%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN062+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 0.25s 0.59s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 10 unt; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 130 ( 58 ~; 43 |; 29 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 78 ( 4 sgn 36 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(infiniteNumbersid,conjecture,
! [X38] :
? [X46,X63] :
( ? [X47] :
( r3(X38,X63,X47)
& id(X47,X46) )
& ! [X40] :
( ~ r1(X40)
| ~ id(X63,X40) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infiniteNumbersid) ).
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( ~ id(X5,X4)
& ~ r2(X3,X5) )
| ( r2(X3,X5)
& id(X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_2) ).
fof(axiom_7a,axiom,
! [X65,X66] :
( ~ r2(X65,X66)
| ! [X67] :
( ~ r1(X67)
| ~ id(X67,X66) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).
fof(axiom_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(axiom_1a,axiom,
! [X38,X39] :
? [X40] :
( ? [X43] :
( r3(X38,X39,X43)
& r2(X43,X40) )
& ? [X41] :
( ? [X42] :
( r3(X38,X42,X41)
& r2(X39,X42) )
& id(X41,X40) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_1a) ).
fof(axiom_8,axiom,
! [X20,X21] :
( ( r1(X21)
& r1(X20) )
| ( ~ r1(X21)
& ~ r1(X20) )
| ~ id(X20,X21) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(c_0_6,negated_conjecture,
~ ! [X38] :
? [X46,X63] :
( ? [X47] :
( r3(X38,X63,X47)
& id(X47,X46) )
& ! [X40] :
( ~ r1(X40)
| ~ id(X63,X40) ) ),
inference(assume_negation,[status(cth)],[infiniteNumbersid]) ).
fof(c_0_7,plain,
! [X3] :
? [X4] :
! [X5] :
( ( ~ id(X5,X4)
& ~ r2(X3,X5) )
| ( r2(X3,X5)
& id(X5,X4) ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(c_0_8,negated_conjecture,
~ ! [X38] :
? [X46,X63] :
( ? [X47] :
( r3(X38,X63,X47)
& id(X47,X46) )
& ! [X40] :
( ~ r1(X40)
| ~ id(X63,X40) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X65,X66] :
( ~ r2(X65,X66)
| ! [X67] :
( ~ r1(X67)
| ~ id(X67,X66) ) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_10,plain,
! [X70,X72] :
( ( r2(X70,X72)
| ~ id(X72,esk2_1(X70)) )
& ( r2(X70,X72)
| ~ r2(X70,X72) )
& ( id(X72,esk2_1(X70))
| ~ id(X72,esk2_1(X70)) )
& ( id(X72,esk2_1(X70))
| ~ r2(X70,X72) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_7])])])]) ).
fof(c_0_11,plain,
! [X81] : id(X81,X81),
inference(variable_rename,[status(thm)],[axiom_5]) ).
fof(c_0_12,negated_conjecture,
! [X136,X137,X139] :
( ( ~ r3(esk21_0,X137,X139)
| ~ id(X139,X136)
| r1(esk22_2(X136,X137)) )
& ( ~ r3(esk21_0,X137,X139)
| ~ id(X139,X136)
| id(X137,esk22_2(X136,X137)) ) ),
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_8])])])])])]) ).
fof(c_0_13,plain,
! [X105,X106] :
( r3(X105,X106,esk8_2(X105,X106))
& r2(esk8_2(X105,X106),esk5_2(X105,X106))
& r3(X105,esk7_2(X105,X106),esk6_2(X105,X106))
& r2(X106,esk7_2(X105,X106))
& id(esk6_2(X105,X106),esk5_2(X105,X106)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
fof(c_0_14,plain,
! [X132,X133,X134] :
( ~ r2(X132,X133)
| ~ r1(X134)
| ~ id(X134,X133) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_9])])]) ).
cnf(c_0_15,plain,
( ~ id(X1,esk2_1(X2))
| r2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X20,X21] :
( ( r1(X21)
& r1(X20) )
| ( ~ r1(X21)
& ~ r1(X20) )
| ~ id(X20,X21) ),
inference(fof_simplification,[status(thm)],[axiom_8]) ).
cnf(c_0_18,negated_conjecture,
( ~ r3(esk21_0,X1,X3)
| ~ id(X3,X2)
| id(X1,esk22_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
r3(X1,X2,esk8_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( ~ r3(esk21_0,X2,X3)
| ~ id(X3,X1)
| r1(esk22_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
( ~ r2(X3,X2)
| ~ r1(X1)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
r2(X1,esk2_1(X1)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_23,plain,
! [X87,X88] :
( ( ~ id(X87,X88)
| ~ r1(X88)
| r1(X88) )
& ( ~ id(X87,X88)
| ~ r1(X88)
| r1(X87) )
& ( ~ id(X87,X88)
| ~ r1(X87)
| r1(X88) )
& ( ~ id(X87,X88)
| ~ r1(X87)
| r1(X87) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_17])])]) ).
cnf(c_0_24,negated_conjecture,
( ~ id(esk8_2(esk21_0,X1),X2)
| id(X1,esk22_2(X2,X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( ~ id(esk8_2(esk21_0,X2),X1)
| r1(esk22_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_26,plain,
( ~ id(X1,esk2_1(X2))
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( ~ id(X1,X2)
| ~ r1(X2)
| r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
id(X1,esk22_2(esk8_2(esk21_0,X1),X1)),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_29,negated_conjecture,
r1(esk22_2(esk8_2(esk21_0,X1),X1)),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_30,plain,
~ r1(esk2_1(X1)),
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_31,negated_conjecture,
r1(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_32,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN062+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 % Computer : n003.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Mon Sep 21 03:25:02 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.49 Running first-order theorem proving
% 0.14/0.49 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
% 0.25/0.59 % Version: 3.5.1
% 0.25/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.59 % Starting sh5l with 300s (1) cores
% 0.25/0.59 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3303125 completed with status 0
% 0.25/0.59 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.25/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.59 % No SInE strategy applied
% 0.25/0.59 % Search class: FGHNM-FFMF21-SFFFFFNN
% 0.25/0.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.25/0.59 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 231s (1) cores
% 0.25/0.59 % Starting new_bool_3 with 211s (1) cores
% 0.25/0.59 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 136s (1) cores
% 0.25/0.59 % G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with pid 3303133 completed with status 0
% 0.25/0.59 % Result found by G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S
% 0.25/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.59 % No SInE strategy applied
% 0.25/0.59 % Search class: FGHNM-FFMF21-SFFFFFNN
% 0.25/0.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.25/0.59 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 231s (1) cores
% 0.25/0.59 % Preprocessing time : 0.003 s
% 0.25/0.59 % Presaturation interreduction done
% 0.25/0.59
% 0.25/0.59 % Proof found!
% 0.25/0.59 % SZS status Theorem
% 0.25/0.59 % SZS output start CNFRefutation
% See solution above
% 0.25/0.59 % Parsed axioms : 19
% 0.25/0.59 % Removed by relevancy pruning/SinE : 0
% 0.25/0.59 % Initial clauses : 60
% 0.25/0.59 % Removed in clause preprocessing : 16
% 0.25/0.59 % Initial clauses in saturation : 44
% 0.25/0.59 % Processed clauses : 493
% 0.25/0.59 % ...of these trivial : 18
% 0.25/0.59 % ...subsumed : 156
% 0.25/0.59 % ...remaining for further processing : 319
% 0.25/0.59 % Other redundant clauses eliminated : 0
% 0.25/0.59 % Clauses deleted for lack of memory : 0
% 0.25/0.59 % Backward-subsumed : 4
% 0.25/0.59 % Backward-rewritten : 112
% 0.25/0.59 % Generated clauses : 2254
% 0.25/0.59 % ...of the previous two non-redundant : 1704
% 0.25/0.59 % ...aggressively subsumed : 0
% 0.25/0.59 % Contextual simplify-reflections : 0
% 0.25/0.59 % Paramodulations : 2254
% 0.25/0.59 % Factorizations : 0
% 0.25/0.59 % NegExts : 0
% 0.25/0.59 % Equation resolutions : 0
% 0.25/0.59 % Disequality decompositions : 0
% 0.25/0.59 % Total rewrite steps : 909
% 0.25/0.59 % ...of those cached : 712
% 0.25/0.59 % Propositional unsat checks : 0
% 0.25/0.59 % Propositional check models : 0
% 0.25/0.59 % Propositional check unsatisfiable : 0
% 0.25/0.59 % Propositional clauses : 0
% 0.25/0.59 % Propositional clauses after purity: 0
% 0.25/0.59 % Propositional unsat core size : 0
% 0.25/0.59 % Propositional preprocessing time : 0.000
% 0.25/0.59 % Propositional encoding time : 0.000
% 0.25/0.59 % Propositional solver time : 0.000
% 0.25/0.59 % Success case prop preproc time : 0.000
% 0.25/0.59 % Success case prop encoding time : 0.000
% 0.25/0.59 % Success case prop solver time : 0.000
% 0.25/0.59 % Current number of processed clauses : 159
% 0.25/0.59 % Positive orientable unit clauses : 101
% 0.25/0.59 % Positive unorientable unit clauses: 0
% 0.25/0.59 % Negative unit clauses : 0
% 0.25/0.59 % Non-unit-clauses : 58
% 0.25/0.59 % Current number of unprocessed clauses: 1266
% 0.25/0.59 % ...number of literals in the above : 2672
% 0.25/0.59 % Current number of archived formulas : 0
% 0.25/0.59 % Current number of archived clauses : 160
% 0.25/0.59 % Clause-clause subsumption calls (NU) : 1490
% 0.25/0.59 % Rec. Clause-clause subsumption calls : 1018
% 0.25/0.59 % Non-unit clause-clause subsumptions : 74
% 0.25/0.59 % Unit Clause-clause subsumption calls : 367
% 0.25/0.59 % Rewrite failures with RHS unbound : 0
% 0.25/0.59 % BW rewrite match attempts : 115
% 0.25/0.59 % BW rewrite match successes : 69
% 0.25/0.59 % Condensation attempts : 0
% 0.25/0.59 % Condensation successes : 0
% 0.25/0.59 % Termbank termtop insertions : 25085
% 0.25/0.59 % Search garbage collected termcells : 407
% 0.25/0.59
% 0.25/0.59 % -------------------------------------------------
% 0.25/0.59 % User time : 0.062 s
% 0.25/0.59 % System time : 0.008 s
% 0.25/0.59 % Total time : 0.070 s
% 0.25/0.59 % Maximum resident set size: 3696 pages
% 0.25/0.59
% 0.25/0.59 % -------------------------------------------------
% 0.25/0.59 % User time : 0.307 s
% 0.25/0.59 % System time : 0.027 s
% 0.25/0.60 % Total time : 0.334 s
% 0.25/0.60 % Maximum resident set size: 4608 pages
% 0.25/0.60 % E exiting
%------------------------------------------------------------------------------