%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN067+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 01:57:38 PM UTC 2026
% Result : Theorem 0.07s 0.34s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 8 unt; 0 def)
% Number of atoms : 56 ( 22 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 63 ( 29 ~; 18 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 0-2 aty)
% Number of variables : 43 ( 9 sgn 20 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(nonzerosexist,conjecture,
? [X39] :
! [X22] :
( X39 != X22
| ~ r1(X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonzerosexist) ).
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( X2 = X1
& r1(X2) )
| ( X2 != X1
& ~ r1(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(axiom_7a,axiom,
! [X41,X42] :
( ~ r2(X41,X42)
| ! [X43] :
( X43 != X42
| ~ r1(X43) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).
fof(axiom_1a,axiom,
! [X14,X15] :
? [X16] :
( ? [X19] :
( r3(X14,X15,X19)
& r2(X19,X16) )
& ? [X17] :
( X17 = X16
& ? [X18] :
( r3(X14,X18,X17)
& r2(X15,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
fof(c_0_4,negated_conjecture,
~ ? [X39] :
! [X22] :
( X39 != X22
| ~ r1(X22) ),
inference(assume_negation,[status(cth)],[nonzerosexist]) ).
fof(c_0_5,negated_conjecture,
~ ? [X39] :
! [X22] :
( X39 != X22
| ~ r1(X22) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_6,plain,
? [X1] :
! [X2] :
( ( X2 = X1
& r1(X2) )
| ( X2 != X1
& ~ r1(X2) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_7,negated_conjecture,
! [X44] :
( X44 = esk1_1(X44)
& r1(esk1_1(X44)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X47] :
( ( X47 != esk2_0
| X47 = esk2_0 )
& ( X47 != esk2_0
| r1(X47) )
& ( ~ r1(X47)
| X47 = esk2_0 )
& ( ~ r1(X47)
| r1(X47) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_9,negated_conjecture,
r1(esk1_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
X1 = esk1_1(X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ r1(X1)
| X1 = esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
r1(X1),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_13,plain,
! [X41,X42] :
( ~ r2(X41,X42)
| ! [X43] :
( X43 != X42
| ~ r1(X43) ) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_14,plain,
! [X62,X63] :
( r3(X62,X63,esk12_2(X62,X63))
& r2(esk12_2(X62,X63),esk9_2(X62,X63))
& esk10_2(X62,X63) = esk9_2(X62,X63)
& r3(X62,esk11_2(X62,X63),esk10_2(X62,X63))
& r2(X63,esk11_2(X62,X63)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
cnf(c_0_15,plain,
X1 = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]) ).
fof(c_0_16,plain,
! [X55,X56,X57] :
( ~ r2(X55,X56)
| X57 != X56
| ~ r1(X57) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_13])])]) ).
cnf(c_0_17,plain,
r2(X1,esk11_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
X1 = X2,
inference(spm,[status(thm)],[c_0_15,c_0_15]) ).
cnf(c_0_19,plain,
( ~ r2(X3,X2)
| X1 != X2
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
r2(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_12]),c_0_20])]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUN067+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 03:23:37 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 0.07/0.34 % Version: 3.5.1
% 0.07/0.34 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.34 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.34 % Starting sh5l with 300s (1) cores
% 0.07/0.34 % new_bool_3 with pid 1460414 completed with status 0
% 0.07/0.34 % Result found by new_bool_3
% 0.07/0.34 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.34 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.34 % Search class: FGHSM-FFMF21-SFFFFFNN
% 0.07/0.34 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.34 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.34 % SubtermCWHack with pid 1460419 completed with status 0
% 0.07/0.34 % Result found by SubtermCWHack
% 0.07/0.34 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.07/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.07/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.07/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.34 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.34 % Search class: FGHSM-FFMF21-SFFFFFNN
% 0.07/0.34 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.34 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.34 % Preprocessing time : 0.001 s
% 0.07/0.34
% 0.07/0.34 % Proof found!
% 0.07/0.34 % SZS status Theorem
% 0.07/0.34 % SZS output start CNFRefutation
% See solution above
% 0.07/0.34 % Parsed axioms : 12
% 0.07/0.34 % Removed by relevancy pruning/SinE : 0
% 0.07/0.34 % Initial clauses : 41
% 0.07/0.34 % Removed in clause preprocessing : 8
% 0.07/0.34 % Initial clauses in saturation : 33
% 0.07/0.34 % Processed clauses : 32
% 0.07/0.34 % ...of these trivial : 7
% 0.07/0.34 % ...subsumed : 6
% 0.07/0.34 % ...remaining for further processing : 18
% 0.07/0.34 % Other redundant clauses eliminated : 0
% 0.07/0.34 % Clauses deleted for lack of memory : 0
% 0.07/0.34 % Backward-subsumed : 1
% 0.07/0.34 % Backward-rewritten : 12
% 0.07/0.34 % Generated clauses : 16
% 0.07/0.34 % ...of the previous two non-redundant : 19
% 0.07/0.34 % ...aggressively subsumed : 0
% 0.07/0.34 % Contextual simplify-reflections : 0
% 0.07/0.34 % Paramodulations : 16
% 0.07/0.34 % Factorizations : 0
% 0.07/0.34 % NegExts : 0
% 0.07/0.34 % Equation resolutions : 0
% 0.07/0.34 % Disequality decompositions : 0
% 0.07/0.34 % Total rewrite steps : 30
% 0.07/0.34 % ...of those cached : 6
% 0.07/0.34 % Propositional unsat checks : 0
% 0.07/0.34 % Propositional check models : 0
% 0.07/0.34 % Propositional check unsatisfiable : 0
% 0.07/0.34 % Propositional clauses : 0
% 0.07/0.34 % Propositional clauses after purity: 0
% 0.07/0.34 % Propositional unsat core size : 0
% 0.07/0.34 % Propositional preprocessing time : 0.000
% 0.07/0.34 % Propositional encoding time : 0.000
% 0.07/0.34 % Propositional solver time : 0.000
% 0.07/0.34 % Success case prop preproc time : 0.000
% 0.07/0.34 % Success case prop encoding time : 0.000
% 0.07/0.34 % Success case prop solver time : 0.000
% 0.07/0.34 % Current number of processed clauses : 5
% 0.07/0.34 % Positive orientable unit clauses : 4
% 0.07/0.34 % Positive unorientable unit clauses: 1
% 0.07/0.34 % Negative unit clauses : 0
% 0.07/0.34 % Non-unit-clauses : 0
% 0.07/0.34 % Current number of unprocessed clauses: 10
% 0.07/0.34 % ...number of literals in the above : 19
% 0.07/0.34 % Current number of archived formulas : 0
% 0.07/0.34 % Current number of archived clauses : 13
% 0.07/0.34 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.34 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.34 % Non-unit clause-clause subsumptions : 0
% 0.07/0.34 % Unit Clause-clause subsumption calls : 2
% 0.07/0.34 % Rewrite failures with RHS unbound : 58
% 0.07/0.34 % BW rewrite match attempts : 21
% 0.07/0.34 % BW rewrite match successes : 15
% 0.07/0.34 % Condensation attempts : 0
% 0.07/0.34 % Condensation successes : 0
% 0.07/0.34 % Termbank termtop insertions : 1426
% 0.07/0.34 % Search garbage collected termcells : 271
% 0.07/0.34
% 0.07/0.34 % -------------------------------------------------
% 0.07/0.34 % User time : 0.003 s
% 0.07/0.34 % System time : 0.001 s
% 0.07/0.34 % Total time : 0.004 s
% 0.07/0.34 % Maximum resident set size: 3668 pages
% 0.07/0.34
% 0.07/0.34 % -------------------------------------------------
% 0.07/0.34 % User time : 0.006 s
% 0.07/0.34 % System time : 0.003 s
% 0.07/0.34 % Total time : 0.008 s
% 0.07/0.34 % Maximum resident set size: 4864 pages
% 0.07/0.34 % E exiting
%------------------------------------------------------------------------------