%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG099+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 : n016.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 02:05:50 PM UTC 2026
% Result : Theorem 0.09s 0.45s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 46 ( 20 unt; 0 def)
% Number of atoms : 133 ( 3 equ)
% Maximal formula atoms : 29 ( 2 avg)
% Number of connectives : 141 ( 54 ~; 55 |; 22 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__1205,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205) ).
fof(m__1319,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1319) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__1294,hypothesis,
( sdtpldt0(xa,xb) = sz10
& aElementOf0(xb,xJ)
& aElementOf0(xa,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1294) ).
fof(mDefMod,axiom,
! [X1,X2,X3] :
( ( aIdeal0(X3)
& aElement0(X2)
& aElement0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aElementOf0(sdtpldt0(X1,smndt0(X2)),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMod) ).
fof(m__1217,hypothesis,
( aElement0(xy)
& aElement0(xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1217) ).
fof(m__,conjecture,
? [X1] :
( sdteqdtlpzmzozddtrp0(X1,xy,xJ)
& sdteqdtlpzmzozddtrp0(X1,xx,xI)
& aElement0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1332,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1332) ).
fof(m__1409,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1409) ).
fof(c_0_12,plain,
! [X62,X63,X64,X65,X66] :
( ( aIdeal0(X66)
| ~ aSet0(X66)
| ~ aElementOf0(sdtpldt0(esk9_1(X66),esk10_1(X66)),X66)
| ~ aElementOf0(sdtasdt0(esk11_1(X66),esk9_1(X66)),X66) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| ~ aElementOf0(sdtpldt0(esk9_1(X66),esk10_1(X66)),X66)
| aElement0(esk11_1(X66)) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| aElementOf0(esk10_1(X66),X66)
| ~ aElementOf0(sdtasdt0(esk11_1(X66),esk9_1(X66)),X66) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| aElementOf0(esk10_1(X66),X66)
| aElement0(esk11_1(X66)) )
& ( aIdeal0(X66)
| ~ aSet0(X66)
| aElementOf0(esk9_1(X66),X66) )
& ( ~ aIdeal0(X62)
| ~ aElementOf0(X63,X62)
| aElementOf0(sdtasdt0(X65,X63),X62)
| ~ aElement0(X65) )
& ( ~ aIdeal0(X62)
| ~ aElementOf0(X63,X62)
| aElementOf0(sdtpldt0(X63,X64),X62)
| ~ aElementOf0(X64,X62) )
& ( ~ aIdeal0(X62)
| aSet0(X62) ) ),
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_13,plain,
! [X9,X10] :
( aElement0(sdtpldt0(X9,X10))
| ~ aElement0(X10)
| ~ aElement0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
fof(c_0_14,plain,
! [X34,X35] :
( aElement0(X35)
| ~ aElementOf0(X35,X34)
| ~ aSet0(X34) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
cnf(c_0_15,plain,
( ~ aIdeal0(X1)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__1205]) ).
cnf(c_0_17,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(split_conjunct,[status(thm)],[m__1319]) ).
fof(c_0_19,plain,
! [X11,X12] :
( aElement0(sdtasdt0(X11,X12))
| ~ aElement0(X12)
| ~ aElement0(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
cnf(c_0_20,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,hypothesis,
aElementOf0(xb,xJ),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_22,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__1205]) ).
fof(c_0_24,plain,
! [X74,X75,X76] :
( ( ~ aIdeal0(X76)
| ~ aElement0(X75)
| ~ aElement0(X74)
| sdteqdtlpzmzozddtrp0(X74,X75,X76)
| ~ aElementOf0(sdtpldt0(X74,smndt0(X75)),X76) )
& ( ~ aIdeal0(X76)
| ~ aElement0(X75)
| ~ aElement0(X74)
| aElementOf0(sdtpldt0(X74,smndt0(X75)),X76)
| ~ sdteqdtlpzmzozddtrp0(X74,X75,X76) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefMod])])])]) ).
cnf(c_0_25,hypothesis,
( ~ aElement0(sdtasdt0(xy,xa))
| ~ aElement0(sdtasdt0(xx,xb))
| aElement0(xw) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
( ~ aElement0(X2)
| ~ aElement0(X1)
| aElement0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,hypothesis,
aElement0(xb),
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,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__1217]) ).
cnf(c_0_29,hypothesis,
aElementOf0(xa,xI),
inference(split_conjunct,[status(thm)],[m__1294]) ).
cnf(c_0_30,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
fof(c_0_31,negated_conjecture,
~ ? [X1] :
( sdteqdtlpzmzozddtrp0(X1,xy,xJ)
& sdteqdtlpzmzozddtrp0(X1,xx,xI)
& aElement0(X1) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_32,plain,
( ~ aIdeal0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| sdteqdtlpzmzozddtrp0(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(split_conjunct,[status(thm)],[m__1332]) ).
cnf(c_0_34,hypothesis,
( ~ aElement0(sdtasdt0(xy,xa))
| aElement0(xw) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_35,hypothesis,
aElement0(xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_29]),c_0_30])]) ).
cnf(c_0_36,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__1217]) ).
fof(c_0_37,negated_conjecture,
! [X78] :
( ~ sdteqdtlpzmzozddtrp0(X78,xy,xJ)
| ~ sdteqdtlpzmzozddtrp0(X78,xx,xI)
| ~ aElement0(X78) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
cnf(c_0_38,hypothesis,
( ~ aElement0(xw)
| sdteqdtlpzmzozddtrp0(xw,xx,xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_23]),c_0_28])]) ).
cnf(c_0_39,hypothesis,
aElement0(xw),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_26]),c_0_35]),c_0_36])]) ).
cnf(c_0_40,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(split_conjunct,[status(thm)],[m__1409]) ).
cnf(c_0_41,negated_conjecture,
( ~ sdteqdtlpzmzozddtrp0(X1,xy,xJ)
| ~ sdteqdtlpzmzozddtrp0(X1,xx,xI)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,hypothesis,
sdteqdtlpzmzozddtrp0(xw,xx,xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_43,hypothesis,
( ~ aElement0(xw)
| sdteqdtlpzmzozddtrp0(xw,xy,xJ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_40]),c_0_16]),c_0_36])]) ).
cnf(c_0_44,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xw,xy,xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_39])]) ).
cnf(c_0_45,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_39])]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG099+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n016.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 04:24:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 0.09/0.45 % Version: 3.5.1
% 0.09/0.45 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.09/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.45 % Starting sh5l with 300s (1) cores
% 0.09/0.45 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1543796 completed with status 0
% 0.09/0.45 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.09/0.45 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.09/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.45 % No SInE strategy applied
% 0.09/0.45 % Search class: FGHSF-FFMM32-SFFFFFNN
% 0.09/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.09/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with 136s (1) cores
% 0.09/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 0.09/0.45 % Starting G-E--_107_C48_F1_PI_AE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.09/0.45 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with pid 1543805 completed with status 0
% 0.09/0.45 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI
% 0.09/0.45 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.09/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.09/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.45 % No SInE strategy applied
% 0.09/0.45 % Search class: FGHSF-FFMM32-SFFFFFNN
% 0.09/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.09/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with 136s (1) cores
% 0.09/0.45 % Preprocessing time : 0.001 s
% 0.09/0.45 % Presaturation interreduction done
% 0.09/0.45
% 0.09/0.45 % Proof found!
% 0.09/0.45 % SZS status Theorem
% 0.09/0.45 % SZS output start CNFRefutation
% See solution above
% 0.09/0.45 % Parsed axioms : 35
% 0.09/0.45 % Removed by relevancy pruning/SinE : 0
% 0.09/0.45 % Initial clauses : 70
% 0.09/0.45 % Removed in clause preprocessing : 2
% 0.09/0.45 % Initial clauses in saturation : 68
% 0.09/0.45 % Processed clauses : 201
% 0.09/0.45 % ...of these trivial : 5
% 0.09/0.45 % ...subsumed : 0
% 0.09/0.45 % ...remaining for further processing : 195
% 0.09/0.45 % Other redundant clauses eliminated : 10
% 0.09/0.45 % Clauses deleted for lack of memory : 0
% 0.09/0.45 % Backward-subsumed : 1
% 0.09/0.45 % Backward-rewritten : 3
% 0.09/0.45 % Generated clauses : 545
% 0.09/0.45 % ...of the previous two non-redundant : 501
% 0.09/0.45 % ...aggressively subsumed : 0
% 0.09/0.45 % Contextual simplify-reflections : 0
% 0.09/0.45 % Paramodulations : 536
% 0.09/0.45 % Factorizations : 0
% 0.09/0.45 % NegExts : 0
% 0.09/0.45 % Equation resolutions : 10
% 0.09/0.45 % Disequality decompositions : 0
% 0.09/0.45 % Total rewrite steps : 171
% 0.09/0.45 % ...of those cached : 154
% 0.09/0.45 % Propositional unsat checks : 0
% 0.09/0.45 % Propositional check models : 0
% 0.09/0.45 % Propositional check unsatisfiable : 0
% 0.09/0.45 % Propositional clauses : 0
% 0.09/0.45 % Propositional clauses after purity: 0
% 0.09/0.45 % Propositional unsat core size : 0
% 0.09/0.45 % Propositional preprocessing time : 0.000
% 0.09/0.45 % Propositional encoding time : 0.000
% 0.09/0.45 % Propositional solver time : 0.000
% 0.09/0.45 % Success case prop preproc time : 0.000
% 0.09/0.45 % Success case prop encoding time : 0.000
% 0.09/0.45 % Success case prop solver time : 0.000
% 0.09/0.45 % Current number of processed clauses : 114
% 0.09/0.45 % Positive orientable unit clauses : 55
% 0.09/0.45 % Positive unorientable unit clauses: 0
% 0.09/0.45 % Negative unit clauses : 2
% 0.09/0.45 % Non-unit-clauses : 57
% 0.09/0.45 % Current number of unprocessed clauses: 436
% 0.09/0.45 % ...number of literals in the above : 1347
% 0.09/0.45 % Current number of archived formulas : 0
% 0.09/0.45 % Current number of archived clauses : 72
% 0.09/0.45 % Clause-clause subsumption calls (NU) : 729
% 0.09/0.45 % Rec. Clause-clause subsumption calls : 296
% 0.09/0.45 % Non-unit clause-clause subsumptions : 1
% 0.09/0.45 % Unit Clause-clause subsumption calls : 340
% 0.09/0.45 % Rewrite failures with RHS unbound : 0
% 0.09/0.45 % BW rewrite match attempts : 2
% 0.09/0.45 % BW rewrite match successes : 1
% 0.09/0.45 % Condensation attempts : 0
% 0.09/0.45 % Condensation successes : 0
% 0.09/0.45 % Termbank termtop insertions : 13149
% 0.09/0.45 % Search garbage collected termcells : 1121
% 0.09/0.45
% 0.09/0.45 % -------------------------------------------------
% 0.09/0.45 % User time : 0.014 s
% 0.09/0.45 % System time : 0.004 s
% 0.09/0.45 % Total time : 0.018 s
% 0.09/0.45 % Maximum resident set size: 3672 pages
% 0.09/0.45
% 0.09/0.45 % -------------------------------------------------
% 0.09/0.45 % User time : 0.043 s
% 0.09/0.45 % System time : 0.015 s
% 0.09/0.45 % Total time : 0.058 s
% 0.09/0.45 % Maximum resident set size: 4608 pages
% 0.09/0.45 % E exiting
%------------------------------------------------------------------------------