%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM474+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 : n006.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 01:55:09 PM UTC 2026
% Result : Theorem 2.17s 0.73s
% Output : CNFRefutation 2.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 13 unt; 0 def)
% Number of atoms : 44 ( 21 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 38 ( 15 ~; 10 |; 12 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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__1360,hypothesis,
( xp = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,xp)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1360) ).
fof(m__1379,hypothesis,
( xq = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
& aNaturalNumber0(xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1379) ).
fof(m__1324,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
fof(m__1422,hypothesis,
( xr = sdtmndt0(xq,xp)
& sdtpldt0(xp,xr) = xq
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1422) ).
fof(c_0_6,negated_conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_7,negated_conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,negated_conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(fof_nnf,[status(thm)],[c_0_7]) ).
fof(c_0_9,plain,
! [X26,X27,X28] :
( ( ~ aNaturalNumber0(X28)
| ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X26)
| sdtasdt0(sdtpldt0(X27,X28),X26) = sdtpldt0(sdtasdt0(X27,X26),sdtasdt0(X28,X26)) )
& ( ~ aNaturalNumber0(X28)
| ~ aNaturalNumber0(X27)
| ~ aNaturalNumber0(X26)
| sdtasdt0(X26,sdtpldt0(X27,X28)) = sdtpldt0(sdtasdt0(X26,X27),sdtasdt0(X26,X28)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])])]) ).
cnf(c_0_10,negated_conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,hypothesis,
xm = sdtasdt0(xl,xp),
inference(split_conjunct,[status(thm)],[m__1360]) ).
cnf(c_0_12,hypothesis,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(split_conjunct,[status(thm)],[m__1379]) ).
cnf(c_0_13,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_9]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1360]) ).
cnf(c_0_15,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__1324]) ).
cnf(c_0_16,negated_conjecture,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtasdt0(xl,xq),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]),c_0_12]) ).
cnf(c_0_17,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtpldt0(xm,sdtasdt0(xl,X1)) = sdtasdt0(xl,sdtpldt0(xp,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_11]),c_0_14]),c_0_15])]) ).
cnf(c_0_18,hypothesis,
sdtpldt0(xp,xr) = xq,
inference(split_conjunct,[status(thm)],[m__1422]) ).
cnf(c_0_19,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__1422]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM474+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:33:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.17/0.73 % Version: 3.5.1
% 2.17/0.73 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.17/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.17/0.73 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.17/0.73 % Starting new_bool_3 with 300s (1) cores
% 2.17/0.73 % Starting new_bool_1 with 300s (1) cores
% 2.17/0.73 % Starting sh5l with 300s (1) cores
% 2.17/0.73 % new_bool_3 with pid 1814522 completed with status 0
% 2.17/0.73 % Result found by new_bool_3
% 2.17/0.73 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.17/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.17/0.73 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.17/0.73 % Starting new_bool_3 with 300s (1) cores
% 2.17/0.73 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.17/0.73 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.17/0.73 % Search class: FGUSF-FFMM22-SFFFFFNN
% 2.17/0.73 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.17/0.73 % Starting SubtermCWHack with 31s (1) cores
% 2.17/0.73 % SubtermCWHack with pid 1814525 completed with status 0
% 2.17/0.73 % Result found by SubtermCWHack
% 2.17/0.73 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.17/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.17/0.73 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.17/0.73 % Starting new_bool_3 with 300s (1) cores
% 2.17/0.73 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.17/0.73 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.17/0.73 % Search class: FGUSF-FFMM22-SFFFFFNN
% 2.17/0.73 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.17/0.73 % Starting SubtermCWHack with 31s (1) cores
% 2.17/0.73 % Preprocessing time : 0.001 s
% 2.17/0.73
% 2.17/0.73 % Proof found!
% 2.17/0.73 % SZS status Theorem
% 2.17/0.73 % SZS output start CNFRefutation
% See solution above
% 2.17/0.73 % Parsed axioms : 41
% 2.17/0.73 % Removed by relevancy pruning/SinE : 5
% 2.17/0.73 % Initial clauses : 72
% 2.17/0.73 % Removed in clause preprocessing : 1
% 2.17/0.73 % Initial clauses in saturation : 71
% 2.17/0.73 % Processed clauses : 4312
% 2.17/0.73 % ...of these trivial : 184
% 2.17/0.73 % ...subsumed : 2717
% 2.17/0.73 % ...remaining for further processing : 1411
% 2.17/0.73 % Other redundant clauses eliminated : 153
% 2.17/0.73 % Clauses deleted for lack of memory : 0
% 2.17/0.73 % Backward-subsumed : 111
% 2.17/0.73 % Backward-rewritten : 241
% 2.17/0.73 % Generated clauses : 28627
% 2.17/0.73 % ...of the previous two non-redundant : 23546
% 2.17/0.73 % ...aggressively subsumed : 0
% 2.17/0.73 % Contextual simplify-reflections : 118
% 2.17/0.73 % Paramodulations : 28467
% 2.17/0.73 % Factorizations : 0
% 2.17/0.73 % NegExts : 0
% 2.17/0.73 % Equation resolutions : 160
% 2.17/0.73 % Disequality decompositions : 0
% 2.17/0.73 % Total rewrite steps : 34097
% 2.17/0.73 % ...of those cached : 33895
% 2.17/0.73 % Propositional unsat checks : 0
% 2.17/0.73 % Propositional check models : 0
% 2.17/0.73 % Propositional check unsatisfiable : 0
% 2.17/0.73 % Propositional clauses : 0
% 2.17/0.73 % Propositional clauses after purity: 0
% 2.17/0.73 % Propositional unsat core size : 0
% 2.17/0.73 % Propositional preprocessing time : 0.000
% 2.17/0.73 % Propositional encoding time : 0.000
% 2.17/0.73 % Propositional solver time : 0.000
% 2.17/0.73 % Success case prop preproc time : 0.000
% 2.17/0.73 % Success case prop encoding time : 0.000
% 2.17/0.73 % Success case prop solver time : 0.000
% 2.17/0.73 % Current number of processed clauses : 1050
% 2.17/0.73 % Positive orientable unit clauses : 221
% 2.17/0.73 % Positive unorientable unit clauses: 0
% 2.17/0.73 % Negative unit clauses : 3
% 2.17/0.73 % Non-unit-clauses : 826
% 2.17/0.73 % Current number of unprocessed clauses: 18950
% 2.17/0.73 % ...number of literals in the above : 97657
% 2.17/0.73 % Current number of archived formulas : 0
% 2.17/0.73 % Current number of archived clauses : 352
% 2.17/0.73 % Clause-clause subsumption calls (NU) : 137013
% 2.17/0.73 % Rec. Clause-clause subsumption calls : 74151
% 2.17/0.73 % Non-unit clause-clause subsumptions : 2885
% 2.17/0.73 % Unit Clause-clause subsumption calls : 4509
% 2.17/0.73 % Rewrite failures with RHS unbound : 0
% 2.17/0.73 % BW rewrite match attempts : 461
% 2.17/0.73 % BW rewrite match successes : 66
% 2.17/0.73 % Condensation attempts : 0
% 2.17/0.73 % Condensation successes : 0
% 2.17/0.73 % Termbank termtop insertions : 482679
% 2.17/0.73 % Search garbage collected termcells : 1004
% 2.17/0.73
% 2.17/0.73 % -------------------------------------------------
% 2.17/0.73 % User time : 0.271 s
% 2.17/0.73 % System time : 0.015 s
% 2.17/0.73 % Total time : 0.286 s
% 2.17/0.73 % Maximum resident set size: 3676 pages
% 2.17/0.73
% 2.17/0.73 % -------------------------------------------------
% 2.17/0.73 % User time : 0.273 s
% 2.17/0.73 % System time : 0.017 s
% 2.17/0.73 % Total time : 0.290 s
% 2.17/0.73 % Maximum resident set size: 4864 pages
% 2.17/0.73 % E exiting
%------------------------------------------------------------------------------