%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM468+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 01:55:08 PM UTC 2026
% Result : Theorem 0.15s 0.73s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 111 ( 56 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 117 ( 38 ~; 31 |; 30 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( xl != sz00
=> ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(m__1240_04,hypothesis,
( doDivides0(xl,xn)
& ? [X1] :
( xn = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) )
& doDivides0(xl,xm)
& ? [X1] :
( xm = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240_04) ).
fof(m__1240,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(c_0_5,negated_conjecture,
~ ( xl != sz00
=> ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_6,plain,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X2,X1) = sdtasdt0(X3,X1)
| sdtasdt0(X1,X2) = sdtasdt0(X1,X3) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[mMulCanc]) ).
fof(c_0_7,negated_conjecture,
~ ( xl != sz00
=> ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X28,X29,X30] :
( ( ~ aNaturalNumber0(X28)
| X28 = sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X29)
| X29 = X30
| sdtasdt0(X29,X28) != sdtasdt0(X30,X28) )
& ( ~ aNaturalNumber0(X28)
| X28 = sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X29)
| X29 = X30
| sdtasdt0(X28,X29) != sdtasdt0(X28,X30) ) ),
inference(distribute,[status(thm)],[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,hypothesis,
( doDivides0(xl,xn)
& xn = sdtasdt0(xl,esk4_0)
& aNaturalNumber0(esk4_0)
& doDivides0(xl,xm)
& xm = sdtasdt0(xl,esk3_0)
& aNaturalNumber0(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1240_04])]) ).
fof(c_0_10,negated_conjecture,
( sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl))
& xl != sz00 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
cnf(c_0_11,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| X1 = sz00
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
xm = sdtasdt0(xl,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,hypothesis,
aNaturalNumber0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1240]) ).
cnf(c_0_15,negated_conjecture,
xl != sz00,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
xn = sdtasdt0(xl,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,hypothesis,
aNaturalNumber0(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_18,plain,
! [X22,X23,X24] :
( ( ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X22)
| sdtasdt0(sdtpldt0(X23,X24),X22) = sdtpldt0(sdtasdt0(X23,X22),sdtasdt0(X24,X22)) )
& ( ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X22)
| sdtasdt0(X22,sdtpldt0(X23,X24)) = sdtpldt0(sdtasdt0(X22,X23),sdtasdt0(X22,X24)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])])]) ).
cnf(c_0_19,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xl,X1) != xm
| X1 = esk3_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_20,negated_conjecture,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xl,X1) != xn
| X1 = esk4_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_16]),c_0_17]),c_0_14])]),c_0_15]) ).
cnf(c_0_23,negated_conjecture,
xn = sdtasdt0(xl,sdtsldt0(xn,xl)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,negated_conjecture,
aNaturalNumber0(sdtsldt0(xn,xl)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,negated_conjecture,
sdtsldt0(xm,xl) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_28,negated_conjecture,
sdtsldt0(xn,xl) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_29,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(sdtasdt0(xl,X1),xn) = sdtasdt0(xl,sdtpldt0(X1,esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_16]),c_0_17]),c_0_14])]) ).
cnf(c_0_30,negated_conjecture,
sdtasdt0(xl,sdtpldt0(esk3_0,esk4_0)) != sdtpldt0(xm,xn),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_31,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_12]),c_0_13])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM468+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.52 % Computer : n009.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Mon Sep 21 02:32:58 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.53 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.57 Running first-order theorem proving
% 0.14/0.57 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
% 0.15/0.73 % Version: 3.5.1
% 0.15/0.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.73 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.73 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.73 % Starting sh5l with 300s (1) cores
% 0.15/0.73 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 653374 completed with status 0
% 0.15/0.73 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.15/0.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.73 % No SInE strategy applied
% 0.15/0.73 % Search class: FGUSF-FFMM22-MFFFFFNN
% 0.15/0.73 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.73 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/0.73 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/0.73 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.73 % Starting new_bool_1 with 136s (1) cores
% 0.15/0.73 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 653382 completed with status 0
% 0.15/0.73 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.15/0.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.73 % No SInE strategy applied
% 0.15/0.73 % Search class: FGUSF-FFMM22-MFFFFFNN
% 0.15/0.73 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.73 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/0.73 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/0.73 % Preprocessing time : 0.001 s
% 0.15/0.73 % Presaturation interreduction done
% 0.15/0.73
% 0.15/0.73 % Proof found!
% 0.15/0.73 % SZS status Theorem
% 0.15/0.73 % SZS output start CNFRefutation
% See solution above
% 0.15/0.73 % Parsed axioms : 35
% 0.15/0.73 % Removed by relevancy pruning/SinE : 0
% 0.15/0.73 % Initial clauses : 71
% 0.15/0.73 % Removed in clause preprocessing : 3
% 0.15/0.73 % Initial clauses in saturation : 68
% 0.15/0.73 % Processed clauses : 2481
% 0.15/0.73 % ...of these trivial : 282
% 0.15/0.73 % ...subsumed : 1425
% 0.15/0.73 % ...remaining for further processing : 774
% 0.15/0.73 % Other redundant clauses eliminated : 148
% 0.15/0.73 % Clauses deleted for lack of memory : 0
% 0.15/0.73 % Backward-subsumed : 46
% 0.15/0.73 % Backward-rewritten : 59
% 0.15/0.73 % Generated clauses : 11692
% 0.15/0.73 % ...of the previous two non-redundant : 9877
% 0.15/0.73 % ...aggressively subsumed : 0
% 0.15/0.73 % Contextual simplify-reflections : 73
% 0.15/0.73 % Paramodulations : 11538
% 0.15/0.73 % Factorizations : 0
% 0.15/0.73 % NegExts : 0
% 0.15/0.73 % Equation resolutions : 154
% 0.15/0.73 % Disequality decompositions : 0
% 0.15/0.73 % Total rewrite steps : 12927
% 0.15/0.73 % ...of those cached : 12871
% 0.15/0.73 % Propositional unsat checks : 0
% 0.15/0.73 % Propositional check models : 0
% 0.15/0.73 % Propositional check unsatisfiable : 0
% 0.15/0.73 % Propositional clauses : 0
% 0.15/0.73 % Propositional clauses after purity: 0
% 0.15/0.73 % Propositional unsat core size : 0
% 0.15/0.73 % Propositional preprocessing time : 0.000
% 0.15/0.73 % Propositional encoding time : 0.000
% 0.15/0.73 % Propositional solver time : 0.000
% 0.15/0.73 % Success case prop preproc time : 0.000
% 0.15/0.73 % Success case prop encoding time : 0.000
% 0.15/0.73 % Success case prop solver time : 0.000
% 0.15/0.73 % Current number of processed clauses : 597
% 0.15/0.73 % Positive orientable unit clauses : 57
% 0.15/0.73 % Positive unorientable unit clauses: 0
% 0.15/0.73 % Negative unit clauses : 5
% 0.15/0.73 % Non-unit-clauses : 535
% 0.15/0.73 % Current number of unprocessed clauses: 7420
% 0.15/0.73 % ...number of literals in the above : 37943
% 0.15/0.73 % Current number of archived formulas : 0
% 0.15/0.73 % Current number of archived clauses : 168
% 0.15/0.73 % Clause-clause subsumption calls (NU) : 41340
% 0.15/0.73 % Rec. Clause-clause subsumption calls : 20205
% 0.15/0.73 % Non-unit clause-clause subsumptions : 1491
% 0.15/0.73 % Unit Clause-clause subsumption calls : 569
% 0.15/0.73 % Rewrite failures with RHS unbound : 0
% 0.15/0.73 % BW rewrite match attempts : 24
% 0.15/0.73 % BW rewrite match successes : 24
% 0.15/0.73 % Condensation attempts : 0
% 0.15/0.73 % Condensation successes : 0
% 0.15/0.73 % Termbank termtop insertions : 188867
% 0.15/0.73 % Search garbage collected termcells : 1054
% 0.15/0.73
% 0.15/0.73 % -------------------------------------------------
% 0.15/0.73 % User time : 0.136 s
% 0.15/0.73 % System time : 0.006 s
% 0.15/0.73 % Total time : 0.142 s
% 0.15/0.73 % Maximum resident set size: 3672 pages
% 0.15/0.73
% 0.15/0.73 % -------------------------------------------------
% 0.15/0.73 % User time : 0.664 s
% 0.15/0.73 % System time : 0.028 s
% 0.15/0.73 % Total time : 0.693 s
% 0.15/0.73 % Maximum resident set size: 4608 pages
% 0.15/0.73 % E exiting
%------------------------------------------------------------------------------