%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN080+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 : n012.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 01:57:41 PM UTC 2026
% Result : Theorem 0.08s 0.45s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 86 ( 34 ~; 25 |; 27 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 0 con; 1-2 aty)
% Number of variables : 76 ( 10 sgn 26 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(xplustwoidy,conjecture,
? [X63,X46,X47] :
( ? [X40] :
( ? [X41] :
( ? [X49] :
( r2(X49,X41)
& r1(X49) )
& r2(X41,X40) )
& r3(X63,X40,X47) )
& id(X47,X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xplustwoidy) ).
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_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_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(axiom_6,axiom,
! [X15,X16] :
( id(X16,X15)
| ~ id(X15,X16) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
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(c_0_6,negated_conjecture,
~ ? [X63,X46,X47] :
( ? [X40] :
( ? [X41] :
( ? [X49] :
( r2(X49,X41)
& r1(X49) )
& r2(X41,X40) )
& r3(X63,X40,X47) )
& id(X47,X46) ),
inference(assume_negation,[status(cth)],[xplustwoidy]) ).
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,
! [X135,X136,X137,X138,X139,X140] :
( ~ r2(X140,X139)
| ~ r1(X140)
| ~ r2(X139,X138)
| ~ r3(X135,X138,X137)
| ~ id(X137,X136) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_9,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_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]) ).
cnf(c_0_12,negated_conjecture,
( ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r3(X3,X4,X1)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
r3(X1,X2,esk8_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ id(X1,esk2_1(X2))
| r2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X15,X16] :
( id(X16,X15)
| ~ id(X15,X16) ),
inference(fof_simplification,[status(thm)],[axiom_6]) ).
cnf(c_0_17,negated_conjecture,
( ~ id(esk8_2(X4,X3),X5)
| ~ r1(X1)
| ~ r2(X2,X3)
| ~ r2(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
r2(X1,esk2_1(X1)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_19,plain,
! [X82,X83] :
( id(X83,X82)
| ~ id(X82,X83) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_16])]) ).
fof(c_0_20,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_21,negated_conjecture,
( ~ id(esk8_2(X3,X2),X4)
| ~ r1(X1)
| ~ r2(esk2_1(X1),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( ~ id(X1,X2)
| id(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
id(esk13_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( ~ id(esk8_2(X2,esk2_1(esk2_1(X1))),X3)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_25,plain,
id(X1,esk13_1(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
~ r1(X1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
$false,
inference(sr,[status(thm)],[c_0_26,c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN080+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 03:24:51 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.38 Running first-order theorem proving
% 0.08/0.38 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
% 0.08/0.45 % Version: 3.5.1
% 0.08/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.08/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.08/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.45 % Starting sh5l with 300s (1) cores
% 0.08/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1462296 completed with status 0
% 0.08/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.08/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.08/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.08/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.45 % No SInE strategy applied
% 0.08/0.45 % Search class: FGHNM-FFMF21-SFFFFFNN
% 0.08/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.08/0.45 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 231s (1) cores
% 0.08/0.45 % Starting new_bool_3 with 211s (1) cores
% 0.08/0.45 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 136s (1) cores
% 0.08/0.45 % new_bool_3 with pid 1462305 completed with status 0
% 0.08/0.45 % Result found by new_bool_3
% 0.08/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.08/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.08/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.45 % No SInE strategy applied
% 0.08/0.45 % Search class: FGHNM-FFMF21-SFFFFFNN
% 0.08/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.08/0.45 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 231s (1) cores
% 0.08/0.45 % Starting new_bool_3 with 211s (1) cores
% 0.08/0.45 % Preprocessing time : 0.001 s
% 0.08/0.45 % Presaturation interreduction done
% 0.08/0.45
% 0.08/0.45 % Proof found!
% 0.08/0.45 % SZS status Theorem
% 0.08/0.45 % SZS output start CNFRefutation
% See solution above
% 0.08/0.45 % Parsed axioms : 19
% 0.08/0.45 % Removed by relevancy pruning/SinE : 0
% 0.08/0.45 % Initial clauses : 59
% 0.08/0.45 % Removed in clause preprocessing : 16
% 0.08/0.45 % Initial clauses in saturation : 43
% 0.08/0.45 % Processed clauses : 143
% 0.08/0.45 % ...of these trivial : 2
% 0.08/0.45 % ...subsumed : 9
% 0.08/0.45 % ...remaining for further processing : 132
% 0.08/0.45 % Other redundant clauses eliminated : 0
% 0.08/0.45 % Clauses deleted for lack of memory : 0
% 0.08/0.45 % Backward-subsumed : 26
% 0.08/0.45 % Backward-rewritten : 0
% 0.08/0.45 % Generated clauses : 263
% 0.08/0.45 % ...of the previous two non-redundant : 191
% 0.08/0.45 % ...aggressively subsumed : 0
% 0.08/0.45 % Contextual simplify-reflections : 0
% 0.08/0.45 % Paramodulations : 253
% 0.08/0.45 % Factorizations : 0
% 0.08/0.45 % NegExts : 0
% 0.08/0.45 % Equation resolutions : 0
% 0.08/0.45 % Disequality decompositions : 0
% 0.08/0.45 % Total rewrite steps : 84
% 0.08/0.45 % ...of those cached : 58
% 0.08/0.45 % Propositional unsat checks : 0
% 0.08/0.45 % Propositional check models : 0
% 0.08/0.45 % Propositional check unsatisfiable : 0
% 0.08/0.45 % Propositional clauses : 0
% 0.08/0.45 % Propositional clauses after purity: 0
% 0.08/0.45 % Propositional unsat core size : 0
% 0.08/0.45 % Propositional preprocessing time : 0.000
% 0.08/0.45 % Propositional encoding time : 0.000
% 0.08/0.45 % Propositional solver time : 0.000
% 0.08/0.45 % Success case prop preproc time : 0.000
% 0.08/0.45 % Success case prop encoding time : 0.000
% 0.08/0.45 % Success case prop solver time : 0.000
% 0.08/0.45 % Current number of processed clauses : 53
% 0.08/0.45 % Positive orientable unit clauses : 29
% 0.08/0.45 % Positive unorientable unit clauses: 0
% 0.08/0.45 % Negative unit clauses : 1
% 0.08/0.45 % Non-unit-clauses : 23
% 0.08/0.45 % Current number of unprocessed clauses: 132
% 0.08/0.45 % ...number of literals in the above : 243
% 0.08/0.45 % Current number of archived formulas : 0
% 0.08/0.45 % Current number of archived clauses : 79
% 0.08/0.45 % Clause-clause subsumption calls (NU) : 270
% 0.08/0.45 % Rec. Clause-clause subsumption calls : 168
% 0.08/0.45 % Non-unit clause-clause subsumptions : 2
% 0.08/0.45 % Unit Clause-clause subsumption calls : 163
% 0.08/0.45 % Rewrite failures with RHS unbound : 0
% 0.08/0.45 % BW rewrite match attempts : 8
% 0.08/0.45 % BW rewrite match successes : 0
% 0.08/0.45 % Condensation attempts : 0
% 0.08/0.45 % Condensation successes : 0
% 0.08/0.45 % Termbank termtop insertions : 5505
% 0.08/0.45 % Search garbage collected termcells : 414
% 0.08/0.45
% 0.08/0.45 % -------------------------------------------------
% 0.08/0.45 % User time : 0.005 s
% 0.08/0.45 % System time : 0.005 s
% 0.08/0.45 % Total time : 0.010 s
% 0.08/0.45 % Maximum resident set size: 3900 pages
% 0.08/0.45
% 0.08/0.45 % -------------------------------------------------
% 0.08/0.45 % User time : 0.046 s
% 0.08/0.45 % System time : 0.014 s
% 0.08/0.45 % Total time : 0.060 s
% 0.08/0.45 % Maximum resident set size: 4608 pages
% 0.08/0.45 % E exiting
%------------------------------------------------------------------------------