%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN065+2 : 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 : n006.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 01:57:38 PM UTC 2026
% Result : Theorem 0.13s 5.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 5 unt; 0 def)
% Number of atoms : 131 ( 55 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 155 ( 66 ~; 67 |; 22 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 81 ( 4 sgn 40 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(nononesexist,conjecture,
? [X39] :
( ! [X16] :
( X39 != X16
| ~ r1(X16) )
& ! [X22] :
( X39 != X22
| ! [X23] :
( ~ r2(X23,X22)
| ~ r1(X23) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nononesexist) ).
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( X2 = X1
& r1(X2) )
| ( X2 != X1
& ~ r1(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(axiom_3a,axiom,
! [X26,X27] :
( X26 = X27
| ! [X28] :
( ~ r2(X27,X28)
| ! [X29] :
( X29 != X28
| ~ r2(X26,X29) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3a) ).
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( X5 = X4
& r2(X3,X5) )
| ( X5 != X4
& ~ r2(X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(axiom_7a,axiom,
! [X41,X42] :
( ~ r2(X41,X42)
| ! [X43] :
( X43 != X42
| ~ r1(X43) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).
fof(c_0_5,negated_conjecture,
~ ? [X39] :
( ! [X16] :
( X39 != X16
| ~ r1(X16) )
& ! [X22] :
( X39 != X22
| ! [X23] :
( ~ r2(X23,X22)
| ~ r1(X23) ) ) ),
inference(assume_negation,[status(cth)],[nononesexist]) ).
fof(c_0_6,negated_conjecture,
~ ? [X39] :
( ! [X16] :
( X39 != X16
| ~ r1(X16) )
& ! [X22] :
( X39 != X22
| ! [X23] :
( ~ r2(X23,X22)
| ~ r1(X23) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
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,plain,
! [X26,X27] :
( X26 = X27
| ! [X28] :
( ~ r2(X27,X28)
| ! [X29] :
( X29 != X28
| ~ r2(X26,X29) ) ) ),
inference(fof_simplification,[status(thm)],[axiom_3a]) ).
fof(c_0_9,plain,
! [X3] :
? [X4] :
! [X5] :
( ( X5 = X4
& r2(X3,X5) )
| ( X5 != X4
& ~ r2(X3,X5) ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(c_0_10,negated_conjecture,
! [X87] :
( ( X87 = esk21_1(X87)
| X87 = esk23_1(X87) )
& ( X87 = esk21_1(X87)
| r1(esk23_1(X87)) )
& ( r2(esk22_1(X87),esk21_1(X87))
| X87 = esk23_1(X87) )
& ( r2(esk22_1(X87),esk21_1(X87))
| r1(esk23_1(X87)) )
& ( r1(esk22_1(X87))
| X87 = esk23_1(X87) )
& ( r1(esk22_1(X87))
| r1(esk23_1(X87)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_11,plain,
! [X45] :
( ( X45 != esk1_0
| X45 = esk1_0 )
& ( X45 != esk1_0
| r1(X45) )
& ( ~ r1(X45)
| X45 = esk1_0 )
& ( ~ r1(X45)
| r1(X45) ) ),
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,
! [X41,X42] :
( ~ r2(X41,X42)
| ! [X43] :
( X43 != X42
| ~ r1(X43) ) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_13,plain,
! [X69,X70,X71,X72] :
( X69 = X70
| ~ r2(X70,X71)
| X72 != X71
| ~ r2(X69,X72) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_8])])]) ).
fof(c_0_14,plain,
! [X46,X48] :
( ( X48 != esk2_1(X46)
| X48 = esk2_1(X46) )
& ( X48 != esk2_1(X46)
| r2(X46,X48) )
& ( ~ r2(X46,X48)
| X48 = esk2_1(X46) )
& ( ~ r2(X46,X48)
| r2(X46,X48) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_15,negated_conjecture,
( r2(esk22_1(X1),esk21_1(X1))
| r1(esk23_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( X1 = esk21_1(X1)
| r1(esk23_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( ~ r1(X1)
| X1 = esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( r1(esk22_1(X1))
| r1(esk23_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
( r2(esk22_1(X1),esk21_1(X1))
| X1 = esk23_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,negated_conjecture,
( X1 = esk21_1(X1)
| X1 = esk23_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
( r1(esk22_1(X1))
| X1 = esk23_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_22,plain,
! [X84,X85,X86] :
( ~ r2(X84,X85)
| X86 != X85
| ~ r1(X86) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_12])])]) ).
cnf(c_0_23,plain,
( ~ r2(X4,X3)
| X2 != X3
| ~ r2(X1,X2)
| X1 = X4 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,plain,
( X2 != esk2_1(X1)
| r2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,negated_conjecture,
( r1(esk23_1(X1))
| r2(esk22_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( r1(esk23_1(X1))
| esk22_1(X1) = esk1_0 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_27,negated_conjecture,
( r2(esk22_1(X1),X1)
| esk23_1(X1) = X1 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( esk23_1(X1) = X1
| esk22_1(X1) = esk1_0 ),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_29,plain,
( ~ r2(X3,X2)
| X1 != X2
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( ~ r2(X1,X3)
| ~ r2(X2,X3)
| X1 = X2 ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
r2(X1,esk2_1(X1)),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_32,negated_conjecture,
( r1(esk23_1(X1))
| r2(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
( r2(esk1_0,X1)
| esk23_1(X1) = X1 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
( ~ r1(X2)
| ~ r2(X1,X2) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
( ~ r2(X1,esk2_1(X2))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( r1(X1)
| r2(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
~ r1(esk2_1(X1)),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_38,plain,
( X1 != esk1_0
| r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_39,negated_conjecture,
esk1_0 = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_40,plain,
r1(esk1_0),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_41,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_39]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN065+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/5.36 % Computer : n006.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 03:24:03 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 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
% 0.13/5.43 % Version: 3.5.1
% 0.13/5.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/5.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/5.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/5.43 % Starting new_bool_3 with 300s (1) cores
% 0.13/5.43 % Starting new_bool_1 with 300s (1) cores
% 0.13/5.43 % Starting sh5l with 300s (1) cores
% 0.13/5.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1906481 completed with status 0
% 0.13/5.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/5.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/5.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/5.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/5.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/5.43 % No SInE strategy applied
% 0.13/5.43 % Search class: FGHSM-FFMF21-SFFFFFNN
% 0.13/5.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/5.43 % Starting SubtermCWHack with 136s (1) cores
% 0.13/5.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/5.43 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.13/5.43 % Starting new_bool_3 with 136s (1) cores
% 0.13/5.43 % Starting new_bool_1 with 136s (1) cores
% 0.13/5.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1906487 completed with status 0
% 0.13/5.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/5.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/5.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/5.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/5.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/5.43 % No SInE strategy applied
% 0.13/5.43 % Search class: FGHSM-FFMF21-SFFFFFNN
% 0.13/5.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/5.43 % Starting SubtermCWHack with 136s (1) cores
% 0.13/5.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/5.43 % Preprocessing time : 0.002 s
% 0.13/5.43 % Presaturation interreduction done
% 0.13/5.43
% 0.13/5.43 % Proof found!
% 0.13/5.43 % SZS status Theorem
% 0.13/5.43 % SZS output start CNFRefutation
% See solution above
% 0.13/5.43 % Parsed axioms : 12
% 0.13/5.43 % Removed by relevancy pruning/SinE : 0
% 0.13/5.43 % Initial clauses : 45
% 0.13/5.43 % Removed in clause preprocessing : 12
% 0.13/5.43 % Initial clauses in saturation : 33
% 0.13/5.43 % Processed clauses : 117
% 0.13/5.43 % ...of these trivial : 0
% 0.13/5.43 % ...subsumed : 10
% 0.13/5.43 % ...remaining for further processing : 107
% 0.13/5.43 % Other redundant clauses eliminated : 6
% 0.13/5.43 % Clauses deleted for lack of memory : 0
% 0.13/5.43 % Backward-subsumed : 1
% 0.13/5.43 % Backward-rewritten : 60
% 0.13/5.43 % Generated clauses : 113
% 0.13/5.43 % ...of the previous two non-redundant : 96
% 0.13/5.43 % ...aggressively subsumed : 0
% 0.13/5.43 % Contextual simplify-reflections : 0
% 0.13/5.43 % Paramodulations : 107
% 0.13/5.43 % Factorizations : 0
% 0.13/5.43 % NegExts : 0
% 0.13/5.43 % Equation resolutions : 6
% 0.13/5.43 % Disequality decompositions : 0
% 0.13/5.43 % Total rewrite steps : 37
% 0.13/5.43 % ...of those cached : 0
% 0.13/5.43 % Propositional unsat checks : 0
% 0.13/5.43 % Propositional check models : 0
% 0.13/5.43 % Propositional check unsatisfiable : 0
% 0.13/5.43 % Propositional clauses : 0
% 0.13/5.43 % Propositional clauses after purity: 0
% 0.13/5.43 % Propositional unsat core size : 0
% 0.13/5.43 % Propositional preprocessing time : 0.000
% 0.13/5.43 % Propositional encoding time : 0.000
% 0.13/5.43 % Propositional solver time : 0.000
% 0.13/5.43 % Success case prop preproc time : 0.000
% 0.13/5.43 % Success case prop encoding time : 0.000
% 0.13/5.43 % Success case prop solver time : 0.000
% 0.13/5.43 % Current number of processed clauses : 7
% 0.13/5.43 % Positive orientable unit clauses : 3
% 0.13/5.43 % Positive unorientable unit clauses: 1
% 0.13/5.43 % Negative unit clauses : 0
% 0.13/5.43 % Non-unit-clauses : 3
% 0.13/5.43 % Current number of unprocessed clauses: 42
% 0.13/5.43 % ...number of literals in the above : 97
% 0.13/5.43 % Current number of archived formulas : 0
% 0.13/5.43 % Current number of archived clauses : 98
% 0.13/5.43 % Clause-clause subsumption calls (NU) : 145
% 0.13/5.43 % Rec. Clause-clause subsumption calls : 132
% 0.13/5.43 % Non-unit clause-clause subsumptions : 8
% 0.13/5.43 % Unit Clause-clause subsumption calls : 40
% 0.13/5.43 % Rewrite failures with RHS unbound : 0
% 0.13/5.43 % BW rewrite match attempts : 77
% 0.13/5.43 % BW rewrite match successes : 35
% 0.13/5.43 % Condensation attempts : 0
% 0.13/5.43 % Condensation successes : 0
% 0.13/5.43 % Termbank termtop insertions : 2768
% 0.13/5.43 % Search garbage collected termcells : 316
% 0.13/5.43
% 0.13/5.43 % -------------------------------------------------
% 0.13/5.43 % User time : 0.011 s
% 0.13/5.43 % System time : 0.003 s
% 0.13/5.43 % Total time : 0.014 s
% 0.13/5.43 % Maximum resident set size: 3668 pages
% 0.13/5.43
% 0.13/5.43 % -------------------------------------------------
% 0.13/5.43 % User time : 0.033 s
% 0.13/5.43 % System time : 0.013 s
% 0.13/5.43 % Total time : 0.047 s
% 0.13/5.43 % Maximum resident set size: 4864 pages
% 0.13/5.43 % E exiting
%------------------------------------------------------------------------------