%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL096-1 : 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 : 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 01:11:45 PM UTC 2026
% Result : Unsatisfiable 3.26s 0.94s
% Output : CNFRefutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of clauses : 47 ( 24 unt; 0 nHn; 19 RR)
% Number of literals : 77 ( 0 equ; 36 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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 : 148 ( 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(lg_2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X4),X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lg_2) ).
cnf(lg_4,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X4),equivalent(equivalent(equivalent(X1,X5),X3),equivalent(equivalent(X2,X5),X4)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lg_4) ).
cnf(lg_3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4),equivalent(equivalent(X2,X3),X4)),X5),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lg_3) ).
cnf(prove_lg_1,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lg_1) ).
cnf(c_0_5,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_6,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X1,X2))
| is_a_theorem(X2) ),
c_0_5 ).
cnf(c_0_7,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X4),X4)),
lg_2 ).
cnf(c_0_8,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X4),equivalent(equivalent(equivalent(X1,X5),X3),equivalent(equivalent(X2,X5),X4)))),
lg_4 ).
cnf(c_0_9,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X4)),equivalent(X3,X4)),X1))
| is_a_theorem(X1) ),
inference(pm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,X4),X3),X5))
| is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X2),X5))) ),
inference(pm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_11,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(equivalent(X4,X2),equivalent(X4,X3)))),
inference(pm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_12,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,X5),X1),equivalent(X5,X3)),X4))
| is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X3)),X4)) ),
inference(pm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( ~ is_a_theorem(equivalent(equivalent(X4,X2),equivalent(X4,X3)))
| is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X3))) ),
inference(pm,[status(thm)],[c_0_6,c_0_11]) ).
cnf(c_0_14,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),X4)),equivalent(equivalent(X3,X2),X4))),
inference(pm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_15,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X3)),equivalent(X1,X3))),
inference(pm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,equivalent(equivalent(X3,X3),X2)))),
inference(pm,[status(thm)],[c_0_13,c_0_8]) ).
cnf(c_0_17,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4),equivalent(equivalent(X2,X3),X4)),X5),X5)),
lg_3 ).
cnf(c_0_18,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X2)),equivalent(X1,X3)),X3)),
inference(pm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_19,plain,
( ~ is_a_theorem(equivalent(X1,X3))
| is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X2),X3))) ),
inference(pm,[status(thm)],[c_0_6,c_0_16]) ).
cnf(c_0_20,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X4)),X5),equivalent(equivalent(X3,X4),X5)),X1))
| is_a_theorem(X1) ),
inference(pm,[status(thm)],[c_0_6,c_0_17]) ).
cnf(c_0_21,plain,
( ~ is_a_theorem(equivalent(equivalent(X2,equivalent(X3,X3)),equivalent(X2,X1)))
| is_a_theorem(X1) ),
inference(pm,[status(thm)],[c_0_6,c_0_18]) ).
cnf(c_0_22,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(equivalent(X3,X2))
| is_a_theorem(equivalent(equivalent(X1,X1),X2)) ),
inference(pm,[status(thm)],[c_0_6,c_0_19]) ).
cnf(c_0_23,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X2)),X3),X3)),
inference(pm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_24,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),
inference(fof_simplification,[status(thm)],[prove_lg_1]) ).
cnf(c_0_25,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X2,equivalent(equivalent(X3,X3),X1)))
| is_a_theorem(X1) ),
inference(pm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
is_a_theorem(equivalent(X1,X1)),
inference(pm,[status(thm)],[c_0_21,c_0_11]) ).
cnf(c_0_27,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X4,X4),X2),X3))
| is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X3))) ),
inference(pm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_28,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X1),equivalent(X3,X2)))),
inference(pm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),
c_0_24 ).
cnf(c_0_30,plain,
( ~ is_a_theorem(equivalent(X1,X4))
| ~ is_a_theorem(equivalent(equivalent(X3,X4),equivalent(X3,X2)))
| is_a_theorem(equivalent(X1,X2)) ),
inference(pm,[status(thm)],[c_0_6,c_0_13]) ).
cnf(c_0_31,plain,
( ~ is_a_theorem(equivalent(equivalent(X4,X2),X5))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X4,X1),X5),X3))
| is_a_theorem(equivalent(equivalent(X1,X2),X3)) ),
inference(pm,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_32,plain,
( ~ is_a_theorem(equivalent(equivalent(X2,X2),X1))
| is_a_theorem(X1) ),
inference(pm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,equivalent(equivalent(X3,equivalent(X4,X4)),equivalent(X3,X2))))),
inference(pm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(X2,X1),equivalent(X2,c)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),X1)) ),
inference(pm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(equivalent(equivalent(X1,X1),X2)) ),
inference(pm,[status(thm)],[c_0_22,c_0_26]) ).
cnf(c_0_36,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X1),equivalent(X5,X2)),X3),X4))
| is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),X4)) ),
inference(pm,[status(thm)],[c_0_31,c_0_7]) ).
cnf(c_0_37,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(X3,X3)),equivalent(X2,X1)))),
inference(pm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( ~ is_a_theorem(equivalent(X1,c))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),X1)) ),
inference(pm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
( ~ is_a_theorem(equivalent(X2,X3))
| is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,X3))) ),
inference(pm,[status(thm)],[c_0_13,c_0_35]) ).
cnf(c_0_40,plain,
( ~ is_a_theorem(equivalent(equivalent(X5,equivalent(X2,X3)),equivalent(X5,X4)))
| is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4)) ),
inference(pm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_41,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X1),X3)),X3)),
inference(pm,[status(thm)],[c_0_36,c_0_18]) ).
cnf(c_0_42,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X1,equivalent(X3,equivalent(equivalent(X3,equivalent(X4,X4)),X2))))),
inference(pm,[status(thm)],[c_0_13,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( ~ is_a_theorem(equivalent(c,X1))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),X1),c)) ),
inference(pm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X1,equivalent(equivalent(X3,X2),X4))),X4)),
inference(pm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
is_a_theorem(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,equivalent(X3,X3)),X1)))),
inference(pm,[status(thm)],[c_0_32,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(pm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL096-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 00:04:33 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 3.26/0.93 % Version: 3.5.1
% 3.26/0.93 % Preprocessing class: FSSSSMSSSSSNFFN.
% 3.26/0.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.26/0.93 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 3.26/0.93 % Starting new_bool_3 with 300s (1) cores
% 3.26/0.93 % Starting new_bool_1 with 300s (1) cores
% 3.26/0.93 % Starting sh5l with 300s (1) cores
% 3.26/0.93 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2113357 completed with status 0
% 3.26/0.93 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 3.26/0.93 % Preprocessing class: FSSSSMSSSSSNFFN.
% 3.26/0.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.26/0.93 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 3.26/0.93 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.26/0.93 % No SInE strategy applied
% 3.26/0.93 % Search class: FHUNS-FFSF22-DFFFFFNN
% 3.26/0.93 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.26/0.93 % Starting SubtermCWHack with 136s (1) cores
% 3.26/0.93 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 3.26/0.93 % Starting G-E--_300_C01_S5PRR_S00 with 136s (1) cores
% 3.26/0.93 % Starting new_bool_3 with 136s (1) cores
% 3.26/0.93 % Starting new_bool_1 with 136s (1) cores
% 3.26/0.94 % G-E--_300_C01_S5PRR_S00 with pid 2113363 completed with status 0
% 3.26/0.94 % Result found by G-E--_300_C01_S5PRR_S00
% 3.26/0.94 % Preprocessing class: FSSSSMSSSSSNFFN.
% 3.26/0.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.26/0.94 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 3.26/0.94 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.26/0.94 % No SInE strategy applied
% 3.26/0.94 % Search class: FHUNS-FFSF22-DFFFFFNN
% 3.26/0.94 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.26/0.94 % Starting SubtermCWHack with 136s (1) cores
% 3.26/0.94 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 3.26/0.94 % Starting G-E--_300_C01_S5PRR_S00 with 136s (1) cores
% 3.26/0.94 % Preprocessing time : 0.001 s
% 3.26/0.94
% 3.26/0.94 % Proof found!
% 3.26/0.94 % SZS status Unsatisfiable
% 3.26/0.94 % SZS output start CNFRefutation
% See solution above
% 3.26/0.94 % Parsed axioms : 5
% 3.26/0.94 % Removed by relevancy pruning/SinE : 0
% 3.26/0.94 % Initial clauses : 5
% 3.26/0.94 % Removed in clause preprocessing : 0
% 3.26/0.94 % Initial clauses in saturation : 5
% 3.26/0.94 % Processed clauses : 910
% 3.26/0.94 % ...of these trivial : 72
% 3.26/0.94 % ...subsumed : 577
% 3.26/0.94 % ...remaining for further processing : 261
% 3.26/0.94 % Other redundant clauses eliminated : 0
% 3.26/0.94 % Clauses deleted for lack of memory : 0
% 3.26/0.94 % Backward-subsumed : 3
% 3.26/0.94 % Backward-rewritten : 4
% 3.26/0.94 % Generated clauses : 14548
% 3.26/0.94 % ...of the previous two non-redundant : 13559
% 3.26/0.94 % ...aggressively subsumed : 0
% 3.26/0.94 % Contextual simplify-reflections : 0
% 3.26/0.94 % Paramodulations : 14548
% 3.26/0.94 % Factorizations : 0
% 3.26/0.94 % NegExts : 0
% 3.26/0.94 % Equation resolutions : 0
% 3.26/0.94 % Disequality decompositions : 0
% 3.26/0.94 % Total rewrite steps : 1481
% 3.26/0.94 % ...of those cached : 1270
% 3.26/0.94 % Propositional unsat checks : 0
% 3.26/0.94 % Propositional check models : 0
% 3.26/0.94 % Propositional check unsatisfiable : 0
% 3.26/0.94 % Propositional clauses : 0
% 3.26/0.94 % Propositional clauses after purity: 0
% 3.26/0.94 % Propositional unsat core size : 0
% 3.26/0.94 % Propositional preprocessing time : 0.000
% 3.26/0.94 % Propositional encoding time : 0.000
% 3.26/0.94 % Propositional solver time : 0.000
% 3.26/0.94 % Success case prop preproc time : 0.000
% 3.26/0.94 % Success case prop encoding time : 0.000
% 3.26/0.94 % Success case prop solver time : 0.000
% 3.26/0.94 % Current number of processed clauses : 254
% 3.26/0.94 % Positive orientable unit clauses : 113
% 3.26/0.94 % Positive unorientable unit clauses: 0
% 3.26/0.94 % Negative unit clauses : 4
% 3.26/0.94 % Non-unit-clauses : 137
% 3.26/0.94 % Current number of unprocessed clauses: 12624
% 3.26/0.94 % ...number of literals in the above : 32088
% 3.26/0.94 % Current number of archived formulas : 0
% 3.26/0.94 % Current number of archived clauses : 7
% 3.26/0.94 % Clause-clause subsumption calls (NU) : 4928
% 3.26/0.94 % Rec. Clause-clause subsumption calls : 4059
% 3.26/0.94 % Non-unit clause-clause subsumptions : 562
% 3.26/0.94 % Unit Clause-clause subsumption calls : 251
% 3.26/0.94 % Rewrite failures with RHS unbound : 0
% 3.26/0.94 % BW rewrite match attempts : 8576
% 3.26/0.94 % BW rewrite match successes : 4
% 3.26/0.94 % Condensation attempts : 0
% 3.26/0.94 % Condensation successes : 0
% 3.26/0.94 % Termbank termtop insertions : 197147
% 3.26/0.94 % Search garbage collected termcells : 8
% 3.26/0.94
% 3.26/0.94 % -------------------------------------------------
% 3.26/0.94 % User time : 0.428 s
% 3.26/0.94 % System time : 0.031 s
% 3.26/0.94 % Total time : 0.459 s
% 3.26/0.94 % Maximum resident set size: 3588 pages
% 3.26/0.94
% 3.26/0.94 % -------------------------------------------------
% 3.26/0.94 % User time : 2.178 s
% 3.26/0.94 % System time : 0.133 s
% 3.26/0.94 % Total time : 2.311 s
% 3.26/0.94 % Maximum resident set size: 4608 pages
% 3.26/0.94 % E exiting
%------------------------------------------------------------------------------