaining for further processing : 489
% 4.98/1.18 % Other redundant clauses eliminated : 0
% 4.98/1.18 % Clauses deleted for lack of memory : 0
% 4.98/1.18 % Backward-subsumed : 0
% 4.98/1.18 % Backward-rewritten : 2
% 4.98/1.18 % Generated clauses : 43230
% 4.98/1.18 % ...of the previous two non-redundant : 26731
% 4.98/1.18 % ...aggressively subsumed : 0
% 4.98/1.18 % Contextual simplify-reflections : 0
% 4.98/1.18 % Paramodulations : 43230
% 4.98/1.18 % Factorizations : 0
% 4.98/1.18 % NegExts : 0
% 4.98/1.18 % Equation resolutions : 0
% 4.98/1.18 % Disequality decompositions : 0
% 4.98/1.18 % Total rewrite steps : 22239
% 4.98/1.18 % ...of those cached : 21745
% 4.98/1.18 % Propositional unsat checks : 0
% 4.98/1.18 % Propositional check models : 0
% 4.98/1.18 % Propositional check unsatisfiable : 0
% 4.98/1.18 % Propositional clauses : 0
% 4.98/1.18 % Propositional clauses after purity: 0
% 4.98/1.18 % Propositional unsat core size : 0
% 4.98/1.18 % Propositional preprocessing time : 0.000
% 4.98/1.18 % Propositional encoding time : 0.000
% 4.98/1.18 % Propositional solver time : 0.000
% 4.98/1.18 % Success case prop preproc time : 0.000
% 4.98/1.18 % Success case prop encoding time : 0.000
% 4.98/1.18 % Success case prop solver time : 0.000
% 4.98/1.18 % Current number of processed clauses : 487
% 4.98/1.18 % Positive orientable unit clauses : 300
% 4.98/1.18 % Positive unorientable unit clauses: 0
% 4.98/1.18 % Negative unit clauses : 0
% 4.98/1.18 % Non-unit-clauses : 187
% 4.98/1.18 % Current number of unprocessed clauses: 19017
% 4.98/1.18 % ...number of literals in the above : 28738
% 4.98/1.18 % Current number of archived formulas : 0
% 4.98/1.18 % Current number of archived clauses : 2
% 4.98/1.18 % Clause-clause subsumption calls (NU) : 57327
% 4.98/1.18 % Rec. Clause-clause subsumption calls : 57327
% 4.98/1.18 % Non-unit clause-clause subsumptions : 4187
% 4.98/1.18 % Unit Clause-clause subsumption calls : 10
% 4.98/1.18 % Rewrite failures with RHS unbound : 0
% 4.98/1.18 % BW rewrite match attempts : 46244
% 4.98/1.18 % BW rewrite match successes : 2
% 4.98/1.18 % Condensation attempts : 0
% 4.98/1.18 % Condensation successes : 0
% 4.98/1.18 % Termbank termtop insertions : 495940
% 4.98/1.18 % Search garbage collected termcells : 8
% 4.98/1.18
% 4.98/1.18 % -------------------------------------------------
% 4.98/1.18 % User time : 0.663 s
% 4.98/1.18 % System time : 0.019 s
% 4.98/1.18 % Total time : 0.682 s
% 4.98/1.18 % Maximum resident set size: 3636 pages
% 4.98/1.18
% 4.98/1.18 % -------------------------------------------------
% 4.98/1.18 % User time : 3.283 s
% 4.98/1.18 % System time : 0.158 s
% 4.98/1.18 % Total time : 3.442 s
% 4.98/1.18 % Maximum resident set size: 4864 pages
% 4.98/1.18 % E exiting
%------------------------------------------------------------------------------