%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN076+1 : 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 : n018.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 01:57:40 PM UTC 2026
% Result : Theorem 0.22s 5.68s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 16 unt; 0 def)
% Number of atoms : 144 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 174 ( 73 ~; 58 |; 43 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 103 ( 12 sgn 29 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_8,axiom,
! [X20,X21] :
( ( r1(X21)
& r1(X20) )
| ( ~ r1(X21)
& ~ r1(X20) )
| ~ id(X20,X21) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(thereexistsanevennumberid,conjecture,
? [X63,X46,X47] :
( ? [X41] :
( r3(X46,X47,X41)
& id(X41,X63) )
& ? [X40] :
( ? [X49] :
( ? [X43] :
( ? [X58] :
( r2(X58,X43)
& r1(X58) )
& r2(X43,X49) )
& r4(X49,X46,X40) )
& id(X40,X63) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thereexistsanevennumberid) ).
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( ~ id(X2,X1)
& ~ r1(X2) )
| ( r1(X2)
& id(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1) ).
fof(axiom_5a,axiom,
! [X57] :
? [X58] :
( ? [X60] :
( r1(X60)
& id(X58,X60) )
& ? [X59] :
( r4(X57,X59,X58)
& r1(X59) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5a) ).
fof(axiom_4a,axiom,
! [X54] :
? [X55] :
( ? [X56] :
( r3(X54,X56,X55)
& r1(X56) )
& id(X55,X54) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_2) ).
fof(axiom_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(c_0_7,plain,
! [X20,X21] :
( ( r1(X21)
& r1(X20) )
| ( ~ r1(X21)
& ~ r1(X20) )
| ~ id(X20,X21) ),
inference(fof_simplification,[status(thm)],[axiom_8]) ).
fof(c_0_8,negated_conjecture,
~ ? [X63,X46,X47] :
( ? [X41] :
( r3(X46,X47,X41)
& id(X41,X63) )
& ? [X40] :
( ? [X49] :
( ? [X43] :
( ? [X58] :
( r2(X58,X43)
& r1(X58) )
& r2(X43,X49) )
& r4(X49,X46,X40) )
& id(X40,X63) ) ),
inference(assume_negation,[status(cth)],[thereexistsanevennumberid]) ).
fof(c_0_9,plain,
? [X1] :
! [X2] :
( ( ~ id(X2,X1)
& ~ r1(X2) )
| ( r1(X2)
& id(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_10,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_7])])]) ).
fof(c_0_11,plain,
! [X124] :
( r1(esk17_1(X124))
& id(esk15_1(X124),esk17_1(X124))
& r4(X124,esk16_1(X124),esk15_1(X124))
& r1(esk16_1(X124)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).
fof(c_0_12,negated_conjecture,
! [X135,X136,X137,X138,X139,X140,X141,X142] :
( ~ r3(X136,X137,X142)
| ~ id(X142,X135)
| ~ r2(X141,X140)
| ~ r1(X141)
| ~ r2(X140,X139)
| ~ r4(X139,X136,X138)
| ~ id(X138,X135) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_13,plain,
! [X69] :
( ( r1(X69)
| ~ id(X69,esk1_0) )
& ( r1(X69)
| ~ r1(X69) )
& ( id(X69,esk1_0)
| ~ id(X69,esk1_0) )
& ( id(X69,esk1_0)
| ~ r1(X69) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_14,plain,
( ~ id(X1,X2)
| ~ r1(X2)
| r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
id(esk15_1(X1),esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
r1(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,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])]) ).
cnf(c_0_18,negated_conjecture,
( ~ r3(X4,X8,X7)
| ~ id(X7,X2)
| ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X3)
| ~ r4(X3,X4,X1)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
r4(X1,esk16_1(X1),esk15_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
( ~ r1(X1)
| id(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
r1(esk15_1(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_22,plain,
id(esk13_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( ~ id(X3,X6)
| ~ id(esk15_1(X1),X6)
| ~ r1(X4)
| ~ r2(X5,X1)
| ~ r2(X4,X5)
| ~ r3(esk16_1(X1),X2,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
id(esk15_1(X1),esk1_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( ~ r1(X1)
| r1(esk13_1(X1)) ),
inference(spm,[status(thm)],[c_0_14,c_0_22]) ).
fof(c_0_26,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_27,negated_conjecture,
( ~ id(X3,esk1_0)
| ~ r1(X4)
| ~ r2(X5,X1)
| ~ r2(X4,X5)
| ~ r3(esk16_1(X1),X2,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( ~ r1(X1)
| id(esk13_1(X1),esk1_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
fof(c_0_29,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_26])])])]) ).
fof(c_0_30,plain,
! [X81] : id(X81,X81),
inference(variable_rename,[status(thm)],[axiom_5]) ).
cnf(c_0_31,negated_conjecture,
( ~ r1(X3)
| ~ r1(X4)
| ~ r2(X5,X1)
| ~ r2(X4,X5)
| ~ r3(esk16_1(X1),X2,esk13_1(X3)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,plain,
r1(esk16_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_34,plain,
( ~ id(X1,esk2_1(X2))
| r2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( ~ r1(X1)
| ~ r2(X2,X3)
| ~ r2(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_37,plain,
r2(X1,esk2_1(X1)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
( ~ r1(X1)
| ~ r2(esk2_1(X1),X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,plain,
r2(X1,esk13_1(esk2_1(X1))),
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_40,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_41,negated_conjecture,
~ r1(X1),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,plain,
$false,
inference(sr,[status(thm)],[c_0_40,c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN076+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/5.47 % Computer : n018.cluster.edu
% 0.16/5.47 % Model : x86_64 x86_64
% 0.16/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.47 % Memory : 8046.5625MB
% 0.16/5.47 % OS : Linux 6.8.0-71-generic
% 0.16/5.47 % CPULimit : 300
% 0.16/5.47 % WCLimit : 300
% 0.16/5.47 % DateTime : Mon Sep 21 03:26:48 UTC 2026
% 0.16/5.48 % CPUTime :
% 0.16/5.48 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/5.54 Running first-order theorem proving
% 0.22/5.54 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
% 0.22/5.68 % Version: 3.5.1
% 0.22/5.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/5.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/5.68 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.68 % Starting new_bool_1 with 300s (1) cores
% 0.22/5.68 % Starting sh5l with 300s (1) cores
% 0.22/5.68 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 865828 completed with status 0
% 0.22/5.68 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.22/5.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/5.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/5.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/5.68 % No SInE strategy applied
% 0.22/5.68 % Search class: FGHNM-FFMF21-SFFFFFNN
% 0.22/5.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/5.68 % Starting SubtermCWHack with 136s (1) cores
% 0.22/5.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/5.68 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 231s (1) cores
% 0.22/5.68 % Starting new_bool_3 with 211s (1) cores
% 0.22/5.68 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 136s (1) cores
% 0.22/5.68 % G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with pid 865836 completed with status 0
% 0.22/5.68 % Result found by G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S
% 0.22/5.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/5.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/5.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/5.68 % No SInE strategy applied
% 0.22/5.68 % Search class: FGHNM-FFMF21-SFFFFFNN
% 0.22/5.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/5.68 % Starting SubtermCWHack with 136s (1) cores
% 0.22/5.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/5.68 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 231s (1) cores
% 0.22/5.68 % Preprocessing time : 0.003 s
% 0.22/5.68 % Presaturation interreduction done
% 0.22/5.68
% 0.22/5.68 % Proof found!
% 0.22/5.68 % SZS status Theorem
% 0.22/5.68 % SZS output start CNFRefutation
% See solution above
% 0.22/5.68 % Parsed axioms : 19
% 0.22/5.68 % Removed by relevancy pruning/SinE : 0
% 0.22/5.68 % Initial clauses : 59
% 0.22/5.68 % Removed in clause preprocessing : 16
% 0.22/5.68 % Initial clauses in saturation : 43
% 0.22/5.68 % Processed clauses : 326
% 0.22/5.68 % ...of these trivial : 4
% 0.22/5.68 % ...subsumed : 88
% 0.22/5.68 % ...remaining for further processing : 234
% 0.22/5.68 % Other redundant clauses eliminated : 0
% 0.22/5.68 % Clauses deleted for lack of memory : 0
% 0.22/5.68 % Backward-subsumed : 60
% 0.22/5.68 % Backward-rewritten : 2
% 0.22/5.68 % Generated clauses : 1148
% 0.22/5.68 % ...of the previous two non-redundant : 908
% 0.22/5.68 % ...aggressively subsumed : 0
% 0.22/5.68 % Contextual simplify-reflections : 0
% 0.22/5.68 % Paramodulations : 1133
% 0.22/5.68 % Factorizations : 0
% 0.22/5.68 % NegExts : 0
% 0.22/5.68 % Equation resolutions : 0
% 0.22/5.68 % Disequality decompositions : 0
% 0.22/5.68 % Total rewrite steps : 308
% 0.22/5.68 % ...of those cached : 222
% 0.22/5.68 % Propositional unsat checks : 0
% 0.22/5.68 % Propositional check models : 0
% 0.22/5.68 % Propositional check unsatisfiable : 0
% 0.22/5.68 % Propositional clauses : 0
% 0.22/5.68 % Propositional clauses after purity: 0
% 0.22/5.68 % Propositional unsat core size : 0
% 0.22/5.68 % Propositional preprocessing time : 0.000
% 0.22/5.68 % Propositional encoding time : 0.000
% 0.22/5.68 % Propositional solver time : 0.000
% 0.22/5.68 % Success case prop preproc time : 0.000
% 0.22/5.68 % Success case prop encoding time : 0.000
% 0.22/5.68 % Success case prop solver time : 0.000
% 0.22/5.68 % Current number of processed clauses : 114
% 0.22/5.68 % Positive orientable unit clauses : 74
% 0.22/5.68 % Positive unorientable unit clauses: 0
% 0.22/5.68 % Negative unit clauses : 1
% 0.22/5.68 % Non-unit-clauses : 39
% 0.22/5.68 % Current number of unprocessed clauses: 664
% 0.22/5.68 % ...number of literals in the above : 1540
% 0.22/5.68 % Current number of archived formulas : 0
% 0.22/5.68 % Current number of archived clauses : 120
% 0.22/5.68 % Clause-clause subsumption calls (NU) : 1260
% 0.22/5.68 % Rec. Clause-clause subsumption calls : 476
% 0.22/5.68 % Non-unit clause-clause subsumptions : 79
% 0.22/5.68 % Unit Clause-clause subsumption calls : 286
% 0.22/5.68 % Rewrite failures with RHS unbound : 0
% 0.22/5.68 % BW rewrite match attempts : 42
% 0.22/5.68 % BW rewrite match successes : 2
% 0.22/5.68 % Condensation attempts : 0
% 0.22/5.68 % Condensation successes : 0
% 0.22/5.68 % Termbank termtop insertions : 14521
% 0.22/5.68 % Search garbage collected termcells : 441
% 0.22/5.68
% 0.22/5.68 % -------------------------------------------------
% 0.22/5.68 % User time : 0.045 s
% 0.22/5.68 % System time : 0.007 s
% 0.22/5.68 % Total time : 0.053 s
% 0.22/5.68 % Maximum resident set size: 3696 pages
% 0.22/5.68
% 0.22/5.68 % -------------------------------------------------
% 0.22/5.68 % User time : 0.287 s
% 0.22/5.68 % System time : 0.038 s
% 0.22/5.68 % Total time : 0.325 s
% 0.22/5.68 % Maximum resident set size: 4864 pages
% 0.22/5.68 % E exiting
%------------------------------------------------------------------------------