%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM467+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 : n007.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 01:49:11 PM UTC 2026
% Result : Theorem 3.15s 0.81s
% Output : CNFRefutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 96 ( 20 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 107 ( 40 ~; 37 |; 25 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 20 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__1240,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240) ).
fof(m__,conjecture,
( doDivides0(xl,sdtpldt0(xm,xn))
| ? [X1] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(c_0_7,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])])])]) ).
fof(c_0_8,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_9,plain,
! [X63,X64,X66] :
( ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| doDivides0(X63,X64)
| X64 != sdtasdt0(X63,X66)
| ~ aNaturalNumber0(X66) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| X64 = sdtasdt0(X63,esk2_2(X63,X64)) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| aNaturalNumber0(esk2_2(X63,X64)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])])]) ).
fof(c_0_10,plain,
! [X7,X8] :
( aNaturalNumber0(sdtasdt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
cnf(c_0_11,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_7]) ).
cnf(c_0_12,hypothesis,
xn = sdtasdt0(xl,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,hypothesis,
aNaturalNumber0(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1240]) ).
fof(c_0_15,negated_conjecture,
~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ? [X1] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_16,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,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_11,c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_19,hypothesis,
xm = sdtasdt0(xl,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,hypothesis,
aNaturalNumber0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_21,negated_conjecture,
! [X75] :
( ~ doDivides0(xl,sdtpldt0(xm,xn))
& ( sdtpldt0(xm,xn) != sdtasdt0(xl,X75)
| ~ aNaturalNumber0(X75) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
cnf(c_0_22,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_17]) ).
cnf(c_0_23,hypothesis,
sdtasdt0(xl,sdtpldt0(esk3_0,esk4_0)) = sdtpldt0(xm,xn),
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,
~ doDivides0(xl,sdtpldt0(xm,xn)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_25,plain,
! [X5,X6] :
( aNaturalNumber0(sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
cnf(c_0_26,hypothesis,
~ aNaturalNumber0(sdtpldt0(esk3_0,esk4_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14])]),c_0_24]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_13]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM467+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n007.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 02:30:35 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 3.15/0.81 % Version: 3.5.1
% 3.15/0.81 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.15/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.15/0.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.15/0.81 % Starting new_bool_3 with 300s (1) cores
% 3.15/0.81 % Starting new_bool_1 with 300s (1) cores
% 3.15/0.81 % Starting sh5l with 300s (1) cores
% 3.15/0.81 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 4171926 completed with status 0
% 3.15/0.81 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 3.15/0.81 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.15/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.15/0.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.15/0.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.15/0.81 % No SInE strategy applied
% 3.15/0.81 % Search class: FGHSF-FFMM22-SFFFFFNN
% 3.15/0.81 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.15/0.81 % Starting SubtermCWHack with 136s (1) cores
% 3.15/0.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.15/0.81 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 3.15/0.81 % Starting new_bool_3 with 136s (1) cores
% 3.15/0.81 % Starting new_bool_1 with 136s (1) cores
% 3.15/0.81 % new_bool_1 with pid 4171934 completed with status 0
% 3.15/0.81 % Result found by new_bool_1
% 3.15/0.81 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.15/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.15/0.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.15/0.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.15/0.81 % No SInE strategy applied
% 3.15/0.81 % Search class: FGHSF-FFMM22-SFFFFFNN
% 3.15/0.81 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.15/0.81 % Starting SubtermCWHack with 136s (1) cores
% 3.15/0.81 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.15/0.81 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 3.15/0.81 % Starting new_bool_3 with 136s (1) cores
% 3.15/0.81 % Starting new_bool_1 with 136s (1) cores
% 3.15/0.81 % Preprocessing time : 0.001 s
% 3.15/0.81 % Presaturation interreduction done
% 3.15/0.81
% 3.15/0.81 % Proof found!
% 3.15/0.81 % SZS status Theorem
% 3.15/0.81 % SZS output start CNFRefutation
% See solution above
% 3.15/0.81 % Parsed axioms : 35
% 3.15/0.81 % Removed by relevancy pruning/SinE : 0
% 3.15/0.81 % Initial clauses : 67
% 3.15/0.81 % Removed in clause preprocessing : 3
% 3.15/0.81 % Initial clauses in saturation : 64
% 3.15/0.81 % Processed clauses : 4738
% 3.15/0.81 % ...of these trivial : 179
% 3.15/0.81 % ...subsumed : 3144
% 3.15/0.81 % ...remaining for further processing : 1415
% 3.15/0.81 % Other redundant clauses eliminated : 106
% 3.15/0.81 % Clauses deleted for lack of memory : 0
% 3.15/0.81 % Backward-subsumed : 83
% 3.15/0.81 % Backward-rewritten : 160
% 3.15/0.81 % Generated clauses : 36152
% 3.15/0.81 % ...of the previous two non-redundant : 32764
% 3.15/0.81 % ...aggressively subsumed : 0
% 3.15/0.81 % Contextual simplify-reflections : 189
% 3.15/0.81 % Paramodulations : 36038
% 3.15/0.81 % Factorizations : 2
% 3.15/0.81 % NegExts : 0
% 3.15/0.81 % Equation resolutions : 112
% 3.15/0.81 % Disequality decompositions : 0
% 3.15/0.81 % Total rewrite steps : 42156
% 3.15/0.81 % ...of those cached : 41840
% 3.15/0.81 % Propositional unsat checks : 0
% 3.15/0.81 % Propositional check models : 0
% 3.15/0.81 % Propositional check unsatisfiable : 0
% 3.15/0.81 % Propositional clauses : 0
% 3.15/0.81 % Propositional clauses after purity: 0
% 3.15/0.81 % Propositional unsat core size : 0
% 3.15/0.81 % Propositional preprocessing time : 0.000
% 3.15/0.81 % Propositional encoding time : 0.000
% 3.15/0.81 % Propositional solver time : 0.000
% 3.15/0.81 % Success case prop preproc time : 0.000
% 3.15/0.81 % Success case prop encoding time : 0.000
% 3.15/0.81 % Success case prop solver time : 0.000
% 3.15/0.81 % Current number of processed clauses : 1104
% 3.15/0.81 % Positive orientable unit clauses : 314
% 3.15/0.81 % Positive unorientable unit clauses: 0
% 3.15/0.81 % Negative unit clauses : 47
% 3.15/0.81 % Non-unit-clauses : 743
% 3.15/0.81 % Current number of unprocessed clauses: 27896
% 3.15/0.81 % ...number of literals in the above : 123398
% 3.15/0.81 % Current number of archived formulas : 0
% 3.15/0.81 % Current number of archived clauses : 302
% 3.15/0.81 % Clause-clause subsumption calls (NU) : 75769
% 3.15/0.81 % Rec. Clause-clause subsumption calls : 33001
% 3.15/0.81 % Non-unit clause-clause subsumptions : 2101
% 3.15/0.81 % Unit Clause-clause subsumption calls : 4929
% 3.15/0.81 % Rewrite failures with RHS unbound : 0
% 3.15/0.81 % BW rewrite match attempts : 141
% 3.15/0.81 % BW rewrite match successes : 79
% 3.15/0.81 % Condensation attempts : 0
% 3.15/0.81 % Condensation successes : 0
% 3.15/0.81 % Termbank termtop insertions : 683435
% 3.15/0.81 % Search garbage collected termcells : 1029
% 3.15/0.81
% 3.15/0.81 % -------------------------------------------------
% 3.15/0.81 % User time : 0.362 s
% 3.15/0.81 % System time : 0.022 s
% 3.15/0.81 % Total time : 0.384 s
% 3.15/0.81 % Maximum resident set size: 3672 pages
% 3.15/0.81
% 3.15/0.81 % -------------------------------------------------
% 3.15/0.81 % User time : 1.842 s
% 3.15/0.81 % System time : 0.091 s
% 3.15/0.81 % Total time : 1.933 s
% 3.15/0.81 % Maximum resident set size: 4608 pages
% 3.15/0.81 % E exiting
%------------------------------------------------------------------------------