%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN085+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 : n017.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 01:57:42 PM UTC 2026
% Result : Theorem 0.21s 0.60s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 27 unt; 0 def)
% Number of atoms : 133 ( 49 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 145 ( 64 ~; 47 |; 34 &)
% ( 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 : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 87 ( 6 sgn 46 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(zeroplusoneidzero,conjecture,
! [X39] :
( ! [X17] :
( ~ r1(X17)
| X39 != X17 )
| ! [X22] :
( ! [X16] :
( ~ r2(X16,X22)
| ~ r1(X16) )
| ! [X23] :
( ~ r3(X23,X22,X39)
| ~ r1(X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zeroplusoneidzero) ).
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_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_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(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_3,axiom,
! [X6,X7] :
? [X8] :
! [X9] :
( ( X9 = X8
& r3(X6,X7,X9) )
| ( X9 != X8
& ~ r3(X6,X7,X9) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_3) ).
fof(c_0_6,negated_conjecture,
~ ! [X39] :
( ! [X17] :
( ~ r1(X17)
| X39 != X17 )
| ! [X22] :
( ! [X16] :
( ~ r2(X16,X22)
| ~ r1(X16) )
| ! [X23] :
( ~ r3(X23,X22,X39)
| ~ r1(X23) ) ) ),
inference(assume_negation,[status(cth)],[zeroplusoneidzero]) ).
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,
~ ! [X39] :
( ! [X17] :
( ~ r1(X17)
| X39 != X17 )
| ! [X22] :
( ! [X16] :
( ~ r2(X16,X22)
| ~ r1(X16) )
| ! [X23] :
( ~ r3(X23,X22,X39)
| ~ r1(X23) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X50] :
( ( X50 != esk6_0
| X50 = esk6_0 )
& ( X50 != esk6_0
| r1(X50) )
& ( ~ r1(X50)
| X50 = esk6_0 )
& ( ~ r1(X50)
| r1(X50) ) ),
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,negated_conjecture,
( r1(esk5_0)
& esk1_0 = esk5_0
& r2(esk4_0,esk2_0)
& r1(esk4_0)
& r3(esk3_0,esk2_0,esk1_0)
& r1(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_11,plain,
( ~ r1(X1)
| X1 = esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,negated_conjecture,
r1(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
esk6_0 = esk4_0,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
( ~ r1(X1)
| X1 = esk4_0 ),
inference(rw,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_15,negated_conjecture,
r1(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X3] :
? [X4] :
! [X5] :
( ( X5 = X4
& r2(X3,X5) )
| ( X5 != X4
& ~ r2(X3,X5) ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
cnf(c_0_17,negated_conjecture,
esk4_0 = esk3_0,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
r1(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
esk1_0 = esk5_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_20,plain,
! [X61,X63] :
( ( X63 != esk12_1(X61)
| X63 = esk12_1(X61) )
& ( X63 != esk12_1(X61)
| r2(X61,X63) )
& ( ~ r2(X61,X63)
| X63 = esk12_1(X61) )
& ( ~ r2(X61,X63)
| r2(X61,X63) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_16])])])]) ).
fof(c_0_21,plain,
! [X64,X65] :
( r3(X64,X65,esk16_2(X64,X65))
& r2(esk16_2(X64,X65),esk13_2(X64,X65))
& esk14_2(X64,X65) = esk13_2(X64,X65)
& r3(X64,esk15_2(X64,X65),esk14_2(X64,X65))
& r2(X65,esk15_2(X64,X65)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
cnf(c_0_22,negated_conjecture,
r2(esk4_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,plain,
( ~ r1(X1)
| X1 = esk3_0 ),
inference(rw,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
r1(esk1_0),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( ~ r2(X2,X1)
| X1 = esk12_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
r2(X1,esk15_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
r2(esk3_0,esk2_0),
inference(rw,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_28,negated_conjecture,
esk3_0 = esk1_0,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_29,plain,
! [X41,X42] :
( ~ r2(X41,X42)
| ! [X43] :
( X43 != X42
| ~ r1(X43) ) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_30,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_31,plain,
r3(X1,esk15_2(X1,X2),esk14_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,plain,
esk15_2(X1,X2) = esk12_1(X2),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
r2(esk1_0,esk2_0),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_34,plain,
! [X58,X59,X60] :
( ~ r2(X58,X59)
| X60 != X59
| ~ r1(X60) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_29])])]) ).
fof(c_0_35,plain,
! [X74,X75,X77] :
( ( X77 != esk17_2(X74,X75)
| X77 = esk17_2(X74,X75) )
& ( X77 != esk17_2(X74,X75)
| r3(X74,X75,X77) )
& ( ~ r3(X74,X75,X77)
| X77 = esk17_2(X74,X75) )
& ( ~ r3(X74,X75,X77)
| r3(X74,X75,X77) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_30])])])]) ).
cnf(c_0_36,negated_conjecture,
r3(esk3_0,esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_37,plain,
r3(X1,esk12_1(X2),esk14_2(X1,X2)),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
esk12_1(esk1_0) = esk2_0,
inference(spm,[status(thm)],[c_0_25,c_0_33]) ).
cnf(c_0_39,plain,
( ~ r2(X3,X2)
| X1 != X2
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,plain,
r2(esk16_2(X1,X2),esk13_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_41,plain,
esk14_2(X1,X2) = esk13_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_42,plain,
( ~ r3(X2,X3,X1)
| X1 = esk17_2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,negated_conjecture,
r3(esk1_0,esk2_0,esk1_0),
inference(rw,[status(thm)],[c_0_36,c_0_28]) ).
cnf(c_0_44,negated_conjecture,
r3(X1,esk2_0,esk14_2(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
( ~ r1(X2)
| ~ r2(X1,X2) ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
r2(esk16_2(X1,X2),esk14_2(X1,X2)),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
esk17_2(esk1_0,esk2_0) = esk1_0,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
esk17_2(X1,esk2_0) = esk14_2(X1,esk1_0),
inference(spm,[status(thm)],[c_0_42,c_0_44]) ).
cnf(c_0_49,plain,
~ r1(esk14_2(X1,X2)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
esk14_2(esk1_0,esk1_0) = esk1_0,
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN085+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.45 % Computer : n017.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 03:20:41 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.52 Running first-order theorem proving
% 0.21/0.53 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
% 0.21/0.60 % Version: 3.5.1
% 0.21/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.60 % Starting sh5l with 300s (1) cores
% 0.21/0.60 % new_bool_1 with pid 1321243 completed with status 0
% 0.21/0.60 % Result found by new_bool_1
% 0.21/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.60 % Search class: FGHSM-FFSM21-SFFFFFNN
% 0.21/0.60 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.60 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.60 % SubtermCWHack with pid 1321246 completed with status 0
% 0.21/0.60 % Result found by SubtermCWHack
% 0.21/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.21/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.60 % Search class: FGHSM-FFSM21-SFFFFFNN
% 0.21/0.60 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.60 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.60 % Preprocessing time : 0.002 s
% 0.21/0.60
% 0.21/0.60 % Proof found!
% 0.21/0.60 % SZS status Theorem
% 0.21/0.60 % SZS output start CNFRefutation
% See solution above
% 0.21/0.60 % Parsed axioms : 12
% 0.21/0.60 % Removed by relevancy pruning/SinE : 3
% 0.21/0.60 % Initial clauses : 32
% 0.21/0.60 % Removed in clause preprocessing : 6
% 0.21/0.60 % Initial clauses in saturation : 26
% 0.21/0.60 % Processed clauses : 63
% 0.21/0.60 % ...of these trivial : 0
% 0.21/0.60 % ...subsumed : 3
% 0.21/0.60 % ...remaining for further processing : 60
% 0.21/0.60 % Other redundant clauses eliminated : 5
% 0.21/0.60 % Clauses deleted for lack of memory : 0
% 0.21/0.60 % Backward-subsumed : 0
% 0.21/0.60 % Backward-rewritten : 16
% 0.21/0.60 % Generated clauses : 55
% 0.21/0.60 % ...of the previous two non-redundant : 57
% 0.21/0.60 % ...aggressively subsumed : 0
% 0.21/0.60 % Contextual simplify-reflections : 0
% 0.21/0.60 % Paramodulations : 50
% 0.21/0.60 % Factorizations : 0
% 0.21/0.60 % NegExts : 0
% 0.21/0.60 % Equation resolutions : 5
% 0.21/0.60 % Disequality decompositions : 0
% 0.21/0.60 % Total rewrite steps : 33
% 0.21/0.60 % ...of those cached : 13
% 0.21/0.60 % Propositional unsat checks : 0
% 0.21/0.60 % Propositional check models : 0
% 0.21/0.60 % Propositional check unsatisfiable : 0
% 0.21/0.60 % Propositional clauses : 0
% 0.21/0.60 % Propositional clauses after purity: 0
% 0.21/0.60 % Propositional unsat core size : 0
% 0.21/0.60 % Propositional preprocessing time : 0.000
% 0.21/0.60 % Propositional encoding time : 0.000
% 0.21/0.60 % Propositional solver time : 0.000
% 0.21/0.60 % Success case prop preproc time : 0.000
% 0.21/0.60 % Success case prop encoding time : 0.000
% 0.21/0.60 % Success case prop solver time : 0.000
% 0.21/0.60 % Current number of processed clauses : 39
% 0.21/0.60 % Positive orientable unit clauses : 23
% 0.21/0.60 % Positive unorientable unit clauses: 0
% 0.21/0.60 % Negative unit clauses : 3
% 0.21/0.60 % Non-unit-clauses : 13
% 0.21/0.60 % Current number of unprocessed clauses: 13
% 0.21/0.60 % ...number of literals in the above : 30
% 0.21/0.60 % Current number of archived formulas : 0
% 0.21/0.60 % Current number of archived clauses : 16
% 0.21/0.60 % Clause-clause subsumption calls (NU) : 47
% 0.21/0.60 % Rec. Clause-clause subsumption calls : 39
% 0.21/0.60 % Non-unit clause-clause subsumptions : 1
% 0.21/0.60 % Unit Clause-clause subsumption calls : 14
% 0.21/0.60 % Rewrite failures with RHS unbound : 0
% 0.21/0.60 % BW rewrite match attempts : 15
% 0.21/0.60 % BW rewrite match successes : 7
% 0.21/0.60 % Condensation attempts : 0
% 0.21/0.60 % Condensation successes : 0
% 0.21/0.60 % Termbank termtop insertions : 1677
% 0.21/0.60 % Search garbage collected termcells : 292
% 0.21/0.60
% 0.21/0.60 % -------------------------------------------------
% 0.21/0.60 % User time : 0.011 s
% 0.21/0.60 % System time : 0.003 s
% 0.21/0.60 % Total time : 0.014 s
% 0.21/0.60 % Maximum resident set size: 3668 pages
% 0.21/0.60
% 0.21/0.60 % -------------------------------------------------
% 0.21/0.60 % User time : 0.013 s
% 0.21/0.60 % System time : 0.010 s
% 0.21/0.60 % Total time : 0.023 s
% 0.21/0.60 % Maximum resident set size: 4608 pages
% 0.21/0.60 % E exiting
%------------------------------------------------------------------------------