%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN062+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 : n019.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 0.22s 5.58s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 26 unt; 0 def)
% Number of atoms : 144 ( 61 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 149 ( 63 ~; 46 |; 40 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 126 ( 8 sgn 42 !; 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_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_3,axiom,
! [X6,X7] :
? [X8] :
! [X9] :
( ( X9 = X8
& r3(X6,X7,X9) )
| ( X9 != X8
& ~ r3(X6,X7,X9) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3) ).
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(infiniteNumbers,conjecture,
! [X14] :
? [X22,X39] :
( ? [X23] :
( X23 = X22
& r3(X14,X39,X23) )
& ! [X16] :
( X39 != X16
| ~ r1(X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infiniteNumbers) ).
fof(axiom_7a,axiom,
! [X41,X42] :
( ~ r2(X41,X42)
| ! [X43] :
( X43 != X42
| ~ r1(X43) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).
fof(c_0_7,plain,
? [X1] :
! [X2] :
( ( X2 = X1
& r1(X2) )
| ( X2 != X1
& ~ r1(X2) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_8,plain,
! [X63] :
( ( X63 != esk10_0
| X63 = esk10_0 )
& ( X63 != esk10_0
| r1(X63) )
& ( ~ r1(X63)
| X63 = esk10_0 )
& ( ~ r1(X63)
| r1(X63) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_7])])])]) ).
fof(c_0_9,plain,
! [X59] :
( esk8_1(X59) = X59
& r3(X59,esk9_1(X59),esk8_1(X59))
& r1(esk9_1(X59)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
fof(c_0_10,plain,
! [X6,X7] :
? [X8] :
! [X9] :
( ( X9 = X8
& r3(X6,X7,X9) )
| ( X9 != X8
& ~ r3(X6,X7,X9) ) ),
inference(fof_simplification,[status(thm)],[axiom_3]) ).
cnf(c_0_11,plain,
( ~ r1(X1)
| X1 = esk10_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
r1(esk9_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X3] :
? [X4] :
! [X5] :
( ( X5 = X4
& r2(X3,X5) )
| ( X5 != X4
& ~ r2(X3,X5) ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(c_0_14,plain,
! [X53,X54] :
( r3(X53,X54,esk7_2(X53,X54))
& r2(esk7_2(X53,X54),esk4_2(X53,X54))
& esk5_2(X53,X54) = esk4_2(X53,X54)
& r3(X53,esk6_2(X53,X54),esk5_2(X53,X54))
& r2(X54,esk6_2(X53,X54)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
fof(c_0_15,plain,
! [X49,X50,X52] :
( ( X52 != esk3_2(X49,X50)
| X52 = esk3_2(X49,X50) )
& ( X52 != esk3_2(X49,X50)
| r3(X49,X50,X52) )
& ( ~ r3(X49,X50,X52)
| X52 = esk3_2(X49,X50) )
& ( ~ r3(X49,X50,X52)
| r3(X49,X50,X52) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_10])])])]) ).
cnf(c_0_16,plain,
r3(X1,esk9_1(X1),esk8_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
esk9_1(X1) = esk10_0,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
esk8_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_19,plain,
! [X71,X73] :
( ( X73 != esk14_1(X71)
| X73 = esk14_1(X71) )
& ( X73 != esk14_1(X71)
| r2(X71,X73) )
& ( ~ r2(X71,X73)
| X73 = esk14_1(X71) )
& ( ~ r2(X71,X73)
| r2(X71,X73) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_13])])])]) ).
cnf(c_0_20,plain,
r2(esk7_2(X1,X2),esk4_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
esk5_2(X1,X2) = esk4_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( ~ r3(X2,X3,X1)
| X1 = esk3_2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
r3(X1,esk10_0,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_24,plain,
r3(X1,X2,esk7_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,plain,
( ~ r2(X2,X1)
| X1 = esk14_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
r2(X1,esk6_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_27,plain,
r2(esk7_2(X1,X2),esk5_2(X1,X2)),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
esk3_2(X1,esk10_0) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
esk3_2(X1,X2) = esk7_2(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_30,plain,
r3(X1,esk6_2(X1,X2),esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_31,plain,
esk6_2(X1,X2) = esk14_1(X2),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
esk14_1(esk7_2(X1,X2)) = esk5_2(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_27]) ).
cnf(c_0_33,plain,
esk7_2(X1,esk10_0) = X1,
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_34,negated_conjecture,
~ ! [X14] :
? [X22,X39] :
( ? [X23] :
( X23 = X22
& r3(X14,X39,X23) )
& ! [X16] :
( X39 != X16
| ~ r1(X16) ) ),
inference(assume_negation,[status(cth)],[infiniteNumbers]) ).
cnf(c_0_35,plain,
r3(X1,esk14_1(X2),esk5_2(X1,X2)),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
esk5_2(X1,esk10_0) = esk14_1(X1),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_37,negated_conjecture,
~ ! [X14] :
? [X22,X39] :
( ? [X23] :
( X23 = X22
& r3(X14,X39,X23) )
& ! [X16] :
( X39 != X16
| ~ r1(X16) ) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
cnf(c_0_38,plain,
( ~ r3(X2,X3,X1)
| X1 = esk7_2(X2,X3) ),
inference(rw,[status(thm)],[c_0_22,c_0_29]) ).
cnf(c_0_39,plain,
r3(X1,esk14_1(esk10_0),esk14_1(X1)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_40,plain,
! [X41,X42] :
( ~ r2(X41,X42)
| ! [X43] :
( X43 != X42
| ~ r1(X43) ) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_41,negated_conjecture,
! [X45,X46,X48] :
( ( X48 != X45
| ~ r3(esk1_0,X46,X48)
| X46 = esk2_2(X45,X46) )
& ( X48 != X45
| ~ r3(esk1_0,X46,X48)
| r1(esk2_2(X45,X46)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])])])]) ).
cnf(c_0_42,plain,
esk7_2(X1,esk14_1(esk10_0)) = esk14_1(X1),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_43,plain,
! [X68,X69,X70] :
( ~ r2(X68,X69)
| X70 != X69
| ~ r1(X70) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_40])])]) ).
cnf(c_0_44,negated_conjecture,
( X3 != X1
| ~ r3(esk1_0,X2,X3)
| r1(esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( X3 != X2
| ~ r3(esk1_0,X1,X3)
| X1 = esk2_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_46,plain,
r2(esk14_1(X1),esk5_2(X1,esk14_1(esk10_0))),
inference(spm,[status(thm)],[c_0_27,c_0_42]) ).
cnf(c_0_47,plain,
( ~ r2(X3,X2)
| X1 != X2
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_48,plain,
( X2 != esk14_1(X1)
| r2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_49,negated_conjecture,
( ~ r3(esk1_0,X2,X1)
| r1(esk2_2(X1,X2)) ),
inference(er,[status(thm)],[c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( ~ r3(esk1_0,X2,X1)
| esk2_2(X1,X2) = X2 ),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
esk5_2(X1,esk14_1(esk10_0)) = esk14_1(esk14_1(X1)),
inference(spm,[status(thm)],[c_0_25,c_0_46]) ).
cnf(c_0_52,plain,
( ~ r1(X2)
| ~ r2(X1,X2) ),
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_53,plain,
r2(X1,esk14_1(X1)),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( ~ r3(esk1_0,X1,X2)
| r1(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,plain,
r3(X1,esk14_1(esk14_1(esk10_0)),esk14_1(esk14_1(X1))),
inference(spm,[status(thm)],[c_0_35,c_0_51]) ).
cnf(c_0_56,plain,
~ r1(esk14_1(X1)),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN062+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/5.43 % Computer : n019.cluster.edu
% 0.18/5.43 % Model : x86_64 x86_64
% 0.18/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.43 % Memory : 8046.5625MB
% 0.18/5.43 % OS : Linux 6.8.0-71-generic
% 0.18/5.44 % CPULimit : 300
% 0.18/5.44 % WCLimit : 300
% 0.18/5.44 % DateTime : Mon Sep 21 03:23:26 UTC 2026
% 0.18/5.44 % CPUTime :
% 0.18/5.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/5.51 Running first-order theorem proving
% 0.22/5.51 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
% 0.22/5.58 % Version: 3.5.1
% 0.22/5.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/5.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/5.58 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.58 % Starting new_bool_1 with 300s (1) cores
% 0.22/5.58 % Starting sh5l with 300s (1) cores
% 0.22/5.58 % new_bool_1 with pid 1589333 completed with status 0
% 0.22/5.58 % Result found by new_bool_1
% 0.22/5.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/5.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/5.58 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.58 % Starting new_bool_1 with 300s (1) cores
% 0.22/5.58 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/5.58 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/5.58 % Search class: FGHSM-FFSF21-SFFFFFNN
% 0.22/5.58 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/5.58 % Starting SubtermCWHack with 31s (1) cores
% 0.22/5.58 % SubtermCWHack with pid 1589341 completed with status 0
% 0.22/5.58 % Result found by SubtermCWHack
% 0.22/5.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/5.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/5.58 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.58 % Starting new_bool_1 with 300s (1) cores
% 0.22/5.58 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/5.58 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/5.58 % Search class: FGHSM-FFSF21-SFFFFFNN
% 0.22/5.58 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/5.58 % Starting SubtermCWHack with 31s (1) cores
% 0.22/5.58 % Preprocessing time : 0.002 s
% 0.22/5.58
% 0.22/5.58 % Proof found!
% 0.22/5.58 % SZS status Theorem
% 0.22/5.58 % SZS output start CNFRefutation
% See solution above
% 0.22/5.58 % Parsed axioms : 12
% 0.22/5.58 % Removed by relevancy pruning/SinE : 3
% 0.22/5.58 % Initial clauses : 28
% 0.22/5.58 % Removed in clause preprocessing : 6
% 0.22/5.58 % Initial clauses in saturation : 22
% 0.22/5.58 % Processed clauses : 73
% 0.22/5.58 % ...of these trivial : 0
% 0.22/5.58 % ...subsumed : 15
% 0.22/5.58 % ...remaining for further processing : 58
% 0.22/5.58 % Other redundant clauses eliminated : 7
% 0.22/5.58 % Clauses deleted for lack of memory : 0
% 0.22/5.58 % Backward-subsumed : 0
% 0.22/5.58 % Backward-rewritten : 8
% 0.22/5.58 % Generated clauses : 114
% 0.22/5.58 % ...of the previous two non-redundant : 98
% 0.22/5.58 % ...aggressively subsumed : 0
% 0.22/5.58 % Contextual simplify-reflections : 1
% 0.22/5.58 % Paramodulations : 107
% 0.22/5.58 % Factorizations : 0
% 0.22/5.58 % NegExts : 0
% 0.22/5.58 % Equation resolutions : 7
% 0.22/5.58 % Disequality decompositions : 0
% 0.22/5.58 % Total rewrite steps : 36
% 0.22/5.58 % ...of those cached : 15
% 0.22/5.58 % Propositional unsat checks : 0
% 0.22/5.58 % Propositional check models : 0
% 0.22/5.58 % Propositional check unsatisfiable : 0
% 0.22/5.58 % Propositional clauses : 0
% 0.22/5.58 % Propositional clauses after purity: 0
% 0.22/5.58 % Propositional unsat core size : 0
% 0.22/5.58 % Propositional preprocessing time : 0.000
% 0.22/5.58 % Propositional encoding time : 0.000
% 0.22/5.58 % Propositional solver time : 0.000
% 0.22/5.58 % Success case prop preproc time : 0.000
% 0.22/5.58 % Success case prop encoding time : 0.000
% 0.22/5.58 % Success case prop solver time : 0.000
% 0.22/5.58 % Current number of processed clauses : 43
% 0.22/5.58 % Positive orientable unit clauses : 19
% 0.22/5.58 % Positive unorientable unit clauses: 0
% 0.22/5.58 % Negative unit clauses : 2
% 0.22/5.58 % Non-unit-clauses : 22
% 0.22/5.58 % Current number of unprocessed clauses: 44
% 0.22/5.58 % ...number of literals in the above : 90
% 0.22/5.58 % Current number of archived formulas : 0
% 0.22/5.58 % Current number of archived clauses : 8
% 0.22/5.58 % Clause-clause subsumption calls (NU) : 81
% 0.22/5.58 % Rec. Clause-clause subsumption calls : 76
% 0.22/5.58 % Non-unit clause-clause subsumptions : 10
% 0.22/5.58 % Unit Clause-clause subsumption calls : 40
% 0.22/5.58 % Rewrite failures with RHS unbound : 0
% 0.22/5.58 % BW rewrite match attempts : 12
% 0.22/5.58 % BW rewrite match successes : 8
% 0.22/5.58 % Condensation attempts : 0
% 0.22/5.58 % Condensation successes : 0
% 0.22/5.58 % Termbank termtop insertions : 2104
% 0.22/5.58 % Search garbage collected termcells : 297
% 0.22/5.58
% 0.22/5.58 % -------------------------------------------------
% 0.22/5.58 % User time : 0.010 s
% 0.22/5.58 % System time : 0.005 s
% 0.22/5.58 % Total time : 0.015 s
% 0.22/5.58 % Maximum resident set size: 3668 pages
% 0.22/5.58
% 0.22/5.58 % -------------------------------------------------
% 0.22/5.58 % User time : 0.014 s
% 0.22/5.58 % System time : 0.011 s
% 0.22/5.58 % Total time : 0.025 s
% 0.22/5.58 % Maximum resident set size: 4608 pages
% 0.22/5.58 % E exiting
%------------------------------------------------------------------------------