%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM465+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 : n005.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 0.69s 0.56s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 12 unt; 0 def)
% Number of atoms : 165 ( 61 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 189 ( 68 ~; 67 |; 41 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 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 : 37 ( 0 sgn 20 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( xm != sz00
=> ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ? [X1] :
( sdtpldt0(xn,X1) = sdtasdt0(xn,xm)
& aNaturalNumber0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& X2 != X3
& X1 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X1,X2) != sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__1007,hypothesis,
( xm != sz00
=> ( sdtlseqdt0(sz10,xm)
& ? [X1] :
( sdtpldt0(sz10,X1) = xm
& aNaturalNumber0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1007) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(m__987,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__987) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(c_0_9,negated_conjecture,
~ ( xm != sz00
=> ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ? [X1] :
( sdtpldt0(xn,X1) = sdtasdt0(xn,xm)
& aNaturalNumber0(X1) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_10,plain,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& X2 != X3
& X1 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X1,X2) != sdtasdt0(X1,X3) ) ) ),
inference(fof_simplification,[status(thm)],[mMonMul]) ).
fof(c_0_11,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_12,hypothesis,
( xm != sz00
=> ( sdtlseqdt0(sz10,xm)
& ? [X1] :
( sdtpldt0(sz10,X1) = xm
& aNaturalNumber0(X1) ) ) ),
inference(fof_simplification,[status(thm)],[m__1007]) ).
fof(c_0_13,negated_conjecture,
~ ( xm != sz00
=> ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ? [X1] :
( sdtpldt0(xn,X1) = sdtasdt0(xn,xm)
& aNaturalNumber0(X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X22,X23,X24] :
( ( ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X22)
| ~ sdtlseqdt0(X23,X24)
| X23 = X24
| X22 = sz00
| sdtlseqdt0(sdtasdt0(X23,X22),sdtasdt0(X24,X22)) )
& ( ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X22)
| ~ sdtlseqdt0(X23,X24)
| X23 = X24
| X22 = sz00
| sdtasdt0(X23,X22) != sdtasdt0(X24,X22) )
& ( ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X22)
| ~ sdtlseqdt0(X23,X24)
| X23 = X24
| X22 = sz00
| sdtlseqdt0(sdtasdt0(X22,X23),sdtasdt0(X22,X24)) )
& ( ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X23)
| ~ aNaturalNumber0(X22)
| ~ sdtlseqdt0(X23,X24)
| X23 = X24
| X22 = sz00
| 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)],[c_0_10])])])]) ).
fof(c_0_15,plain,
! [X25] :
( ( ~ aNaturalNumber0(X25)
| X25 = sdtasdt0(sz10,X25) )
& ( ~ aNaturalNumber0(X25)
| sdtasdt0(X25,sz10) = X25 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_16,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
fof(c_0_17,hypothesis,
( ( xm = sz00
| sdtlseqdt0(sz10,xm) )
& ( xm = sz00
| sdtpldt0(sz10,esk1_0) = xm )
& ( xm = sz00
| aNaturalNumber0(esk1_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
fof(c_0_18,negated_conjecture,
! [X5] :
( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& ( sdtpldt0(xn,X5) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X5) )
& xm != sz00 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_19,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mLETotal]) ).
cnf(c_0_20,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| X2 = X3
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,hypothesis,
( xm = sz00
| sdtlseqdt0(sz10,xm) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,plain,
! [X17,X18] :
( ( ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X17)
| sdtlseqdt0(X17,X18)
| sdtlseqdt0(X18,X17) )
& ( ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X17)
| sdtlseqdt0(X17,X18)
| X18 != X17 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
cnf(c_0_26,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(sz10,X1)
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| X2 = sz00
| sz10 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_28,hypothesis,
sdtlseqdt0(sz10,xm),
inference(sr,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__987]) ).
cnf(c_0_30,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__987]) ).
cnf(c_0_31,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_33,negated_conjecture,
( sz10 = xm
| xn = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29]),c_0_30])]) ).
fof(c_0_34,plain,
! [X43] :
( ( ~ aNaturalNumber0(X43)
| sz00 = sdtasdt0(sz00,X43) )
& ( ~ aNaturalNumber0(X43)
| sdtasdt0(X43,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
cnf(c_0_35,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sz00)
| sdtlseqdt0(sz00,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( ~ sdtlseqdt0(sz00,sdtasdt0(sz00,xm))
| sz10 = xm ),
inference(spm,[status(thm)],[c_0_26,c_0_33]) ).
cnf(c_0_37,plain,
( ~ aNaturalNumber0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,plain,
sdtlseqdt0(sz00,sz00),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_39,negated_conjecture,
sz10 = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_29])]) ).
cnf(c_0_40,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,xn)
| sdtlseqdt0(xn,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_41,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,xm) = X1 ),
inference(rw,[status(thm)],[c_0_21,c_0_39]) ).
cnf(c_0_42,hypothesis,
sdtlseqdt0(xn,xn),
inference(spm,[status(thm)],[c_0_40,c_0_30]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_41]),c_0_42]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM465+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 02:32:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.69/0.56 % Version: 3.5.1
% 0.69/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.69/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.69/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.69/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.69/0.56 % Starting sh5l with 300s (1) cores
% 0.69/0.56 % new_bool_3 with pid 2359814 completed with status 0
% 0.69/0.56 % Result found by new_bool_3
% 0.69/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.69/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.69/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.69/0.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.69/0.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.69/0.56 % Search class: FGHSF-FFMM22-SFFFFFNN
% 0.69/0.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.69/0.56 % Starting SubtermCWHack with 31s (1) cores
% 0.69/0.56 % SubtermCWHack with pid 2359819 completed with status 0
% 0.69/0.56 % Result found by SubtermCWHack
% 0.69/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.69/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.69/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.69/0.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.69/0.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.69/0.56 % Search class: FGHSF-FFMM22-SFFFFFNN
% 0.69/0.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.69/0.56 % Starting SubtermCWHack with 31s (1) cores
% 0.69/0.56 % Preprocessing time : 0.001 s
% 0.69/0.56
% 0.69/0.56 % Proof found!
% 0.69/0.56 % SZS status Theorem
% 0.69/0.56 % SZS output start CNFRefutation
% See solution above
% 0.69/0.56 % Parsed axioms : 29
% 0.69/0.56 % Removed by relevancy pruning/SinE : 1
% 0.69/0.56 % Initial clauses : 51
% 0.69/0.56 % Removed in clause preprocessing : 2
% 0.69/0.56 % Initial clauses in saturation : 49
% 0.69/0.56 % Processed clauses : 2436
% 0.69/0.56 % ...of these trivial : 66
% 0.69/0.56 % ...subsumed : 1715
% 0.69/0.56 % ...remaining for further processing : 655
% 0.69/0.56 % Other redundant clauses eliminated : 88
% 0.69/0.56 % Clauses deleted for lack of memory : 0
% 0.69/0.56 % Backward-subsumed : 52
% 0.69/0.56 % Backward-rewritten : 272
% 0.69/0.56 % Generated clauses : 12231
% 0.69/0.56 % ...of the previous two non-redundant : 10581
% 0.69/0.56 % ...aggressively subsumed : 0
% 0.69/0.56 % Contextual simplify-reflections : 71
% 0.69/0.56 % Paramodulations : 12134
% 0.69/0.56 % Factorizations : 0
% 0.69/0.56 % NegExts : 0
% 0.69/0.56 % Equation resolutions : 94
% 0.69/0.56 % Disequality decompositions : 0
% 0.69/0.56 % Total rewrite steps : 14432
% 0.69/0.56 % ...of those cached : 14348
% 0.69/0.56 % Propositional unsat checks : 0
% 0.69/0.56 % Propositional check models : 0
% 0.69/0.56 % Propositional check unsatisfiable : 0
% 0.69/0.56 % Propositional clauses : 0
% 0.69/0.56 % Propositional clauses after purity: 0
% 0.69/0.56 % Propositional unsat core size : 0
% 0.69/0.56 % Propositional preprocessing time : 0.000
% 0.69/0.56 % Propositional encoding time : 0.000
% 0.69/0.56 % Propositional solver time : 0.000
% 0.69/0.56 % Success case prop preproc time : 0.000
% 0.69/0.56 % Success case prop encoding time : 0.000
% 0.69/0.56 % Success case prop solver time : 0.000
% 0.69/0.56 % Current number of processed clauses : 326
% 0.69/0.56 % Positive orientable unit clauses : 52
% 0.69/0.56 % Positive unorientable unit clauses: 0
% 0.69/0.56 % Negative unit clauses : 31
% 0.69/0.56 % Non-unit-clauses : 243
% 0.69/0.56 % Current number of unprocessed clauses: 8006
% 0.69/0.56 % ...number of literals in the above : 41986
% 0.69/0.56 % Current number of archived formulas : 0
% 0.69/0.56 % Current number of archived clauses : 327
% 0.69/0.56 % Clause-clause subsumption calls (NU) : 23035
% 0.69/0.56 % Rec. Clause-clause subsumption calls : 12122
% 0.69/0.56 % Non-unit clause-clause subsumptions : 1186
% 0.69/0.56 % Unit Clause-clause subsumption calls : 1390
% 0.69/0.56 % Rewrite failures with RHS unbound : 0
% 0.69/0.56 % BW rewrite match attempts : 76
% 0.69/0.56 % BW rewrite match successes : 27
% 0.69/0.56 % Condensation attempts : 0
% 0.69/0.56 % Condensation successes : 0
% 0.69/0.56 % Termbank termtop insertions : 205538
% 0.69/0.56 % Search garbage collected termcells : 753
% 0.69/0.56
% 0.69/0.56 % -------------------------------------------------
% 0.69/0.56 % User time : 0.115 s
% 0.69/0.56 % System time : 0.007 s
% 0.69/0.56 % Total time : 0.122 s
% 0.69/0.56 % Maximum resident set size: 3664 pages
% 0.69/0.56
% 0.69/0.56 % -------------------------------------------------
% 0.69/0.56 % User time : 0.117 s
% 0.69/0.56 % System time : 0.011 s
% 0.69/0.56 % Total time : 0.128 s
% 0.69/0.56 % Maximum resident set size: 4864 pages
% 0.69/0.56 % E exiting
%------------------------------------------------------------------------------