%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN070+1 : 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 : n001.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 0.24s 0.52s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 88 ( 37 ~; 28 |; 23 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 0 con; 1-1 aty)
% Number of variables : 55 ( 2 sgn 16 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(onepluszeroidone,conjecture,
? [X63] :
( ? [X47] :
( ? [X49] :
( r2(X49,X47)
& r1(X49) )
& id(X63,X47) )
& ? [X46] :
( ? [X41] :
( r2(X41,X46)
& r1(X41) )
& ? [X40] :
( r3(X46,X40,X63)
& r1(X40) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',onepluszeroidone) ).
fof(axiom_4a,axiom,
! [X54] :
? [X55] :
( ? [X56] :
( r3(X54,X56,X55)
& r1(X56) )
& id(X55,X54) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_4a) ).
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_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(c_0_4,negated_conjecture,
~ ? [X63] :
( ? [X47] :
( ? [X49] :
( r2(X49,X47)
& r1(X49) )
& id(X63,X47) )
& ? [X46] :
( ? [X41] :
( r2(X41,X46)
& r1(X41) )
& ? [X40] :
( r3(X46,X40,X63)
& r1(X40) ) ) ),
inference(assume_negation,[status(cth)],[onepluszeroidone]) ).
fof(c_0_5,negated_conjecture,
! [X135,X136,X137,X138,X139,X140] :
( ~ r2(X140,X139)
| ~ r1(X140)
| ~ id(X135,X139)
| ~ r2(X138,X136)
| ~ r1(X138)
| ~ r3(X136,X137,X135)
| ~ r1(X137) ),
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,
! [X121] :
( r3(X121,esk14_1(X121),esk13_1(X121))
& r1(esk14_1(X121))
& id(esk13_1(X121),X121) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
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]) ).
cnf(c_0_8,negated_conjecture,
( ~ r2(X6,X5)
| ~ r1(X6)
| ~ id(X3,X5)
| ~ r2(X4,X2)
| ~ r1(X4)
| ~ r3(X2,X1,X3)
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,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_12,plain,
! [X81] : id(X81,X81),
inference(variable_rename,[status(thm)],[axiom_5]) ).
cnf(c_0_13,negated_conjecture,
( ~ id(esk13_1(X4),X2)
| ~ r1(X3)
| ~ r1(X1)
| ~ r2(X3,X4)
| ~ r2(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]) ).
cnf(c_0_14,plain,
id(esk13_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,plain,
( ~ id(X1,esk2_1(X2))
| r2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( ~ r1(X3)
| ~ r1(X1)
| ~ r2(X3,X2)
| ~ r2(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
r2(X1,esk2_1(X1)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( ~ r1(X1)
| ~ r1(X2)
| ~ r2(X1,esk2_1(X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,negated_conjecture,
~ r1(X1),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_21,plain,
$false,
inference(sr,[status(thm)],[c_0_10,c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN070+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.38 % Computer : n001.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Mon Sep 21 03:30:00 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 Running first-order theorem proving
% 0.16/0.43 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
% 0.24/0.52 % Version: 3.5.1
% 0.24/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.52 % Starting sh5l with 300s (1) cores
% 0.24/0.52 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2091389 completed with status 0
% 0.24/0.52 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.24/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.52 % No SInE strategy applied
% 0.24/0.52 % Search class: FGHNM-FFMF21-SFFFFFNN
% 0.24/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.24/0.52 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 231s (1) cores
% 0.24/0.52 % Starting new_bool_3 with 211s (1) cores
% 0.24/0.52 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 136s (1) cores
% 0.24/0.52 % G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with pid 2091395 completed with status 0
% 0.24/0.52 % Result found by G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S
% 0.24/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.52 % No SInE strategy applied
% 0.24/0.52 % Search class: FGHNM-FFMF21-SFFFFFNN
% 0.24/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.24/0.52 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 231s (1) cores
% 0.24/0.52 % Preprocessing time : 0.003 s
% 0.24/0.52 % Presaturation interreduction done
% 0.24/0.52
% 0.24/0.52 % Proof found!
% 0.24/0.52 % SZS status Theorem
% 0.24/0.52 % SZS output start CNFRefutation
% See solution above
% 0.24/0.53 % Parsed axioms : 19
% 0.24/0.53 % Removed by relevancy pruning/SinE : 0
% 0.24/0.53 % Initial clauses : 59
% 0.24/0.53 % Removed in clause preprocessing : 16
% 0.24/0.53 % Initial clauses in saturation : 43
% 0.24/0.53 % Processed clauses : 156
% 0.24/0.53 % ...of these trivial : 0
% 0.24/0.53 % ...subsumed : 17
% 0.24/0.53 % ...remaining for further processing : 139
% 0.24/0.53 % Other redundant clauses eliminated : 0
% 0.24/0.53 % Clauses deleted for lack of memory : 0
% 0.24/0.53 % Backward-subsumed : 26
% 0.24/0.53 % Backward-rewritten : 0
% 0.24/0.53 % Generated clauses : 369
% 0.24/0.53 % ...of the previous two non-redundant : 299
% 0.24/0.53 % ...aggressively subsumed : 0
% 0.24/0.53 % Contextual simplify-reflections : 0
% 0.24/0.53 % Paramodulations : 360
% 0.24/0.53 % Factorizations : 0
% 0.24/0.53 % NegExts : 0
% 0.24/0.53 % Equation resolutions : 0
% 0.24/0.53 % Disequality decompositions : 0
% 0.24/0.53 % Total rewrite steps : 84
% 0.24/0.53 % ...of those cached : 57
% 0.24/0.53 % Propositional unsat checks : 0
% 0.24/0.53 % Propositional check models : 0
% 0.24/0.53 % Propositional check unsatisfiable : 0
% 0.24/0.53 % Propositional clauses : 0
% 0.24/0.53 % Propositional clauses after purity: 0
% 0.24/0.53 % Propositional unsat core size : 0
% 0.24/0.53 % Propositional preprocessing time : 0.000
% 0.24/0.53 % Propositional encoding time : 0.000
% 0.24/0.53 % Propositional solver time : 0.000
% 0.24/0.53 % Success case prop preproc time : 0.000
% 0.24/0.53 % Success case prop encoding time : 0.000
% 0.24/0.53 % Success case prop solver time : 0.000
% 0.24/0.53 % Current number of processed clauses : 61
% 0.24/0.53 % Positive orientable unit clauses : 36
% 0.24/0.53 % Positive unorientable unit clauses: 0
% 0.24/0.53 % Negative unit clauses : 1
% 0.24/0.53 % Non-unit-clauses : 24
% 0.24/0.53 % Current number of unprocessed clauses: 227
% 0.24/0.53 % ...number of literals in the above : 566
% 0.24/0.53 % Current number of archived formulas : 0
% 0.24/0.53 % Current number of archived clauses : 78
% 0.24/0.53 % Clause-clause subsumption calls (NU) : 346
% 0.24/0.53 % Rec. Clause-clause subsumption calls : 206
% 0.24/0.53 % Non-unit clause-clause subsumptions : 3
% 0.24/0.53 % Unit Clause-clause subsumption calls : 177
% 0.24/0.53 % Rewrite failures with RHS unbound : 0
% 0.24/0.53 % BW rewrite match attempts : 11
% 0.24/0.53 % BW rewrite match successes : 0
% 0.24/0.53 % Condensation attempts : 0
% 0.24/0.53 % Condensation successes : 0
% 0.24/0.53 % Termbank termtop insertions : 6789
% 0.24/0.53 % Search garbage collected termcells : 430
% 0.24/0.53
% 0.24/0.53 % -------------------------------------------------
% 0.24/0.53 % User time : 0.023 s
% 0.24/0.53 % System time : 0.005 s
% 0.24/0.53 % Total time : 0.029 s
% 0.24/0.53 % Maximum resident set size: 3696 pages
% 0.24/0.53
% 0.24/0.53 % -------------------------------------------------
% 0.24/0.53 % User time : 0.083 s
% 0.24/0.53 % System time : 0.028 s
% 0.24/0.53 % Total time : 0.111 s
% 0.24/0.53 % Maximum resident set size: 4864 pages
% 0.24/0.53 % E exiting
%------------------------------------------------------------------------------