%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN080+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 : n018.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 01:57:41 PM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 5 unt; 0 def)
% Number of atoms : 80 ( 24 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 97 ( 39 ~; 28 |; 30 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 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 : 62 ( 7 sgn 19 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(xplustwoeqy,conjecture,
? [X39,X22,X23] :
( ? [X16] :
( ? [X17] :
( ? [X25] :
( r2(X25,X17)
& r1(X25) )
& r2(X17,X16) )
& r3(X39,X16,X23) )
& X23 = X22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xplustwoeqy) ).
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(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/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
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(c_0_4,negated_conjecture,
~ ? [X39,X22,X23] :
( ? [X16] :
( ? [X17] :
( ? [X25] :
( r2(X25,X17)
& r1(X25) )
& r2(X17,X16) )
& r3(X39,X16,X23) )
& X23 = X22 ),
inference(assume_negation,[status(cth)],[xplustwoeqy]) ).
fof(c_0_5,negated_conjecture,
! [X44,X45,X46,X47,X48,X49] :
( ~ r2(X49,X48)
| ~ r1(X49)
| ~ r2(X48,X47)
| ~ r3(X44,X47,X46)
| X46 != X45 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X3] :
? [X4] :
! [X5] :
( ( X5 = X4
& r2(X3,X5) )
| ( X5 != X4
& ~ r2(X3,X5) ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
cnf(c_0_7,negated_conjecture,
( ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r3(X3,X4,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X53,X54] :
( r3(X53,X54,esk5_2(X53,X54))
& r2(esk5_2(X53,X54),esk2_2(X53,X54))
& esk3_2(X53,X54) = esk2_2(X53,X54)
& r3(X53,esk4_2(X53,X54),esk3_2(X53,X54))
& r2(X54,esk4_2(X53,X54)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
fof(c_0_9,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_6])])])]) ).
fof(c_0_10,plain,
? [X1] :
! [X2] :
( ( X2 = X1
& r1(X2) )
| ( X2 != X1
& ~ r1(X2) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
cnf(c_0_11,negated_conjecture,
( ~ r1(X4)
| ~ r2(X5,X2)
| ~ r2(X4,X5)
| ~ r3(X1,X2,X3) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
r3(X1,X2,esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( X2 != esk1_1(X1)
| r2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,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_10])])])]) ).
cnf(c_0_15,negated_conjecture,
( ~ r1(X1)
| ~ r2(X2,X3)
| ~ r2(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
r2(X1,esk1_1(X1)),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( X1 != esk9_0
| r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( ~ r1(X1)
| ~ r2(esk1_1(X1),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
r1(esk9_0),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_20,negated_conjecture,
~ r1(X1),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_21,plain,
$false,
inference(sr,[status(thm)],[c_0_19,c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN080+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.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 03:27:13 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.44 % Version: 3.5.1
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % new_bool_1 with pid 867065 completed with status 0
% 0.14/0.44 % Result found by new_bool_1
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.44 % Search class: FGHSM-FFSF21-SFFFFFNN
% 0.14/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.44 % SubtermCWHack with pid 867067 completed with status 0
% 0.14/0.44 % Result found by SubtermCWHack
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.44 % Search class: FGHSM-FFSF21-SFFFFFNN
% 0.14/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.44 % Preprocessing time : 0.001 s
% 0.14/0.44
% 0.14/0.44 % Proof found!
% 0.14/0.44 % SZS status Theorem
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.44 % Parsed axioms : 12
% 0.14/0.44 % Removed by relevancy pruning/SinE : 3
% 0.14/0.44 % Initial clauses : 27
% 0.14/0.44 % Removed in clause preprocessing : 6
% 0.14/0.44 % Initial clauses in saturation : 21
% 0.14/0.44 % Processed clauses : 93
% 0.14/0.44 % ...of these trivial : 1
% 0.14/0.44 % ...subsumed : 25
% 0.14/0.44 % ...remaining for further processing : 67
% 0.14/0.44 % Other redundant clauses eliminated : 6
% 0.14/0.44 % Clauses deleted for lack of memory : 0
% 0.14/0.44 % Backward-subsumed : 12
% 0.14/0.44 % Backward-rewritten : 10
% 0.14/0.44 % Generated clauses : 172
% 0.14/0.44 % ...of the previous two non-redundant : 148
% 0.14/0.44 % ...aggressively subsumed : 0
% 0.14/0.44 % Contextual simplify-reflections : 2
% 0.14/0.44 % Paramodulations : 161
% 0.14/0.44 % Factorizations : 0
% 0.14/0.44 % NegExts : 0
% 0.14/0.44 % Equation resolutions : 6
% 0.14/0.44 % Disequality decompositions : 0
% 0.14/0.44 % Total rewrite steps : 73
% 0.14/0.44 % ...of those cached : 34
% 0.14/0.44 % Propositional unsat checks : 0
% 0.14/0.44 % Propositional check models : 0
% 0.14/0.44 % Propositional check unsatisfiable : 0
% 0.14/0.44 % Propositional clauses : 0
% 0.14/0.44 % Propositional clauses after purity: 0
% 0.14/0.44 % Propositional unsat core size : 0
% 0.14/0.44 % Propositional preprocessing time : 0.000
% 0.14/0.44 % Propositional encoding time : 0.000
% 0.14/0.44 % Propositional solver time : 0.000
% 0.14/0.44 % Success case prop preproc time : 0.000
% 0.14/0.44 % Success case prop encoding time : 0.000
% 0.14/0.44 % Success case prop solver time : 0.000
% 0.14/0.44 % Current number of processed clauses : 34
% 0.14/0.44 % Positive orientable unit clauses : 20
% 0.14/0.44 % Positive unorientable unit clauses: 0
% 0.14/0.44 % Negative unit clauses : 1
% 0.14/0.44 % Non-unit-clauses : 13
% 0.14/0.44 % Current number of unprocessed clauses: 65
% 0.14/0.44 % ...number of literals in the above : 152
% 0.14/0.44 % Current number of archived formulas : 0
% 0.14/0.44 % Current number of archived clauses : 27
% 0.14/0.44 % Clause-clause subsumption calls (NU) : 204
% 0.14/0.44 % Rec. Clause-clause subsumption calls : 161
% 0.14/0.44 % Non-unit clause-clause subsumptions : 22
% 0.14/0.44 % Unit Clause-clause subsumption calls : 22
% 0.14/0.44 % Rewrite failures with RHS unbound : 0
% 0.14/0.44 % BW rewrite match attempts : 15
% 0.14/0.44 % BW rewrite match successes : 10
% 0.14/0.44 % Condensation attempts : 0
% 0.14/0.44 % Condensation successes : 0
% 0.14/0.44 % Termbank termtop insertions : 2667
% 0.14/0.44 % Search garbage collected termcells : 295
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.008 s
% 0.14/0.44 % System time : 0.001 s
% 0.14/0.44 % Total time : 0.009 s
% 0.14/0.44 % Maximum resident set size: 3668 pages
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.009 s
% 0.14/0.44 % System time : 0.007 s
% 0.14/0.44 % Total time : 0.016 s
% 0.14/0.44 % Maximum resident set size: 4608 pages
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------