%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG105+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 02:05:52 PM UTC 2026
% Result : Theorem 0.15s 0.46s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 12 unt; 0 def)
% Number of atoms : 137 ( 37 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 161 ( 61 ~; 60 |; 34 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 43 ( 0 sgn 24 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefPrIdeal,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( X2 = slsdtgt0(X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtasdt0(X1,X4) = X3
& aElement0(X4) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(m__,conjecture,
( ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ? [X1] :
( sdtasdt0(xc,X1) = sdtasdt0(xz,xx)
& aElement0(X1) ) )
& ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ? [X1] :
( sdtasdt0(xc,X1) = sdtpldt0(xx,xy)
& aElement0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__1933,hypothesis,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& ? [X1] :
( sdtasdt0(xc,X1) = xy
& aElement0(X1) )
& aElementOf0(xx,slsdtgt0(xc))
& ? [X1] :
( sdtasdt0(xc,X1) = xx
& aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1933) ).
fof(m__2010,hypothesis,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2010) ).
fof(m__1905,hypothesis,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1905) ).
fof(m__2043,hypothesis,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2043) ).
fof(m__1956,hypothesis,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1956) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(m__1979,hypothesis,
( sdtasdt0(xc,xv) = xy
& aElement0(xv) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1979) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(c_0_11,plain,
! [X18,X19,X20,X22,X23,X24,X26] :
( ( ~ aElement0(X18)
| X24 = slsdtgt0(X18)
| ~ aSet0(X24)
| aElementOf0(esk6_2(X18,X24),X24)
| sdtasdt0(X18,esk7_2(X18,X24)) = esk6_2(X18,X24) )
& ( ~ aElement0(X18)
| X24 = slsdtgt0(X18)
| ~ aSet0(X24)
| aElementOf0(esk6_2(X18,X24),X24)
| aElement0(esk7_2(X18,X24)) )
& ( ~ aElement0(X18)
| X24 = slsdtgt0(X18)
| ~ aSet0(X24)
| sdtasdt0(X18,X26) != esk6_2(X18,X24)
| ~ aElement0(X26)
| ~ aElementOf0(esk6_2(X18,X24),X24) )
& ( ~ aElement0(X18)
| X19 != slsdtgt0(X18)
| aElementOf0(X22,X19)
| sdtasdt0(X18,X23) != X22
| ~ aElement0(X23) )
& ( ~ aElement0(X18)
| X19 != slsdtgt0(X18)
| ~ aElementOf0(X20,X19)
| sdtasdt0(X18,esk5_3(X18,X19,X20)) = X20 )
& ( ~ aElement0(X18)
| X19 != slsdtgt0(X18)
| ~ aElementOf0(X20,X19)
| aElement0(esk5_3(X18,X19,X20)) )
& ( ~ aElement0(X18)
| X19 != slsdtgt0(X18)
| aSet0(X19) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrIdeal])])])])])])]) ).
fof(c_0_12,negated_conjecture,
~ ( ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ? [X1] :
( sdtasdt0(xc,X1) = sdtasdt0(xz,xx)
& aElement0(X1) ) )
& ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ? [X1] :
( sdtasdt0(xc,X1) = sdtpldt0(xx,xy)
& aElement0(X1) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_13,plain,
( ~ aElement0(X2)
| X4 != slsdtgt0(X2)
| sdtasdt0(X2,X1) != X3
| ~ aElement0(X1)
| aElementOf0(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X30,X31] :
( sdtasdt0(X30,X31) = sdtasdt0(X31,X30)
| ~ aElement0(X31)
| ~ aElement0(X30) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
fof(c_0_15,hypothesis,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& sdtasdt0(xc,esk2_0) = xy
& aElement0(esk2_0)
& aElementOf0(xx,slsdtgt0(xc))
& sdtasdt0(xc,esk1_0) = xx
& aElement0(esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1933])]) ).
fof(c_0_16,negated_conjecture,
! [X9,X10] :
( ( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) )
& ( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| sdtasdt0(xc,X10) != sdtasdt0(xz,xx)
| ~ aElement0(X10) )
& ( sdtasdt0(xc,X9) != sdtpldt0(xx,xy)
| ~ aElement0(X9)
| ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) )
& ( sdtasdt0(xc,X9) != sdtpldt0(xx,xy)
| ~ aElement0(X9)
| sdtasdt0(xc,X10) != sdtasdt0(xz,xx)
| ~ aElement0(X10) ) ),
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_12])])])])]) ).
cnf(c_0_17,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElementOf0(sdtasdt0(X1,X2),slsdtgt0(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_13])]) ).
cnf(c_0_18,hypothesis,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(split_conjunct,[status(thm)],[m__2010]) ).
cnf(c_0_19,hypothesis,
aElement0(xc),
inference(split_conjunct,[status(thm)],[m__1905]) ).
cnf(c_0_20,hypothesis,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(split_conjunct,[status(thm)],[m__2043]) ).
cnf(c_0_21,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,hypothesis,
aElement0(xu),
inference(split_conjunct,[status(thm)],[m__1956]) ).
cnf(c_0_23,hypothesis,
aElement0(xz),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,hypothesis,
( ~ aElement0(sdtpldt0(xu,xv))
| aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_26,hypothesis,
sdtasdt0(xc,sdtasdt0(xz,xu)) = sdtasdt0(xz,xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_27,hypothesis,
( ~ aElement0(sdtpldt0(xu,xv))
| ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,hypothesis,
( ~ aElement0(sdtasdt0(xz,xu))
| aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_26]),c_0_19])]) ).
fof(c_0_29,plain,
! [X38,X39] :
( aElement0(sdtpldt0(X38,X39))
| ~ aElement0(X39)
| ~ aElement0(X38) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
cnf(c_0_30,hypothesis,
( ~ aElement0(sdtasdt0(xz,xu))
| ~ aElement0(sdtpldt0(xu,xv)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,hypothesis,
aElement0(xv),
inference(split_conjunct,[status(thm)],[m__1979]) ).
fof(c_0_33,plain,
! [X28,X29] :
( aElement0(sdtasdt0(X28,X29))
| ~ aElement0(X29)
| ~ aElement0(X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
cnf(c_0_34,hypothesis,
~ aElement0(sdtasdt0(xz,xu)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_22])]) ).
cnf(c_0_35,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_22]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG105+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:23:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.15/0.46 % Version: 3.5.1
% 0.15/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.46 % Starting sh5l with 300s (1) cores
% 0.15/0.46 % new_bool_3 with pid 1355249 completed with status 0
% 0.15/0.46 % Result found by new_bool_3
% 0.15/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.46 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.15/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.46 % SubtermCWHack with pid 1355253 completed with status 0
% 0.15/0.46 % Result found by SubtermCWHack
% 0.15/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.46 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.15/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.46 % Preprocessing time : 0.002 s
% 0.15/0.46
% 0.15/0.46 % Proof found!
% 0.15/0.46 % SZS status Theorem
% 0.15/0.46 % SZS output start CNFRefutation
% See solution above
% 0.15/0.46 % Parsed axioms : 44
% 0.15/0.46 % Removed by relevancy pruning/SinE : 20
% 0.15/0.46 % Initial clauses : 54
% 0.15/0.46 % Removed in clause preprocessing : 2
% 0.15/0.46 % Initial clauses in saturation : 52
% 0.15/0.46 % Processed clauses : 101
% 0.15/0.46 % ...of these trivial : 2
% 0.15/0.46 % ...subsumed : 26
% 0.15/0.46 % ...remaining for further processing : 73
% 0.15/0.46 % Other redundant clauses eliminated : 3
% 0.15/0.46 % Clauses deleted for lack of memory : 0
% 0.15/0.46 % Backward-subsumed : 3
% 0.15/0.46 % Backward-rewritten : 5
% 0.15/0.46 % Generated clauses : 144
% 0.15/0.46 % ...of the previous two non-redundant : 106
% 0.15/0.46 % ...aggressively subsumed : 0
% 0.15/0.46 % Contextual simplify-reflections : 0
% 0.15/0.46 % Paramodulations : 142
% 0.15/0.46 % Factorizations : 0
% 0.15/0.46 % NegExts : 0
% 0.15/0.46 % Equation resolutions : 3
% 0.15/0.46 % Disequality decompositions : 0
% 0.15/0.46 % Total rewrite steps : 146
% 0.15/0.46 % ...of those cached : 130
% 0.15/0.46 % Propositional unsat checks : 0
% 0.15/0.46 % Propositional check models : 0
% 0.15/0.46 % Propositional check unsatisfiable : 0
% 0.15/0.46 % Propositional clauses : 0
% 0.15/0.46 % Propositional clauses after purity: 0
% 0.15/0.46 % Propositional unsat core size : 0
% 0.15/0.46 % Propositional preprocessing time : 0.000
% 0.15/0.46 % Propositional encoding time : 0.000
% 0.15/0.46 % Propositional solver time : 0.000
% 0.15/0.46 % Success case prop preproc time : 0.000
% 0.15/0.46 % Success case prop encoding time : 0.000
% 0.15/0.46 % Success case prop solver time : 0.000
% 0.15/0.46 % Current number of processed clauses : 63
% 0.15/0.46 % Positive orientable unit clauses : 26
% 0.15/0.46 % Positive unorientable unit clauses: 0
% 0.15/0.46 % Negative unit clauses : 1
% 0.15/0.46 % Non-unit-clauses : 36
% 0.15/0.46 % Current number of unprocessed clauses: 41
% 0.15/0.46 % ...number of literals in the above : 155
% 0.15/0.46 % Current number of archived formulas : 0
% 0.15/0.46 % Current number of archived clauses : 8
% 0.15/0.46 % Clause-clause subsumption calls (NU) : 122
% 0.15/0.46 % Rec. Clause-clause subsumption calls : 104
% 0.15/0.46 % Non-unit clause-clause subsumptions : 26
% 0.15/0.46 % Unit Clause-clause subsumption calls : 21
% 0.15/0.46 % Rewrite failures with RHS unbound : 0
% 0.15/0.46 % BW rewrite match attempts : 5
% 0.15/0.46 % BW rewrite match successes : 5
% 0.15/0.46 % Condensation attempts : 0
% 0.15/0.46 % Condensation successes : 0
% 0.15/0.46 % Termbank termtop insertions : 5460
% 0.15/0.46 % Search garbage collected termcells : 964
% 0.15/0.46
% 0.15/0.46 % -------------------------------------------------
% 0.15/0.46 % User time : 0.009 s
% 0.15/0.46 % System time : 0.004 s
% 0.15/0.46 % Total time : 0.014 s
% 0.15/0.46 % Maximum resident set size: 3692 pages
% 0.15/0.46
% 0.15/0.46 % -------------------------------------------------
% 0.15/0.46 % User time : 0.012 s
% 0.15/0.46 % System time : 0.007 s
% 0.15/0.46 % Total time : 0.019 s
% 0.15/0.46 % Maximum resident set size: 4864 pages
% 0.15/0.46 % E exiting
%------------------------------------------------------------------------------