%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYN078+1 : TPTP v9.3.1. Released v2.0.0.
% 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 03:23:03 PM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 65 ( 9 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 67 ( 23 ~; 30 |; 8 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 17 ( 0 sgn 7 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel56,conjecture,
( ! [X1] :
( ? [X2] :
( X1 = f(X2)
& big_p(X2) )
=> big_p(X1) )
<=> ! [X3] :
( big_p(X3)
=> big_p(f(X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel56) ).
fof(c_0_1,negated_conjecture,
~ ( ! [X1] :
( ? [X2] :
( X1 = f(X2)
& big_p(X2) )
=> big_p(X1) )
<=> ! [X3] :
( big_p(X3)
=> big_p(f(X3)) ) ),
inference(assume_negation,[status(cth)],[pel56]) ).
fof(c_0_2,negated_conjecture,
! [X7,X8,X9] :
( ( big_p(f(X9))
| ~ big_p(X9)
| big_p(X7)
| X7 != f(X8)
| ~ big_p(X8) )
& ( ~ big_p(esk1_0)
| ~ big_p(f(esk3_0)) )
& ( ~ big_p(esk1_0)
| big_p(esk3_0) )
& ( esk1_0 = f(esk2_0)
| ~ big_p(f(esk3_0)) )
& ( esk1_0 = f(esk2_0)
| big_p(esk3_0) )
& ( big_p(esk2_0)
| ~ big_p(f(esk3_0)) )
& ( big_p(esk2_0)
| big_p(esk3_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])])]) ).
cnf(c_0_3,negated_conjecture,
( ~ big_p(X3)
| X2 != f(X1)
| ~ big_p(X1)
| big_p(f(X3))
| big_p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
( ~ big_p(X1)
| ~ big_p(X2)
| big_p(f(X2))
| big_p(f(X1)) ),
inference(er,[status(thm)],[c_0_3]) ).
cnf(c_0_5,negated_conjecture,
( big_p(esk2_0)
| big_p(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6,negated_conjecture,
( ~ big_p(X1)
| big_p(esk3_0)
| big_p(f(X1))
| big_p(f(esk2_0)) ),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,negated_conjecture,
( big_p(esk3_0)
| big_p(f(esk2_0)) ),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( esk1_0 = f(esk2_0)
| big_p(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_9,negated_conjecture,
( ~ big_p(esk1_0)
| big_p(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_10,negated_conjecture,
big_p(esk3_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
cnf(c_0_11,negated_conjecture,
( ~ big_p(X1)
| big_p(f(X1))
| big_p(f(esk3_0)) ),
inference(spm,[status(thm)],[c_0_4,c_0_10]) ).
cnf(c_0_12,negated_conjecture,
( ~ big_p(f(esk3_0))
| big_p(esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_13,negated_conjecture,
big_p(f(esk3_0)),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( ~ big_p(f(esk3_0))
| esk1_0 = f(esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_15,negated_conjecture,
( ~ big_p(esk1_0)
| ~ big_p(f(esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_16,negated_conjecture,
big_p(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13])]) ).
cnf(c_0_17,negated_conjecture,
f(esk2_0) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_13])]) ).
cnf(c_0_18,negated_conjecture,
~ big_p(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_13])]) ).
cnf(c_0_19,negated_conjecture,
( ~ big_p(X1)
| big_p(f(X1)) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_16]),c_0_17]),c_0_18]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_16])]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN078+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n004.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 10:41:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 0.09/0.41 % Version: 3.5.1
% 0.09/0.41 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.09/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.41 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.09/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.41 % Starting sh5l with 300s (1) cores
% 0.09/0.41 % new_bool_3 with pid 2936590 completed with status 0
% 0.09/0.41 % Result found by new_bool_3
% 0.09/0.41 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.09/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.41 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.09/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.41 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.41 % Search class: FGHSF-FFSF11-SFFFFFNN
% 0.09/0.41 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.41 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.41 % SubtermCWHack with pid 2936595 completed with status 0
% 0.09/0.41 % Result found by SubtermCWHack
% 0.09/0.41 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.09/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.41 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.09/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.41 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.41 % Search class: FGHSF-FFSF11-SFFFFFNN
% 0.09/0.41 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.41 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.41 % Preprocessing time : 0.001 s
% 0.09/0.41
% 0.09/0.41 % Proof found!
% 0.09/0.41 % SZS status Theorem
% 0.09/0.41 % SZS output start CNFRefutation
% See solution above
% 0.09/0.41 % Parsed axioms : 1
% 0.09/0.41 % Removed by relevancy pruning/SinE : 0
% 0.09/0.41 % Initial clauses : 7
% 0.09/0.41 % Removed in clause preprocessing : 0
% 0.09/0.41 % Initial clauses in saturation : 7
% 0.09/0.41 % Processed clauses : 18
% 0.09/0.41 % ...of these trivial : 0
% 0.09/0.41 % ...subsumed : 0
% 0.09/0.41 % ...remaining for further processing : 18
% 0.09/0.41 % Other redundant clauses eliminated : 1
% 0.09/0.41 % Clauses deleted for lack of memory : 0
% 0.09/0.41 % Backward-subsumed : 2
% 0.09/0.41 % Backward-rewritten : 9
% 0.09/0.41 % Generated clauses : 12
% 0.09/0.41 % ...of the previous two non-redundant : 14
% 0.09/0.41 % ...aggressively subsumed : 0
% 0.09/0.41 % Contextual simplify-reflections : 1
% 0.09/0.41 % Paramodulations : 11
% 0.09/0.41 % Factorizations : 0
% 0.09/0.41 % NegExts : 0
% 0.09/0.41 % Equation resolutions : 1
% 0.09/0.41 % Disequality decompositions : 0
% 0.09/0.41 % Total rewrite steps : 11
% 0.09/0.41 % ...of those cached : 7
% 0.09/0.41 % Propositional unsat checks : 0
% 0.09/0.41 % Propositional check models : 0
% 0.09/0.41 % Propositional check unsatisfiable : 0
% 0.09/0.41 % Propositional clauses : 0
% 0.09/0.41 % Propositional clauses after purity: 0
% 0.09/0.41 % Propositional unsat core size : 0
% 0.09/0.41 % Propositional preprocessing time : 0.000
% 0.09/0.41 % Propositional encoding time : 0.000
% 0.09/0.41 % Propositional solver time : 0.000
% 0.09/0.41 % Success case prop preproc time : 0.000
% 0.09/0.41 % Success case prop encoding time : 0.000
% 0.09/0.41 % Success case prop solver time : 0.000
% 0.09/0.41 % Current number of processed clauses : 6
% 0.09/0.41 % Positive orientable unit clauses : 4
% 0.09/0.41 % Positive unorientable unit clauses: 0
% 0.09/0.41 % Negative unit clauses : 1
% 0.09/0.41 % Non-unit-clauses : 1
% 0.09/0.41 % Current number of unprocessed clauses: 2
% 0.09/0.41 % ...number of literals in the above : 6
% 0.09/0.41 % Current number of archived formulas : 0
% 0.09/0.41 % Current number of archived clauses : 11
% 0.09/0.41 % Clause-clause subsumption calls (NU) : 19
% 0.09/0.41 % Rec. Clause-clause subsumption calls : 13
% 0.09/0.41 % Non-unit clause-clause subsumptions : 3
% 0.09/0.41 % Unit Clause-clause subsumption calls : 0
% 0.09/0.41 % Rewrite failures with RHS unbound : 0
% 0.09/0.41 % BW rewrite match attempts : 2
% 0.09/0.41 % BW rewrite match successes : 2
% 0.09/0.41 % Condensation attempts : 0
% 0.09/0.41 % Condensation successes : 0
% 0.09/0.41 % Termbank termtop insertions : 633
% 0.09/0.41 % Search garbage collected termcells : 132
% 0.09/0.41
% 0.09/0.41 % -------------------------------------------------
% 0.09/0.41 % User time : 0.002 s
% 0.09/0.41 % System time : 0.002 s
% 0.09/0.41 % Total time : 0.004 s
% 0.09/0.41 % Maximum resident set size: 3628 pages
% 0.09/0.41
% 0.09/0.41 % -------------------------------------------------
% 0.09/0.41 % User time : 0.006 s
% 0.09/0.41 % System time : 0.003 s
% 0.09/0.41 % Total time : 0.009 s
% 0.09/0.41 % Maximum resident set size: 4608 pages
% 0.09/0.41 % E exiting
%------------------------------------------------------------------------------