%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN067+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 : n014.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 0.22s 0.61s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 8 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 126 ( 60 ~; 44 |; 22 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 61 ( 8 sgn 34 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(nonzerosexistid,conjecture,
? [X63] :
! [X46] :
( ~ r1(X46)
| ~ id(X63,X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonzerosexistid) ).
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_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(axiom_1,axiom,
? [X1] :
! [X2] :
( ( ~ id(X2,X1)
& ~ r1(X2) )
| ( r1(X2)
& id(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_1) ).
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_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(c_0_6,negated_conjecture,
~ ? [X63] :
! [X46] :
( ~ r1(X46)
| ~ id(X63,X46) ),
inference(assume_negation,[status(cth)],[nonzerosexistid]) ).
fof(c_0_7,plain,
! [X15,X16] :
( id(X16,X15)
| ~ id(X15,X16) ),
inference(fof_simplification,[status(thm)],[axiom_6]) ).
fof(c_0_8,negated_conjecture,
~ ? [X63] :
! [X46] :
( ~ r1(X46)
| ~ id(X63,X46) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X20,X21] :
( ( r1(X21)
& r1(X20) )
| ( ~ r1(X21)
& ~ r1(X20) )
| ~ id(X20,X21) ),
inference(fof_simplification,[status(thm)],[axiom_8]) ).
fof(c_0_10,plain,
! [X85,X86] :
( id(X86,X85)
| ~ id(X85,X86) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
fof(c_0_11,negated_conjecture,
! [X68] :
( r1(esk1_1(X68))
& id(X68,esk1_1(X68)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
? [X1] :
! [X2] :
( ( ~ id(X2,X1)
& ~ r1(X2) )
| ( r1(X2)
& id(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_13,plain,
! [X72,X73] :
( ( ~ id(X72,X73)
| ~ r1(X73)
| r1(X73) )
& ( ~ id(X72,X73)
| ~ r1(X73)
| r1(X72) )
& ( ~ id(X72,X73)
| ~ r1(X72)
| r1(X73) )
& ( ~ id(X72,X73)
| ~ r1(X72)
| r1(X72) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_9])])]) ).
cnf(c_0_14,plain,
( ~ id(X1,X2)
| id(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
id(X1,esk1_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X71] :
( ( r1(X71)
| ~ id(X71,esk2_0) )
& ( r1(X71)
| ~ r1(X71) )
& ( id(X71,esk2_0)
| ~ id(X71,esk2_0) )
& ( id(X71,esk2_0)
| ~ r1(X71) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_12])])])]) ).
cnf(c_0_17,plain,
( ~ id(X2,X1)
| ~ r1(X2)
| r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
id(esk1_1(X1),X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
r1(esk1_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_20,plain,
! [X65,X66] :
( ~ r2(X65,X66)
| ! [X67] :
( ~ r1(X67)
| ~ id(X67,X66) ) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_21,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_22,plain,
( ~ r1(X1)
| id(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
r1(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
fof(c_0_24,plain,
! [X81,X82,X83] :
( ~ r2(X81,X82)
| ~ r1(X83)
| ~ id(X83,X82) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_20])])]) ).
fof(c_0_25,plain,
! [X112,X114] :
( ( r2(X112,X114)
| ~ id(X114,esk17_1(X112)) )
& ( r2(X112,X114)
| ~ r2(X112,X114) )
& ( id(X114,esk17_1(X112))
| ~ id(X114,esk17_1(X112)) )
& ( id(X114,esk17_1(X112))
| ~ r2(X112,X114) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_26,plain,
id(X1,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_27,plain,
( ~ r2(X3,X2)
| ~ r1(X1)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
( ~ id(X1,esk17_1(X2))
| r2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,plain,
id(esk2_0,X1),
inference(spm,[status(thm)],[c_0_14,c_0_26]) ).
cnf(c_0_30,plain,
( ~ id(X3,X2)
| ~ r2(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_23])]) ).
cnf(c_0_31,plain,
r2(X1,esk2_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN067+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.47 % Computer : n014.cluster.edu
% 0.17/0.47 % Model : x86_64 x86_64
% 0.17/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.47 % Memory : 8046.5625MB
% 0.17/0.47 % OS : Linux 6.8.0-71-generic
% 0.17/0.47 % CPULimit : 300
% 0.17/0.47 % WCLimit : 300
% 0.17/0.47 % DateTime : Mon Sep 21 03:24:05 UTC 2026
% 0.17/0.47 % CPUTime :
% 0.17/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.55 Running first-order theorem proving
% 0.22/0.55 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
% 0.22/0.61 % Version: 3.5.1
% 0.22/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.61 % Starting sh5l with 300s (1) cores
% 0.22/0.61 % new_bool_3 with pid 3031195 completed with status 0
% 0.22/0.61 % Result found by new_bool_3
% 0.22/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.61 % Search class: FGHNM-FFMF21-SFFFFFNN
% 0.22/0.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.61 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.61 % SubtermCWHack with pid 3031198 completed with status 0
% 0.22/0.61 % Result found by SubtermCWHack
% 0.22/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.61 % Search class: FGHNM-FFMF21-SFFFFFNN
% 0.22/0.61 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.61 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.61 % Preprocessing time : 0.002 s
% 0.22/0.61
% 0.22/0.61 % Proof found!
% 0.22/0.61 % SZS status Theorem
% 0.22/0.61 % SZS output start CNFRefutation
% See solution above
% 0.22/0.61 % Parsed axioms : 19
% 0.22/0.61 % Removed by relevancy pruning/SinE : 0
% 0.22/0.61 % Initial clauses : 60
% 0.22/0.61 % Removed in clause preprocessing : 16
% 0.22/0.61 % Initial clauses in saturation : 44
% 0.22/0.61 % Processed clauses : 54
% 0.22/0.61 % ...of these trivial : 4
% 0.22/0.61 % ...subsumed : 1
% 0.22/0.61 % ...remaining for further processing : 49
% 0.22/0.61 % Other redundant clauses eliminated : 0
% 0.22/0.61 % Clauses deleted for lack of memory : 0
% 0.22/0.61 % Backward-subsumed : 1
% 0.22/0.61 % Backward-rewritten : 17
% 0.22/0.61 % Generated clauses : 77
% 0.22/0.61 % ...of the previous two non-redundant : 44
% 0.22/0.61 % ...aggressively subsumed : 0
% 0.22/0.61 % Contextual simplify-reflections : 0
% 0.22/0.61 % Paramodulations : 77
% 0.22/0.61 % Factorizations : 0
% 0.22/0.61 % NegExts : 0
% 0.22/0.61 % Equation resolutions : 0
% 0.22/0.61 % Disequality decompositions : 0
% 0.22/0.61 % Total rewrite steps : 69
% 0.22/0.61 % ...of those cached : 35
% 0.22/0.61 % Propositional unsat checks : 0
% 0.22/0.61 % Propositional check models : 0
% 0.22/0.61 % Propositional check unsatisfiable : 0
% 0.22/0.61 % Propositional clauses : 0
% 0.22/0.61 % Propositional clauses after purity: 0
% 0.22/0.61 % Propositional unsat core size : 0
% 0.22/0.61 % Propositional preprocessing time : 0.000
% 0.22/0.61 % Propositional encoding time : 0.000
% 0.22/0.61 % Propositional solver time : 0.000
% 0.22/0.61 % Success case prop preproc time : 0.000
% 0.22/0.61 % Success case prop encoding time : 0.000
% 0.22/0.61 % Success case prop solver time : 0.000
% 0.22/0.61 % Current number of processed clauses : 31
% 0.22/0.61 % Positive orientable unit clauses : 25
% 0.22/0.61 % Positive unorientable unit clauses: 0
% 0.22/0.61 % Negative unit clauses : 0
% 0.22/0.61 % Non-unit-clauses : 6
% 0.22/0.61 % Current number of unprocessed clauses: 21
% 0.22/0.61 % ...number of literals in the above : 60
% 0.22/0.61 % Current number of archived formulas : 0
% 0.22/0.61 % Current number of archived clauses : 18
% 0.22/0.61 % Clause-clause subsumption calls (NU) : 16
% 0.22/0.61 % Rec. Clause-clause subsumption calls : 16
% 0.22/0.61 % Non-unit clause-clause subsumptions : 1
% 0.22/0.61 % Unit Clause-clause subsumption calls : 20
% 0.22/0.61 % Rewrite failures with RHS unbound : 0
% 0.22/0.61 % BW rewrite match attempts : 19
% 0.22/0.61 % BW rewrite match successes : 16
% 0.22/0.61 % Condensation attempts : 0
% 0.22/0.61 % Condensation successes : 0
% 0.22/0.61 % Termbank termtop insertions : 3337
% 0.22/0.61 % Search garbage collected termcells : 363
% 0.22/0.61
% 0.22/0.61 % -------------------------------------------------
% 0.22/0.61 % User time : 0.011 s
% 0.22/0.61 % System time : 0.004 s
% 0.22/0.61 % Total time : 0.016 s
% 0.22/0.61 % Maximum resident set size: 3696 pages
% 0.22/0.61
% 0.22/0.61 % -------------------------------------------------
% 0.22/0.61 % User time : 0.014 s
% 0.22/0.61 % System time : 0.011 s
% 0.22/0.61 % Total time : 0.025 s
% 0.22/0.61 % Maximum resident set size: 4608 pages
% 0.22/0.61 % E exiting
%------------------------------------------------------------------------------