%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM505+3 : 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 : n026.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 01:49:21 PM UTC 2026
% Result : Theorem 0.21s 5.53s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 8 unt; 0 def)
% Number of atoms : 81 ( 26 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 89 ( 32 ~; 28 |; 23 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 21 ( 0 sgn 10 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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__,conjecture,
( ~ ( sdtlseqdt0(xp,xk)
| ? [X1] :
( sdtpldt0(xp,X1) = xk
& aNaturalNumber0(X1) ) )
=> ( ( sdtlseqdt0(xk,xp)
| ? [X1] :
( sdtpldt0(xk,X1) = xp
& aNaturalNumber0(X1) ) )
& xk != xp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2306,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_6,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& X2 != X1 )
| sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mLETotal]) ).
fof(c_0_7,negated_conjecture,
~ ( ~ ( sdtlseqdt0(xp,xk)
| ? [X1] :
( sdtpldt0(xp,X1) = xk
& aNaturalNumber0(X1) ) )
=> ( ( sdtlseqdt0(xk,xp)
| ? [X1] :
( sdtpldt0(xk,X1) = xp
& aNaturalNumber0(X1) ) )
& xk != xp ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,plain,
! [X102,X103] :
( ( ~ aNaturalNumber0(X103)
| ~ aNaturalNumber0(X102)
| sdtlseqdt0(X102,X103)
| sdtlseqdt0(X103,X102) )
& ( ~ aNaturalNumber0(X103)
| ~ aNaturalNumber0(X102)
| sdtlseqdt0(X102,X103)
| X103 != X102 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_9,negated_conjecture,
~ ( ~ ( sdtlseqdt0(xp,xk)
| ? [X1] :
( sdtpldt0(xp,X1) = xk
& aNaturalNumber0(X1) ) )
=> ( ( sdtlseqdt0(xk,xp)
| ? [X1] :
( sdtpldt0(xk,X1) = xp
& aNaturalNumber0(X1) ) )
& xk != xp ) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,hypothesis,
aNaturalNumber0(xk),
inference(split_conjunct,[status(thm)],[m__2306]) ).
fof(c_0_12,negated_conjecture,
! [X26,X27] :
( ( xk = xp
| ~ sdtlseqdt0(xk,xp) )
& ( xk = xp
| sdtpldt0(xk,X27) != xp
| ~ aNaturalNumber0(X27) )
& ~ sdtlseqdt0(xp,xk)
& ( sdtpldt0(xp,X26) != xk
| ~ aNaturalNumber0(X26) ) ),
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_9])])])])]) ).
fof(c_0_13,plain,
! [X76] :
( ( ~ aNaturalNumber0(X76)
| X76 = sdtpldt0(sz00,X76) )
& ( ~ aNaturalNumber0(X76)
| sdtpldt0(X76,sz00) = X76 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).
cnf(c_0_14,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,xk)
| sdtlseqdt0(xk,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_16,negated_conjecture,
~ sdtlseqdt0(xp,xk),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( sdtpldt0(xp,X1) != xk
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_20,negated_conjecture,
( ~ sdtlseqdt0(xk,xp)
| xk = xp ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,hypothesis,
sdtlseqdt0(xk,xp),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_22,negated_conjecture,
xk != xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_15])]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM505+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.44 % Computer : n026.cluster.edu
% 0.15/5.44 % Model : x86_64 x86_64
% 0.15/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.44 % Memory : 8046.5625MB
% 0.15/5.44 % OS : Linux 6.8.0-71-generic
% 0.15/5.44 % CPULimit : 300
% 0.15/5.44 % WCLimit : 300
% 0.15/5.44 % DateTime : Mon Sep 21 02:38:42 UTC 2026
% 0.15/5.44 % CPUTime :
% 0.15/5.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.48 Running first-order theorem proving
% 0.15/5.48 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
% 0.21/5.53 % Version: 3.5.1
% 0.21/5.53 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/5.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/5.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/5.53 % Starting new_bool_3 with 300s (1) cores
% 0.21/5.53 % Starting new_bool_1 with 300s (1) cores
% 0.21/5.53 % Starting sh5l with 300s (1) cores
% 0.21/5.53 % new_bool_3 with pid 1185962 completed with status 0
% 0.21/5.53 % Result found by new_bool_3
% 0.21/5.53 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/5.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/5.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/5.53 % Starting new_bool_3 with 300s (1) cores
% 0.21/5.53 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/5.53 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/5.53 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.21/5.53 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/5.53 % Starting SubtermCWHack with 31s (1) cores
% 0.21/5.53 % SubtermCWHack with pid 1185965 completed with status 0
% 0.21/5.53 % Result found by SubtermCWHack
% 0.21/5.53 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/5.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/5.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/5.53 % Starting new_bool_3 with 300s (1) cores
% 0.21/5.53 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/5.53 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/5.53 % Search class: FGHSF-FSLM32-SFFFFFNN
% 0.21/5.53 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/5.53 % Starting SubtermCWHack with 31s (1) cores
% 0.21/5.53 % Preprocessing time : 0.004 s
% 0.21/5.53
% 0.21/5.53 % Proof found!
% 0.21/5.53 % SZS status Theorem
% 0.21/5.53 % SZS output start CNFRefutation
% See solution above
% 0.21/5.53 % Parsed axioms : 50
% 0.21/5.53 % Removed by relevancy pruning/SinE : 1
% 0.21/5.53 % Initial clauses : 241
% 0.21/5.53 % Removed in clause preprocessing : 3
% 0.21/5.53 % Initial clauses in saturation : 238
% 0.21/5.53 % Processed clauses : 193
% 0.21/5.53 % ...of these trivial : 2
% 0.21/5.53 % ...subsumed : 34
% 0.21/5.53 % ...remaining for further processing : 157
% 0.21/5.53 % Other redundant clauses eliminated : 3
% 0.21/5.53 % Clauses deleted for lack of memory : 0
% 0.21/5.53 % Backward-subsumed : 0
% 0.21/5.53 % Backward-rewritten : 3
% 0.21/5.53 % Generated clauses : 200
% 0.21/5.53 % ...of the previous two non-redundant : 186
% 0.21/5.53 % ...aggressively subsumed : 0
% 0.21/5.53 % Contextual simplify-reflections : 0
% 0.21/5.53 % Paramodulations : 197
% 0.21/5.53 % Factorizations : 0
% 0.21/5.53 % NegExts : 0
% 0.21/5.53 % Equation resolutions : 3
% 0.21/5.53 % Disequality decompositions : 0
% 0.21/5.53 % Total rewrite steps : 73
% 0.21/5.53 % ...of those cached : 55
% 0.21/5.53 % Propositional unsat checks : 0
% 0.21/5.53 % Propositional check models : 0
% 0.21/5.53 % Propositional check unsatisfiable : 0
% 0.21/5.53 % Propositional clauses : 0
% 0.21/5.53 % Propositional clauses after purity: 0
% 0.21/5.53 % Propositional unsat core size : 0
% 0.21/5.53 % Propositional preprocessing time : 0.000
% 0.21/5.53 % Propositional encoding time : 0.000
% 0.21/5.53 % Propositional solver time : 0.000
% 0.21/5.53 % Success case prop preproc time : 0.000
% 0.21/5.53 % Success case prop encoding time : 0.000
% 0.21/5.53 % Success case prop solver time : 0.000
% 0.21/5.53 % Current number of processed clauses : 151
% 0.21/5.53 % Positive orientable unit clauses : 38
% 0.21/5.53 % Positive unorientable unit clauses: 0
% 0.21/5.53 % Negative unit clauses : 15
% 0.21/5.53 % Non-unit-clauses : 98
% 0.21/5.53 % Current number of unprocessed clauses: 231
% 0.21/5.53 % ...number of literals in the above : 1738
% 0.21/5.53 % Current number of archived formulas : 0
% 0.21/5.53 % Current number of archived clauses : 3
% 0.21/5.53 % Clause-clause subsumption calls (NU) : 1807
% 0.21/5.53 % Rec. Clause-clause subsumption calls : 1701
% 0.21/5.53 % Non-unit clause-clause subsumptions : 22
% 0.21/5.53 % Unit Clause-clause subsumption calls : 352
% 0.21/5.53 % Rewrite failures with RHS unbound : 0
% 0.21/5.53 % BW rewrite match attempts : 2
% 0.21/5.53 % BW rewrite match successes : 2
% 0.21/5.53 % Condensation attempts : 0
% 0.21/5.53 % Condensation successes : 0
% 0.21/5.53 % Termbank termtop insertions : 18527
% 0.21/5.53 % Search garbage collected termcells : 2389
% 0.21/5.53
% 0.21/5.53 % -------------------------------------------------
% 0.21/5.53 % User time : 0.021 s
% 0.21/5.53 % System time : 0.006 s
% 0.21/5.53 % Total time : 0.027 s
% 0.21/5.53 % Maximum resident set size: 4216 pages
% 0.21/5.53
% 0.21/5.53 % -------------------------------------------------
% 0.21/5.53 % User time : 0.023 s
% 0.21/5.53 % System time : 0.011 s
% 0.21/5.53 % Total time : 0.034 s
% 0.21/5.53 % Maximum resident set size: 4608 pages
% 0.21/5.53 % E exiting
%------------------------------------------------------------------------------