%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN059+2 : TPTP v9.3.1. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 01:57:37 PM UTC 2026
% Result : Theorem 0.16s 0.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 16 unt; 0 def)
% Number of atoms : 77 ( 22 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 76 ( 30 ~; 21 |; 25 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 70 ( 8 sgn 14 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( X2 = X1
& r1(X2) )
| ( X2 != X1
& ~ r1(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(axiom_5a,axiom,
! [X33] :
? [X34] :
( ? [X36] :
( X34 = X36
& r1(X36) )
& ? [X35] :
( r4(X33,X35,X34)
& r1(X35) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).
fof(fermattothepoweroftwo,conjecture,
? [X39,X23,X22,X16] :
( ? [X25] :
( ? [X19] :
( r3(X19,X25,X16)
& r4(X39,X39,X19) )
& r4(X23,X23,X25) )
& ? [X17] :
( X16 = X17
& r4(X22,X22,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fermattothepoweroftwo) ).
fof(axiom_4a,axiom,
! [X30] :
? [X31] :
( X31 = X30
& ? [X32] :
( r3(X30,X32,X31)
& r1(X32) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(c_0_4,plain,
? [X1] :
! [X2] :
( ( X2 = X1
& r1(X2) )
| ( X2 != X1
& ~ r1(X2) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_5,plain,
! [X76] :
( esk15_1(X76) = esk17_1(X76)
& r1(esk17_1(X76))
& r4(X76,esk16_1(X76),esk15_1(X76))
& r1(esk16_1(X76)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).
fof(c_0_6,negated_conjecture,
~ ? [X39,X23,X22,X16] :
( ? [X25] :
( ? [X19] :
( r3(X19,X25,X16)
& r4(X39,X39,X19) )
& r4(X23,X23,X25) )
& ? [X17] :
( X16 = X17
& r4(X22,X22,X17) ) ),
inference(assume_negation,[status(cth)],[fermattothepoweroftwo]) ).
fof(c_0_7,plain,
! [X45] :
( ( X45 != esk1_0
| X45 = esk1_0 )
& ( X45 != esk1_0
| r1(X45) )
& ( ~ r1(X45)
| X45 = esk1_0 )
& ( ~ r1(X45)
| r1(X45) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_4])])])]) ).
cnf(c_0_8,plain,
r1(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
esk15_1(X1) = esk17_1(X1),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_10,negated_conjecture,
! [X87,X88,X89,X90,X91,X92,X93] :
( ~ r3(X93,X92,X90)
| ~ r4(X87,X87,X93)
| ~ r4(X88,X88,X92)
| X90 != X91
| ~ r4(X89,X89,X91) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_11,plain,
( ~ r1(X1)
| X1 = esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
r1(esk16_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
r1(esk15_1(X1)),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
fof(c_0_14,plain,
! [X73] :
( esk13_1(X73) = X73
& r3(X73,esk14_1(X73),esk13_1(X73))
& r1(esk14_1(X73)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
cnf(c_0_15,negated_conjecture,
( ~ r3(X7,X5,X3)
| ~ r4(X6,X6,X7)
| ~ r4(X4,X4,X5)
| X3 != X2
| ~ r4(X1,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
r4(X1,esk16_1(X1),esk15_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,plain,
esk16_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
esk15_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_19,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
esk13_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
( ~ r3(X2,X4,X6)
| ~ r4(X5,X5,X6)
| ~ r4(X3,X3,X4)
| ~ r4(X1,X1,X2) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
r4(X1,esk1_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_24,plain,
r3(X1,esk14_1(X1),X1),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
esk14_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_11,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( ~ r3(esk1_0,X2,X4)
| ~ r4(X3,X3,X4)
| ~ r4(X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
r3(X1,esk1_0,X1),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( ~ r4(X2,X2,esk1_0)
| ~ r4(X1,X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
~ r4(X1,X1,esk1_0),
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_29,c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN059+2 : TPTP v9.3.1. Bugfixed v7.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 03:23:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 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
% 0.16/0.44 % Version: 3.5.1
% 0.16/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.44 % Starting sh5l with 300s (1) cores
% 0.16/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4124723 completed with status 0
% 0.16/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.44 % No SInE strategy applied
% 0.16/0.44 % Search class: FGHSM-FFMF21-SFFFFFNN
% 0.16/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.44 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.16/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.16/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4124732 completed with status 0
% 0.16/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.44 % No SInE strategy applied
% 0.16/0.44 % Search class: FGHSM-FFMF21-SFFFFFNN
% 0.16/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.44 % Preprocessing time : 0.001 s
% 0.16/0.44 % Presaturation interreduction done
% 0.16/0.44
% 0.16/0.44 % Proof found!
% 0.16/0.44 % SZS status Theorem
% 0.16/0.44 % SZS output start CNFRefutation
% See solution above
% 0.16/0.44 % Parsed axioms : 12
% 0.16/0.44 % Removed by relevancy pruning/SinE : 0
% 0.16/0.44 % Initial clauses : 40
% 0.16/0.44 % Removed in clause preprocessing : 12
% 0.16/0.44 % Initial clauses in saturation : 28
% 0.16/0.44 % Processed clauses : 88
% 0.16/0.44 % ...of these trivial : 0
% 0.16/0.44 % ...subsumed : 2
% 0.16/0.44 % ...remaining for further processing : 86
% 0.16/0.44 % Other redundant clauses eliminated : 7
% 0.16/0.44 % Clauses deleted for lack of memory : 0
% 0.16/0.44 % Backward-subsumed : 1
% 0.16/0.44 % Backward-rewritten : 13
% 0.16/0.44 % Generated clauses : 58
% 0.16/0.44 % ...of the previous two non-redundant : 58
% 0.16/0.44 % ...aggressively subsumed : 0
% 0.16/0.44 % Contextual simplify-reflections : 0
% 0.16/0.44 % Paramodulations : 51
% 0.16/0.44 % Factorizations : 0
% 0.16/0.44 % NegExts : 0
% 0.16/0.44 % Equation resolutions : 7
% 0.16/0.44 % Disequality decompositions : 0
% 0.16/0.44 % Total rewrite steps : 29
% 0.16/0.44 % ...of those cached : 9
% 0.16/0.44 % Propositional unsat checks : 0
% 0.16/0.44 % Propositional check models : 0
% 0.16/0.44 % Propositional check unsatisfiable : 0
% 0.16/0.44 % Propositional clauses : 0
% 0.16/0.44 % Propositional clauses after purity: 0
% 0.16/0.44 % Propositional unsat core size : 0
% 0.16/0.44 % Propositional preprocessing time : 0.000
% 0.16/0.44 % Propositional encoding time : 0.000
% 0.16/0.44 % Propositional solver time : 0.000
% 0.16/0.44 % Success case prop preproc time : 0.000
% 0.16/0.44 % Success case prop encoding time : 0.000
% 0.16/0.44 % Success case prop solver time : 0.000
% 0.16/0.44 % Current number of processed clauses : 37
% 0.16/0.44 % Positive orientable unit clauses : 18
% 0.16/0.44 % Positive unorientable unit clauses: 0
% 0.16/0.44 % Negative unit clauses : 3
% 0.16/0.44 % Non-unit-clauses : 16
% 0.16/0.44 % Current number of unprocessed clauses: 24
% 0.16/0.44 % ...number of literals in the above : 53
% 0.16/0.44 % Current number of archived formulas : 0
% 0.16/0.44 % Current number of archived clauses : 46
% 0.16/0.44 % Clause-clause subsumption calls (NU) : 65
% 0.16/0.44 % Rec. Clause-clause subsumption calls : 42
% 0.16/0.44 % Non-unit clause-clause subsumptions : 0
% 0.16/0.44 % Unit Clause-clause subsumption calls : 30
% 0.16/0.44 % Rewrite failures with RHS unbound : 0
% 0.16/0.44 % BW rewrite match attempts : 25
% 0.16/0.44 % BW rewrite match successes : 13
% 0.16/0.44 % Condensation attempts : 0
% 0.16/0.44 % Condensation successes : 0
% 0.16/0.44 % Termbank termtop insertions : 2248
% 0.16/0.44 % Search garbage collected termcells : 320
% 0.16/0.44
% 0.16/0.44 % -------------------------------------------------
% 0.16/0.44 % User time : 0.008 s
% 0.16/0.44 % System time : 0.002 s
% 0.16/0.44 % Total time : 0.010 s
% 0.16/0.44 % Maximum resident set size: 3412 pages
% 0.16/0.44
% 0.16/0.44 % -------------------------------------------------
% 0.16/0.44 % User time : 0.023 s
% 0.16/0.44 % System time : 0.010 s
% 0.16/0.44 % Total time : 0.033 s
% 0.16/0.44 % Maximum resident set size: 4608 pages
% 0.16/0.44 % E exiting
%------------------------------------------------------------------------------