%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN068+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 : n014.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 0.28s 0.61s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 8 unt; 0 def)
% Number of atoms : 134 ( 56 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 155 ( 66 ~; 67 |; 22 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 87 ( 10 sgn 40 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(nonzerosnononesexist,conjecture,
? [X39] :
( ! [X16] :
( X39 != X16
| ~ r1(X16) )
& ! [X22] :
( X39 != X22
| ! [X23] :
( ~ r2(X23,X22)
| ~ r1(X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonzerosnononesexist) ).
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_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( X5 = X4
& r2(X3,X5) )
| ( X5 != X4
& ~ r2(X3,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(axiom_3a,axiom,
! [X26,X27] :
( X26 = X27
| ! [X28] :
( ~ r2(X27,X28)
| ! [X29] :
( X29 != X28
| ~ r2(X26,X29) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_3a) ).
fof(c_0_5,negated_conjecture,
~ ? [X39] :
( ! [X16] :
( X39 != X16
| ~ r1(X16) )
& ! [X22] :
( X39 != X22
| ! [X23] :
( ~ r2(X23,X22)
| ~ r1(X23) ) ) ),
inference(assume_negation,[status(cth)],[nonzerosnononesexist]) ).
fof(c_0_6,negated_conjecture,
~ ? [X39] :
( ! [X16] :
( X39 != X16
| ~ r1(X16) )
& ! [X22] :
( X39 != X22
| ! [X23] :
( ~ r2(X23,X22)
| ~ r1(X23) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
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,negated_conjecture,
! [X44] :
( ( X44 = esk1_1(X44)
| X44 = esk3_1(X44) )
& ( X44 = esk1_1(X44)
| r1(esk3_1(X44)) )
& ( r2(esk2_1(X44),esk1_1(X44))
| X44 = esk3_1(X44) )
& ( r2(esk2_1(X44),esk1_1(X44))
| r1(esk3_1(X44)) )
& ( r1(esk2_1(X44))
| X44 = esk3_1(X44) )
& ( r1(esk2_1(X44))
| r1(esk3_1(X44)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_9,plain,
! [X49] :
( ( X49 != esk4_0
| X49 = esk4_0 )
& ( X49 != esk4_0
| r1(X49) )
& ( ~ r1(X49)
| X49 = esk4_0 )
& ( ~ r1(X49)
| r1(X49) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_7])])])]) ).
fof(c_0_10,plain,
! [X41,X42] :
( ~ r2(X41,X42)
| ! [X43] :
( X43 != X42
| ~ r1(X43) ) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
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(esk2_1(X1),esk1_1(X1))
| r1(esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( X1 = esk1_1(X1)
| r1(esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ r1(X1)
| X1 = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( r1(esk2_1(X1))
| r1(esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
( r2(esk2_1(X1),esk1_1(X1))
| X1 = esk3_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
( X1 = esk1_1(X1)
| X1 = esk3_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,negated_conjecture,
( r1(esk2_1(X1))
| X1 = esk3_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_19,plain,
! [X61,X62,X63] :
( ~ r2(X61,X62)
| X63 != X62
| ~ r1(X63) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_10])])]) ).
fof(c_0_20,plain,
! [X64,X66] :
( ( X66 != esk13_1(X64)
| X66 = esk13_1(X64) )
& ( X66 != esk13_1(X64)
| r2(X64,X66) )
& ( ~ r2(X64,X66)
| X66 = esk13_1(X64) )
& ( ~ r2(X64,X66)
| r2(X64,X66) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_21,negated_conjecture,
( r1(esk3_1(X1))
| r2(esk2_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_22,negated_conjecture,
( r1(esk3_1(X1))
| esk2_1(X1) = esk4_0 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,negated_conjecture,
( r2(esk2_1(X1),X1)
| esk3_1(X1) = X1 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( esk3_1(X1) = X1
| esk2_1(X1) = esk4_0 ),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_25,plain,
( ~ r2(X3,X2)
| X1 != X2
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( X2 != esk13_1(X1)
| r2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( r1(esk3_1(X1))
| r2(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( r2(esk4_0,X1)
| esk3_1(X1) = X1 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( ~ r1(X2)
| ~ r2(X1,X2) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
r2(X1,esk13_1(X1)),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( ~ r2(X2,X1)
| X1 = esk13_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,negated_conjecture,
( r1(X1)
| r2(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_33,plain,
! [X26,X27] :
( X26 = X27
| ! [X28] :
( ~ r2(X27,X28)
| ! [X29] :
( X29 != X28
| ~ r2(X26,X29) ) ) ),
inference(fof_simplification,[status(thm)],[axiom_3a]) ).
cnf(c_0_34,plain,
~ r1(esk13_1(X1)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( r1(X1)
| X1 = esk13_1(esk4_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_36,plain,
! [X79,X80,X81,X82] :
( X79 = X80
| ~ r2(X80,X81)
| X82 != X81
| ~ r2(X79,X82) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_33])])]) ).
cnf(c_0_37,negated_conjecture,
esk13_1(X1) = esk13_1(esk4_0),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
( ~ r2(X4,X3)
| X2 != X3
| ~ r2(X1,X2)
| X1 = X4 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_39,negated_conjecture,
r2(X1,esk13_1(esk4_0)),
inference(spm,[status(thm)],[c_0_30,c_0_37]) ).
cnf(c_0_40,plain,
( ~ r2(X1,X3)
| ~ r2(X2,X3)
| X1 = X2 ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_41,negated_conjecture,
r2(X1,esk13_1(X2)),
inference(spm,[status(thm)],[c_0_39,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
X1 = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_41])]) ).
cnf(c_0_43,negated_conjecture,
~ r1(X1),
inference(spm,[status(thm)],[c_0_34,c_0_42]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_15,c_0_43]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN068+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n014.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 03:23:49 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.28/0.51 Running first-order theorem proving
% 0.28/0.51 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
% 0.28/0.61 % Version: 3.5.1
% 0.28/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.61 % Starting sh5l with 300s (1) cores
% 0.28/0.61 % sh5l with pid 3030797 completed with status 0
% 0.28/0.61 % Result found by sh5l
% 0.28/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.61 % Starting sh5l with 300s (1) cores
% 0.28/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.28/0.61 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.28/0.61 % Search class: FGHSM-FFMF21-SFFFFFNN
% 0.28/0.61 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.61 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.61 % SubtermCWHack with pid 3030800 completed with status 0
% 0.28/0.61 % Result found by SubtermCWHack
% 0.28/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.61 % Starting sh5l with 300s (1) cores
% 0.28/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.28/0.61 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.28/0.61 % Search class: FGHSM-FFMF21-SFFFFFNN
% 0.28/0.61 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.61 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.61 % Preprocessing time : 0.002 s
% 0.28/0.61
% 0.28/0.61 % Proof found!
% 0.28/0.61 % SZS status Theorem
% 0.28/0.61 % SZS output start CNFRefutation
% See solution above
% 0.28/0.61 % Parsed axioms : 12
% 0.28/0.61 % Removed by relevancy pruning/SinE : 0
% 0.28/0.61 % Initial clauses : 45
% 0.28/0.61 % Removed in clause preprocessing : 8
% 0.28/0.61 % Initial clauses in saturation : 37
% 0.28/0.61 % Processed clauses : 288
% 0.28/0.61 % ...of these trivial : 7
% 0.28/0.61 % ...subsumed : 155
% 0.28/0.61 % ...remaining for further processing : 126
% 0.28/0.61 % Other redundant clauses eliminated : 13
% 0.28/0.61 % Clauses deleted for lack of memory : 0
% 0.28/0.61 % Backward-subsumed : 74
% 0.28/0.61 % Backward-rewritten : 24
% 0.28/0.61 % Generated clauses : 1366
% 0.28/0.61 % ...of the previous two non-redundant : 1128
% 0.28/0.61 % ...aggressively subsumed : 0
% 0.28/0.61 % Contextual simplify-reflections : 1
% 0.28/0.61 % Paramodulations : 1332
% 0.28/0.61 % Factorizations : 10
% 0.28/0.61 % NegExts : 0
% 0.28/0.61 % Equation resolutions : 13
% 0.28/0.61 % Disequality decompositions : 0
% 0.28/0.61 % Total rewrite steps : 386
% 0.28/0.61 % ...of those cached : 331
% 0.28/0.61 % Propositional unsat checks : 0
% 0.28/0.61 % Propositional check models : 0
% 0.28/0.61 % Propositional check unsatisfiable : 0
% 0.28/0.61 % Propositional clauses : 0
% 0.28/0.61 % Propositional clauses after purity: 0
% 0.28/0.61 % Propositional unsat core size : 0
% 0.28/0.61 % Propositional preprocessing time : 0.000
% 0.28/0.61 % Propositional encoding time : 0.000
% 0.28/0.61 % Propositional solver time : 0.000
% 0.28/0.61 % Success case prop preproc time : 0.000
% 0.28/0.61 % Success case prop encoding time : 0.000
% 0.28/0.61 % Success case prop solver time : 0.000
% 0.28/0.61 % Current number of processed clauses : 11
% 0.28/0.61 % Positive orientable unit clauses : 9
% 0.28/0.61 % Positive unorientable unit clauses: 1
% 0.28/0.61 % Negative unit clauses : 1
% 0.28/0.61 % Non-unit-clauses : 0
% 0.28/0.61 % Current number of unprocessed clauses: 811
% 0.28/0.61 % ...number of literals in the above : 2378
% 0.28/0.61 % Current number of archived formulas : 0
% 0.28/0.61 % Current number of archived clauses : 109
% 0.28/0.61 % Clause-clause subsumption calls (NU) : 673
% 0.28/0.61 % Rec. Clause-clause subsumption calls : 627
% 0.28/0.61 % Non-unit clause-clause subsumptions : 146
% 0.28/0.61 % Unit Clause-clause subsumption calls : 199
% 0.28/0.61 % Rewrite failures with RHS unbound : 129
% 0.28/0.61 % BW rewrite match attempts : 198
% 0.28/0.61 % BW rewrite match successes : 112
% 0.28/0.61 % Condensation attempts : 0
% 0.28/0.61 % Condensation successes : 0
% 0.28/0.61 % Termbank termtop insertions : 9994
% 0.28/0.61 % Search garbage collected termcells : 316
% 0.28/0.61
% 0.28/0.61 % -------------------------------------------------
% 0.28/0.61 % User time : 0.032 s
% 0.28/0.61 % System time : 0.005 s
% 0.28/0.61 % Total time : 0.037 s
% 0.28/0.61 % Maximum resident set size: 3668 pages
% 0.28/0.61
% 0.28/0.61 % -------------------------------------------------
% 0.28/0.61 % User time : 0.035 s
% 0.28/0.61 % System time : 0.011 s
% 0.28/0.61 % Total time : 0.046 s
% 0.28/0.61 % Maximum resident set size: 4864 pages
% 0.28/0.61 % E exiting
%------------------------------------------------------------------------------