%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM479+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 01:55:11 PM UTC 2026
% Result : Theorem 0.09s 0.46s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 16 unt; 0 def)
% Number of atoms : 105 ( 51 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 107 ( 38 ~; 31 |; 24 &)
% ( 0 <=>; 14 =>; 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 19 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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__1524_04,hypothesis,
( doDivides0(xl,xm)
& ? [X1] :
( xm = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) )
& xl != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1524_04) ).
fof(m__,conjecture,
( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))
& aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl)) )
=> sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1524,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1524) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(m__1553,hypothesis,
aNaturalNumber0(xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1553) ).
fof(c_0_7,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_8,hypothesis,
( doDivides0(xl,xm)
& ? [X1] :
( xm = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) )
& xl != sz00 ),
inference(fof_simplification,[status(thm)],[m__1524_04]) ).
fof(c_0_9,plain,
! [X32,X33,X34] :
( ( ~ aNaturalNumber0(X32)
| X32 = sz00
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X33)
| X33 = X34
| sdtasdt0(X33,X32) != sdtasdt0(X34,X32) )
& ( ~ aNaturalNumber0(X32)
| X32 = sz00
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X33)
| X33 = X34
| sdtasdt0(X32,X33) != sdtasdt0(X32,X34) ) ),
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_7])])])])]) ).
fof(c_0_10,hypothesis,
( doDivides0(xl,xm)
& xm = sdtasdt0(xl,esk1_0)
& aNaturalNumber0(esk1_0)
& xl != sz00 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_8])])]) ).
fof(c_0_11,negated_conjecture,
~ ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))
& aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl)) )
=> sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_12,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| X1 = sz00
| X2 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,hypothesis,
xm = sdtasdt0(xl,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1524]) ).
cnf(c_0_16,hypothesis,
xl != sz00,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_17,negated_conjecture,
( sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))
& sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))
& aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
cnf(c_0_18,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xl,X1) != xm
| X1 = esk1_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_19,negated_conjecture,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,negated_conjecture,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_21,plain,
! [X25,X26,X27] :
( sdtasdt0(sdtasdt0(X25,X26),X27) = sdtasdt0(X25,sdtasdt0(X26,X27))
| ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X26)
| ~ aNaturalNumber0(X25) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
cnf(c_0_22,negated_conjecture,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
sdtsldt0(xm,xl) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_24,negated_conjecture,
sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_26,plain,
! [X23,X24] :
( sdtasdt0(X23,X24) = sdtasdt0(X24,X23)
| ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_27,negated_conjecture,
sdtasdt0(sdtasdt0(xl,xn),esk1_0) != sdtasdt0(xn,xm),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_28,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1553]) ).
cnf(c_0_29,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xl,sdtasdt0(esk1_0,X1)) = sdtasdt0(xm,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_30,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
sdtasdt0(xl,sdtasdt0(xn,esk1_0)) != sdtasdt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_14]),c_0_28]),c_0_15])]) ).
cnf(c_0_32,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtasdt0(xl,sdtasdt0(X1,esk1_0)) = sdtasdt0(xm,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_14])]) ).
cnf(c_0_33,hypothesis,
sdtasdt0(xn,xm) != sdtasdt0(xm,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_28])]) ).
cnf(c_0_34,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1524]) ).
cnf(c_0_35,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_30]),c_0_34]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM479+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:33:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.46 % Version: 3.5.1
% 0.09/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.46 % Starting sh5l with 300s (1) cores
% 0.09/0.46 % new_bool_3 with pid 656605 completed with status 0
% 0.09/0.46 % Result found by new_bool_3
% 0.09/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.46 % Search class: FGUSF-FFMM22-MFFFFFNN
% 0.09/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.46 % SubtermCWHack with pid 656613 completed with status 0
% 0.09/0.46 % Result found by SubtermCWHack
% 0.09/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.46 % Search class: FGUSF-FFMM22-MFFFFFNN
% 0.09/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.46 % Preprocessing time : 0.002 s
% 0.09/0.46
% 0.09/0.46 % Proof found!
% 0.09/0.46 % SZS status Theorem
% 0.09/0.46 % SZS output start CNFRefutation
% See solution above
% 0.09/0.46 % Parsed axioms : 39
% 0.09/0.46 % Removed by relevancy pruning/SinE : 6
% 0.09/0.46 % Initial clauses : 60
% 0.09/0.46 % Removed in clause preprocessing : 1
% 0.09/0.46 % Initial clauses in saturation : 59
% 0.09/0.46 % Processed clauses : 411
% 0.09/0.46 % ...of these trivial : 19
% 0.09/0.46 % ...subsumed : 175
% 0.09/0.46 % ...remaining for further processing : 217
% 0.09/0.46 % Other redundant clauses eliminated : 19
% 0.09/0.46 % Clauses deleted for lack of memory : 0
% 0.09/0.46 % Backward-subsumed : 5
% 0.09/0.46 % Backward-rewritten : 16
% 0.09/0.46 % Generated clauses : 1293
% 0.09/0.46 % ...of the previous two non-redundant : 1070
% 0.09/0.46 % ...aggressively subsumed : 0
% 0.09/0.46 % Contextual simplify-reflections : 1
% 0.09/0.46 % Paramodulations : 1270
% 0.09/0.46 % Factorizations : 0
% 0.09/0.46 % NegExts : 0
% 0.09/0.46 % Equation resolutions : 23
% 0.09/0.46 % Disequality decompositions : 0
% 0.09/0.46 % Total rewrite steps : 1337
% 0.09/0.46 % ...of those cached : 1302
% 0.09/0.46 % Propositional unsat checks : 0
% 0.09/0.46 % Propositional check models : 0
% 0.09/0.46 % Propositional check unsatisfiable : 0
% 0.09/0.46 % Propositional clauses : 0
% 0.09/0.46 % Propositional clauses after purity: 0
% 0.09/0.46 % Propositional unsat core size : 0
% 0.09/0.46 % Propositional preprocessing time : 0.000
% 0.09/0.46 % Propositional encoding time : 0.000
% 0.09/0.46 % Propositional solver time : 0.000
% 0.09/0.46 % Success case prop preproc time : 0.000
% 0.09/0.46 % Success case prop encoding time : 0.000
% 0.09/0.46 % Success case prop solver time : 0.000
% 0.09/0.46 % Current number of processed clauses : 190
% 0.09/0.46 % Positive orientable unit clauses : 35
% 0.09/0.46 % Positive unorientable unit clauses: 0
% 0.09/0.46 % Negative unit clauses : 4
% 0.09/0.46 % Non-unit-clauses : 151
% 0.09/0.46 % Current number of unprocessed clauses: 700
% 0.09/0.46 % ...number of literals in the above : 3076
% 0.09/0.46 % Current number of archived formulas : 0
% 0.09/0.46 % Current number of archived clauses : 21
% 0.09/0.46 % Clause-clause subsumption calls (NU) : 2127
% 0.09/0.46 % Rec. Clause-clause subsumption calls : 1395
% 0.09/0.46 % Non-unit clause-clause subsumptions : 178
% 0.09/0.46 % Unit Clause-clause subsumption calls : 194
% 0.09/0.46 % Rewrite failures with RHS unbound : 0
% 0.09/0.46 % BW rewrite match attempts : 9
% 0.09/0.46 % BW rewrite match successes : 7
% 0.09/0.46 % Condensation attempts : 0
% 0.09/0.46 % Condensation successes : 0
% 0.09/0.46 % Termbank termtop insertions : 25509
% 0.09/0.46 % Search garbage collected termcells : 1036
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.031 s
% 0.09/0.46 % System time : 0.006 s
% 0.09/0.46 % Total time : 0.037 s
% 0.09/0.46 % Maximum resident set size: 3676 pages
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.033 s
% 0.09/0.46 % System time : 0.011 s
% 0.09/0.46 % Total time : 0.044 s
% 0.09/0.46 % Maximum resident set size: 4864 pages
% 0.09/0.46 % E exiting
%------------------------------------------------------------------------------