%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG119+1 : 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 : n003.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 02:05:55 PM UTC 2026
% Result : Theorem 0.09s 1.03s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 18 unt; 0 def)
% Number of atoms : 142 ( 30 equ)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 164 ( 65 ~; 57 |; 29 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 31 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
xr != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2273,hypothesis,
( ! [X1] :
( ( X1 != sz00
& aElementOf0(X1,xI) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
fof(mDefIdeal,axiom,
! [X1] :
( aIdeal0(X1)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) )
& ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) ) ) )
& aSet0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(m__2666,hypothesis,
( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 )
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& aElement0(xr)
& aElement0(xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2666) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2174,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( sdtasdt0(X1,X3) = X2
& aElement0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(m__2612,hypothesis,
~ doDivides0(xu,xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2612) ).
fof(c_0_11,negated_conjecture,
~ ( xr != sz00 ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,negated_conjecture,
xr = sz00,
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_13,hypothesis,
( ! [X1] :
( ( X1 != sz00
& aElementOf0(X1,xI) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(fof_simplification,[status(thm)],[m__2273]) ).
fof(c_0_14,plain,
! [X50,X51,X52,X53,X54] :
( ( aIdeal0(X54)
| ~ aSet0(X54)
| ~ aElementOf0(sdtpldt0(esk13_1(X54),esk14_1(X54)),X54)
| ~ aElementOf0(sdtasdt0(esk15_1(X54),esk13_1(X54)),X54) )
& ( aIdeal0(X54)
| ~ aSet0(X54)
| ~ aElementOf0(sdtpldt0(esk13_1(X54),esk14_1(X54)),X54)
| aElement0(esk15_1(X54)) )
& ( aIdeal0(X54)
| ~ aSet0(X54)
| aElementOf0(esk14_1(X54),X54)
| ~ aElementOf0(sdtasdt0(esk15_1(X54),esk13_1(X54)),X54) )
& ( aIdeal0(X54)
| ~ aSet0(X54)
| aElementOf0(esk14_1(X54),X54)
| aElement0(esk15_1(X54)) )
& ( aIdeal0(X54)
| ~ aSet0(X54)
| aElementOf0(esk13_1(X54),X54) )
& ( ~ aIdeal0(X50)
| ~ aElementOf0(X51,X50)
| aElementOf0(sdtasdt0(X53,X51),X50)
| ~ aElement0(X53) )
& ( ~ aIdeal0(X50)
| ~ aElementOf0(X51,X50)
| aElementOf0(sdtpldt0(X51,X52),X50)
| ~ aElementOf0(X52,X50) )
& ( ~ aIdeal0(X50)
| aSet0(X50) ) ),
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)],[mDefIdeal])])])])])])]) ).
fof(c_0_15,plain,
! [X12] :
( ( ~ aElement0(X12)
| X12 = sdtpldt0(sz00,X12) )
& ( ~ aElement0(X12)
| sdtpldt0(X12,sz00) = X12 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])])]) ).
cnf(c_0_16,hypothesis,
xb = sdtpldt0(sdtasdt0(xq,xu),xr),
inference(split_conjunct,[status(thm)],[m__2666]) ).
cnf(c_0_17,negated_conjecture,
xr = sz00,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X89,X90] :
( aElement0(X90)
| ~ aElementOf0(X90,X89)
| ~ aSet0(X89) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
fof(c_0_19,hypothesis,
! [X8] :
( ( ~ iLess0(sbrdtbr0(X8),sbrdtbr0(xu))
| X8 = sz00
| ~ aElementOf0(X8,xI) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
cnf(c_0_20,plain,
( ~ aIdeal0(X1)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__2174]) ).
cnf(c_0_22,plain,
( ~ aElement0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,hypothesis,
sdtpldt0(sdtasdt0(xq,xu),sz00) = xb,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_24,plain,
! [X77,X78] :
( aElement0(sdtasdt0(X77,X78))
| ~ aElement0(X78)
| ~ aElement0(X77) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
cnf(c_0_25,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,hypothesis,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_28,plain,
! [X84,X85,X87] :
( ( ~ aElement0(X85)
| ~ aElement0(X84)
| doDivides0(X84,X85)
| sdtasdt0(X84,X87) != X85
| ~ aElement0(X87) )
& ( ~ aElement0(X85)
| ~ aElement0(X84)
| ~ doDivides0(X84,X85)
| sdtasdt0(X84,esk18_2(X84,X85)) = X85 )
& ( ~ aElement0(X85)
| ~ aElement0(X84)
| ~ doDivides0(X84,X85)
| aElement0(esk18_2(X84,X85)) ) ),
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])])])])])]) ).
cnf(c_0_29,hypothesis,
( ~ aElement0(sdtasdt0(xq,xu))
| sdtasdt0(xq,xu) = xb ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,hypothesis,
aElement0(xu),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_32,hypothesis,
aElement0(xq),
inference(split_conjunct,[status(thm)],[m__2666]) ).
fof(c_0_33,plain,
! [X79,X80] :
( sdtasdt0(X79,X80) = sdtasdt0(X80,X79)
| ~ aElement0(X80)
| ~ aElement0(X79) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
fof(c_0_34,hypothesis,
~ doDivides0(xu,xb),
inference(fof_simplification,[status(thm)],[m__2612]) ).
cnf(c_0_35,plain,
( ~ aElement0(X3)
| ~ aElement0(X2)
| sdtasdt0(X2,X1) != X3
| ~ aElement0(X1)
| doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,hypothesis,
sdtasdt0(xq,xu) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_37,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_38,hypothesis,
~ doDivides0(xu,xb),
inference(fof_nnf,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_35]),c_0_30]) ).
cnf(c_0_40,hypothesis,
sdtasdt0(xu,xq) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_32]),c_0_31])]) ).
cnf(c_0_41,hypothesis,
~ doDivides0(xu,xb),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_42,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_31]),c_0_32])]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG119+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.96 % Computer : n003.cluster.edu
% 0.09/0.96 % Model : x86_64 x86_64
% 0.09/0.96 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.96 % Memory : 8046.5625MB
% 0.09/0.96 % OS : Linux 6.8.0-71-generic
% 0.09/0.96 % CPULimit : 300
% 0.09/0.96 % WCLimit : 300
% 0.09/0.96 % DateTime : Mon Sep 21 04:23:17 UTC 2026
% 0.09/0.96 % CPUTime :
% 0.09/0.96 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/1.00 Running first-order theorem proving
% 0.09/1.00 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
% 0.09/1.03 % Version: 3.5.1
% 0.09/1.03 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.09/1.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/1.03 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.09/1.03 % Starting new_bool_3 with 300s (1) cores
% 0.09/1.03 % Starting new_bool_1 with 300s (1) cores
% 0.09/1.03 % Starting sh5l with 300s (1) cores
% 0.09/1.03 % new_bool_1 with pid 3395504 completed with status 0
% 0.09/1.03 % Result found by new_bool_1
% 0.09/1.03 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.09/1.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/1.03 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.09/1.03 % Starting new_bool_3 with 300s (1) cores
% 0.09/1.03 % Starting new_bool_1 with 300s (1) cores
% 0.09/1.03 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/1.03 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/1.03 % Search class: FGHSF-FFMM32-MFFFFFNN
% 0.09/1.03 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/1.03 % Starting SubtermCWHack with 31s (1) cores
% 0.09/1.03 % SubtermCWHack with pid 3395511 completed with status 0
% 0.09/1.03 % Result found by SubtermCWHack
% 0.09/1.03 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.09/1.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/1.03 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.09/1.03 % Starting new_bool_3 with 300s (1) cores
% 0.09/1.03 % Starting new_bool_1 with 300s (1) cores
% 0.09/1.03 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/1.03 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/1.03 % Search class: FGHSF-FFMM32-MFFFFFNN
% 0.09/1.03 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/1.03 % Starting SubtermCWHack with 31s (1) cores
% 0.09/1.03 % Preprocessing time : 0.001 s
% 0.09/1.03
% 0.09/1.03 % Proof found!
% 0.09/1.03 % SZS status Theorem
% 0.09/1.03 % SZS output start CNFRefutation
% See solution above
% 0.09/1.03 % Parsed axioms : 51
% 0.09/1.03 % Removed by relevancy pruning/SinE : 11
% 0.09/1.03 % Initial clauses : 92
% 0.09/1.03 % Removed in clause preprocessing : 4
% 0.09/1.03 % Initial clauses in saturation : 88
% 0.09/1.03 % Processed clauses : 134
% 0.09/1.03 % ...of these trivial : 7
% 0.09/1.03 % ...subsumed : 30
% 0.09/1.03 % ...remaining for further processing : 97
% 0.09/1.03 % Other redundant clauses eliminated : 6
% 0.09/1.03 % Clauses deleted for lack of memory : 0
% 0.09/1.03 % Backward-subsumed : 2
% 0.09/1.03 % Backward-rewritten : 5
% 0.09/1.03 % Generated clauses : 181
% 0.09/1.03 % ...of the previous two non-redundant : 116
% 0.09/1.03 % ...aggressively subsumed : 0
% 0.09/1.03 % Contextual simplify-reflections : 1
% 0.09/1.03 % Paramodulations : 176
% 0.09/1.03 % Factorizations : 0
% 0.09/1.03 % NegExts : 0
% 0.09/1.03 % Equation resolutions : 6
% 0.09/1.03 % Disequality decompositions : 0
% 0.09/1.03 % Total rewrite steps : 188
% 0.09/1.03 % ...of those cached : 168
% 0.09/1.03 % Propositional unsat checks : 0
% 0.09/1.03 % Propositional check models : 0
% 0.09/1.03 % Propositional check unsatisfiable : 0
% 0.09/1.03 % Propositional clauses : 0
% 0.09/1.03 % Propositional clauses after purity: 0
% 0.09/1.03 % Propositional unsat core size : 0
% 0.09/1.03 % Propositional preprocessing time : 0.000
% 0.09/1.03 % Propositional encoding time : 0.000
% 0.09/1.03 % Propositional solver time : 0.000
% 0.09/1.03 % Success case prop preproc time : 0.000
% 0.09/1.03 % Success case prop encoding time : 0.000
% 0.09/1.03 % Success case prop solver time : 0.000
% 0.09/1.03 % Current number of processed clauses : 86
% 0.09/1.03 % Positive orientable unit clauses : 34
% 0.09/1.03 % Positive unorientable unit clauses: 0
% 0.09/1.03 % Negative unit clauses : 4
% 0.09/1.03 % Non-unit-clauses : 48
% 0.09/1.03 % Current number of unprocessed clauses: 48
% 0.09/1.03 % ...number of literals in the above : 241
% 0.09/1.03 % Current number of archived formulas : 0
% 0.09/1.03 % Current number of archived clauses : 7
% 0.09/1.03 % Clause-clause subsumption calls (NU) : 739
% 0.09/1.03 % Rec. Clause-clause subsumption calls : 476
% 0.09/1.03 % Non-unit clause-clause subsumptions : 32
% 0.09/1.03 % Unit Clause-clause subsumption calls : 13
% 0.09/1.03 % Rewrite failures with RHS unbound : 0
% 0.09/1.03 % BW rewrite match attempts : 4
% 0.09/1.03 % BW rewrite match successes : 4
% 0.09/1.03 % Condensation attempts : 0
% 0.09/1.03 % Condensation successes : 0
% 0.09/1.03 % Termbank termtop insertions : 8456
% 0.09/1.03 % Search garbage collected termcells : 1552
% 0.09/1.03
% 0.09/1.03 % -------------------------------------------------
% 0.09/1.03 % User time : 0.007 s
% 0.09/1.03 % System time : 0.007 s
% 0.09/1.03 % Total time : 0.014 s
% 0.09/1.03 % Maximum resident set size: 3956 pages
% 0.09/1.03
% 0.09/1.03 % -------------------------------------------------
% 0.09/1.03 % User time : 0.009 s
% 0.09/1.03 % System time : 0.009 s
% 0.09/1.03 % Total time : 0.018 s
% 0.09/1.03 % Maximum resident set size: 4864 pages
% 0.09/1.03 % E exiting
%------------------------------------------------------------------------------