%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN070+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:57:39 PM UTC 2026
% Result : Theorem 0.24s 0.56s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 94 ( 27 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 115 ( 48 ~; 37 |; 30 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 62 ( 3 sgn 17 !; 18 ?)
% 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(onepluszeroeqone,conjecture,
? [X39] :
( ? [X23] :
( ? [X25] :
( r2(X25,X23)
& r1(X25) )
& X39 = X23 )
& ? [X22] :
( ? [X17] :
( r2(X17,X22)
& r1(X17) )
& ? [X16] :
( r3(X22,X16,X39)
& r1(X16) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',onepluszeroeqone) ).
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(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( X5 = X4
& r2(X3,X5) )
| ( X5 != X4
& ~ r2(X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
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,negated_conjecture,
~ ? [X39] :
( ? [X23] :
( ? [X25] :
( r2(X25,X23)
& r1(X25) )
& X39 = X23 )
& ? [X22] :
( ? [X17] :
( r2(X17,X22)
& r1(X17) )
& ? [X16] :
( r3(X22,X16,X39)
& r1(X16) ) ) ),
inference(assume_negation,[status(cth)],[onepluszeroeqone]) ).
fof(c_0_6,plain,
! [X71] :
( ( X71 != esk9_0
| X71 = esk9_0 )
& ( X71 != esk9_0
| r1(X71) )
& ( ~ r1(X71)
| X71 = esk9_0 )
& ( ~ r1(X71)
| r1(X71) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_4])])])]) ).
fof(c_0_7,plain,
! [X72] :
( esk10_1(X72) = X72
& r3(X72,esk11_1(X72),esk10_1(X72))
& r1(esk11_1(X72)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
fof(c_0_8,negated_conjecture,
! [X44,X45,X46,X47,X48,X49] :
( ~ r2(X49,X48)
| ~ r1(X49)
| X44 != X48
| ~ r2(X47,X45)
| ~ r1(X47)
| ~ r3(X45,X46,X44)
| ~ r1(X46) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_9,plain,
( ~ r1(X1)
| X1 = esk9_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
r1(esk11_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X3] :
? [X4] :
! [X5] :
( ( X5 = X4
& r2(X3,X5) )
| ( X5 != X4
& ~ r2(X3,X5) ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
cnf(c_0_12,negated_conjecture,
( ~ r2(X6,X5)
| ~ r1(X6)
| X3 != X5
| ~ r2(X4,X2)
| ~ r1(X4)
| ~ r3(X2,X1,X3)
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
r3(X1,esk11_1(X1),esk10_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
esk11_1(X1) = esk9_0,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
esk10_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
( X1 != esk9_0
| r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_17,plain,
! [X50,X52] :
( ( X52 != esk1_1(X50)
| X52 = esk1_1(X50) )
& ( X52 != esk1_1(X50)
| r2(X50,X52) )
& ( ~ r2(X50,X52)
| X52 = esk1_1(X50) )
& ( ~ r2(X50,X52)
| r2(X50,X52) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_18,negated_conjecture,
( ~ r1(X2)
| ~ r1(X5)
| ~ r1(X4)
| ~ r2(X5,X1)
| ~ r2(X4,X3)
| ~ r3(X1,X2,X3) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
r3(X1,esk9_0,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_20,plain,
r1(esk9_0),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( X2 != esk1_1(X1)
| r2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( ~ r1(X3)
| ~ r1(X1)
| ~ r2(X3,X2)
| ~ r2(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_23,plain,
r2(X1,esk1_1(X1)),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( ~ r1(X1)
| ~ r1(X2)
| ~ r2(X1,esk1_1(X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,negated_conjecture,
~ r1(X1),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_26,plain,
$false,
inference(sr,[status(thm)],[c_0_20,c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN070+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n015.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 03:27:38 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.53 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
% 0.24/0.56 % Version: 3.5.1
% 0.24/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.56 % Starting sh5l with 300s (1) cores
% 0.24/0.56 % new_bool_3 with pid 458790 completed with status 0
% 0.24/0.56 % Result found by new_bool_3
% 0.24/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.56 % Search class: FGHSM-FFSF21-SFFFFFNN
% 0.24/0.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.56 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.56 % SubtermCWHack with pid 458793 completed with status 0
% 0.24/0.56 % Result found by SubtermCWHack
% 0.24/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.56 % Search class: FGHSM-FFSF21-SFFFFFNN
% 0.24/0.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.56 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.56 % Preprocessing time : 0.001 s
% 0.24/0.56
% 0.24/0.56 % Proof found!
% 0.24/0.56 % SZS status Theorem
% 0.24/0.56 % SZS output start CNFRefutation
% See solution above
% 0.24/0.56 % Parsed axioms : 12
% 0.24/0.56 % Removed by relevancy pruning/SinE : 3
% 0.24/0.56 % Initial clauses : 27
% 0.24/0.56 % Removed in clause preprocessing : 6
% 0.24/0.56 % Initial clauses in saturation : 21
% 0.24/0.56 % Processed clauses : 96
% 0.24/0.56 % ...of these trivial : 1
% 0.24/0.56 % ...subsumed : 27
% 0.24/0.56 % ...remaining for further processing : 68
% 0.24/0.56 % Other redundant clauses eliminated : 6
% 0.24/0.56 % Clauses deleted for lack of memory : 0
% 0.24/0.56 % Backward-subsumed : 11
% 0.24/0.56 % Backward-rewritten : 10
% 0.24/0.56 % Generated clauses : 195
% 0.24/0.56 % ...of the previous two non-redundant : 168
% 0.24/0.56 % ...aggressively subsumed : 0
% 0.24/0.56 % Contextual simplify-reflections : 2
% 0.24/0.56 % Paramodulations : 184
% 0.24/0.56 % Factorizations : 0
% 0.24/0.56 % NegExts : 0
% 0.24/0.56 % Equation resolutions : 6
% 0.24/0.56 % Disequality decompositions : 0
% 0.24/0.56 % Total rewrite steps : 77
% 0.24/0.56 % ...of those cached : 38
% 0.24/0.56 % Propositional unsat checks : 0
% 0.24/0.56 % Propositional check models : 0
% 0.24/0.56 % Propositional check unsatisfiable : 0
% 0.24/0.56 % Propositional clauses : 0
% 0.24/0.56 % Propositional clauses after purity: 0
% 0.24/0.56 % Propositional unsat core size : 0
% 0.24/0.56 % Propositional preprocessing time : 0.000
% 0.24/0.56 % Propositional encoding time : 0.000
% 0.24/0.56 % Propositional solver time : 0.000
% 0.24/0.56 % Success case prop preproc time : 0.000
% 0.24/0.56 % Success case prop encoding time : 0.000
% 0.24/0.56 % Success case prop solver time : 0.000
% 0.24/0.56 % Current number of processed clauses : 36
% 0.24/0.56 % Positive orientable unit clauses : 20
% 0.24/0.56 % Positive unorientable unit clauses: 0
% 0.24/0.56 % Negative unit clauses : 1
% 0.24/0.56 % Non-unit-clauses : 15
% 0.24/0.56 % Current number of unprocessed clauses: 82
% 0.24/0.56 % ...number of literals in the above : 226
% 0.24/0.56 % Current number of archived formulas : 0
% 0.24/0.56 % Current number of archived clauses : 26
% 0.24/0.56 % Clause-clause subsumption calls (NU) : 250
% 0.24/0.56 % Rec. Clause-clause subsumption calls : 174
% 0.24/0.56 % Non-unit clause-clause subsumptions : 22
% 0.24/0.56 % Unit Clause-clause subsumption calls : 23
% 0.24/0.56 % Rewrite failures with RHS unbound : 0
% 0.24/0.56 % BW rewrite match attempts : 15
% 0.24/0.56 % BW rewrite match successes : 10
% 0.24/0.56 % Condensation attempts : 0
% 0.24/0.56 % Condensation successes : 0
% 0.24/0.56 % Termbank termtop insertions : 2998
% 0.24/0.56 % Search garbage collected termcells : 312
% 0.24/0.56
% 0.24/0.56 % -------------------------------------------------
% 0.24/0.56 % User time : 0.009 s
% 0.24/0.56 % System time : 0.003 s
% 0.24/0.56 % Total time : 0.012 s
% 0.24/0.56 % Maximum resident set size: 3668 pages
% 0.24/0.56
% 0.24/0.56 % -------------------------------------------------
% 0.24/0.56 % User time : 0.012 s
% 0.24/0.56 % System time : 0.009 s
% 0.24/0.56 % Total time : 0.021 s
% 0.24/0.56 % Maximum resident set size: 4608 pages
% 0.24/0.56 % E exiting
%------------------------------------------------------------------------------