%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV606+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 02:35:19 PM UTC 2026
% Result : Theorem 0.21s 0.51s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 38 ( 11 ~; 8 |; 5 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('_HAMMER_GOAL',conjecture,
! [X25] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X25)
=> ! [X51] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X51)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X25))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X51))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X51,X51),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X25,X25)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X51,X25)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof('Coq.ZArith.BinInt.Z.square_le_simpl_nonneg',axiom,
! [X25] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X25)
=> ! [X51] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X51)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X51))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X25,X25),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X51,X51)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X25,X51)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.ZArith.BinInt.Z.square_le_simpl_nonneg') ).
fof(c_0_2,negated_conjecture,
~ ! [X25] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X25)
=> ! [X51] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X51)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X25))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X51))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X51,X51),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X25,X25)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X51,X25)) ) ) ) ) ),
inference(assume_negation,[status(cth)],['_HAMMER_GOAL']) ).
fof(c_0_3,plain,
! [X971,X972] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X971,X972))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X971,X971),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X972,X972)))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X972))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X972)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X971) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['Coq.ZArith.BinInt.Z.square_le_simpl_nonneg'])])])]) ).
fof(c_0_4,negated_conjecture,
( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(esk2_0,esk1_0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(esk2_0,esk2_0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(esk1_0,esk1_0)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,esk2_0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,esk1_0))
& cCoq_2eNumbers_2eBinNums_2eZ___24t(esk2_0)
& cCoq_2eNumbers_2eBinNums_2eZ___24t(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])]) ).
cnf(c_0_5,plain,
( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X2,X2)))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X2))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X2)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(esk2_0,esk2_0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(esk1_0,esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
cCoq_2eNumbers_2eBinNums_2eZ___24t(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
cCoq_2eNumbers_2eBinNums_2eZ___24t(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,negated_conjecture,
p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(esk2_0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]),c_0_8]),c_0_9])]),c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV606+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 07:29:41 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.21/0.51 % Version: 3.5.1
% 0.21/0.51 % Preprocessing class: FMLMSMSLSSSNFFN.
% 0.21/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 0.21/0.51 % Starting new_bool_3 with 600s (2) cores
% 0.21/0.51 % Starting new_bool_1 with 600s (2) cores
% 0.21/0.51 % Starting sh5l with 300s (1) cores
% 0.21/0.51 % new_bool_1 with pid 374967 completed with status 0
% 0.21/0.51 % Result found by new_bool_1
% 0.21/0.51 % Preprocessing class: FMLMSMSLSSSNFFN.
% 0.21/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 0.21/0.51 % Starting new_bool_3 with 600s (2) cores
% 0.21/0.51 % Starting new_bool_1 with 600s (2) cores
% 0.21/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.51 % Search class: FGHSF-FSLM21-SFFFFFNN
% 0.21/0.51 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.21/0.51 % Starting SubtermCWHack with 61s (1) cores
% 0.21/0.51 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 0.21/0.51 % SAT001_MinMin_p005000_rr_RG with pid 374977 completed with status 0
% 0.21/0.51 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.21/0.51 % Preprocessing class: FMLMSMSLSSSNFFN.
% 0.21/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 0.21/0.51 % Starting new_bool_3 with 600s (2) cores
% 0.21/0.51 % Starting new_bool_1 with 600s (2) cores
% 0.21/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.51 % Search class: FGHSF-FSLM21-SFFFFFNN
% 0.21/0.51 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.21/0.51 % Starting SubtermCWHack with 61s (1) cores
% 0.21/0.51 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 0.21/0.51 % Preprocessing time : 0.005 s
% 0.21/0.51 % Presaturation interreduction done
% 0.21/0.51
% 0.21/0.51 % Proof found!
% 0.21/0.51 % SZS status Theorem
% 0.21/0.51 % SZS output start CNFRefutation
% See solution above
% 0.21/0.51 % Parsed axioms : 1728
% 0.21/0.51 % Removed by relevancy pruning/SinE : 1601
% 0.21/0.51 % Initial clauses : 172
% 0.21/0.51 % Removed in clause preprocessing : 18
% 0.21/0.51 % Initial clauses in saturation : 154
% 0.21/0.51 % Processed clauses : 239
% 0.21/0.51 % ...of these trivial : 1
% 0.21/0.51 % ...subsumed : 82
% 0.21/0.51 % ...remaining for further processing : 156
% 0.21/0.51 % Other redundant clauses eliminated : 9
% 0.21/0.51 % Clauses deleted for lack of memory : 0
% 0.21/0.51 % Backward-subsumed : 1
% 0.21/0.51 % Backward-rewritten : 0
% 0.21/0.51 % Generated clauses : 196
% 0.21/0.51 % ...of the previous two non-redundant : 151
% 0.21/0.51 % ...aggressively subsumed : 0
% 0.21/0.51 % Contextual simplify-reflections : 0
% 0.21/0.51 % Paramodulations : 185
% 0.21/0.51 % Factorizations : 0
% 0.21/0.51 % NegExts : 0
% 0.21/0.51 % Equation resolutions : 11
% 0.21/0.51 % Disequality decompositions : 0
% 0.21/0.51 % Total rewrite steps : 151
% 0.21/0.51 % ...of those cached : 144
% 0.21/0.51 % Propositional unsat checks : 0
% 0.21/0.51 % Propositional check models : 0
% 0.21/0.51 % Propositional check unsatisfiable : 0
% 0.21/0.51 % Propositional clauses : 0
% 0.21/0.51 % Propositional clauses after purity: 0
% 0.21/0.51 % Propositional unsat core size : 0
% 0.21/0.51 % Propositional preprocessing time : 0.000
% 0.21/0.51 % Propositional encoding time : 0.000
% 0.21/0.51 % Propositional solver time : 0.000
% 0.21/0.51 % Success case prop preproc time : 0.000
% 0.21/0.51 % Success case prop encoding time : 0.000
% 0.21/0.51 % Success case prop solver time : 0.000
% 0.21/0.51 % Current number of processed clauses : 49
% 0.21/0.51 % Positive orientable unit clauses : 7
% 0.21/0.51 % Positive unorientable unit clauses: 0
% 0.21/0.51 % Negative unit clauses : 3
% 0.21/0.51 % Non-unit-clauses : 39
% 0.21/0.51 % Current number of unprocessed clauses: 150
% 0.21/0.51 % ...number of literals in the above : 789
% 0.21/0.51 % Current number of archived formulas : 0
% 0.21/0.51 % Current number of archived clauses : 98
% 0.21/0.51 % Clause-clause subsumption calls (NU) : 3859
% 0.21/0.51 % Rec. Clause-clause subsumption calls : 863
% 0.21/0.51 % Non-unit clause-clause subsumptions : 77
% 0.21/0.51 % Unit Clause-clause subsumption calls : 1
% 0.21/0.51 % Rewrite failures with RHS unbound : 0
% 0.21/0.51 % BW rewrite match attempts : 0
% 0.21/0.51 % BW rewrite match successes : 0
% 0.21/0.51 % Condensation attempts : 0
% 0.21/0.51 % Condensation successes : 0
% 0.21/0.51 % Termbank termtop insertions : 54925
% 0.21/0.51 % Search garbage collected termcells : 20411
% 0.21/0.51
% 0.21/0.51 % -------------------------------------------------
% 0.21/0.51 % User time : 0.029 s
% 0.21/0.51 % System time : 0.012 s
% 0.21/0.51 % Total time : 0.041 s
% 0.21/0.51 % Maximum resident set size: 8692 pages
% 0.21/0.51
% 0.21/0.51 % -------------------------------------------------
% 0.21/0.51 % User time : 0.073 s
% 0.21/0.51 % System time : 0.028 s
% 0.21/0.51 % Total time : 0.102 s
% 0.21/0.51 % Maximum resident set size: 7936 pages
% 0.21/0.51 % E exiting
%------------------------------------------------------------------------------