%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM574+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 : n008.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 01:49:37 PM UTC 2026
% Result : Theorem 0.15s 10.49s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 13 unt; 0 def)
% Number of atoms : 123 ( 22 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 131 ( 50 ~; 47 |; 21 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 17 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__3786_02,hypothesis,
( ( ? [X1] :
( szszuzczcdt0(X1) = xi
& aElementOf0(X1,szNzAzT0) )
& sdtlseqdt0(xj,xi) )
=> ( sdtlseqdt0(xj,xi)
=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3786_02) ).
fof(m__,conjecture,
( sdtlseqdt0(xj,xi)
=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mNatExtra,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ? [X2] :
( X1 = szszuzczcdt0(X2)
& aElementOf0(X2,szNzAzT0) )
| X1 = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtra) ).
fof(mNoScLessZr,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ~ sdtlseqdt0(szszuzczcdt0(X1),sz00) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNoScLessZr) ).
fof(m__3786,hypothesis,
( aElementOf0(xi,szNzAzT0)
& aElementOf0(xj,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3786) ).
fof(m__3623,hypothesis,
( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(m__3435,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(c_0_10,hypothesis,
! [X187] :
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ~ sdtlseqdt0(xj,xi)
| szszuzczcdt0(X187) != xi
| ~ aElementOf0(X187,szNzAzT0)
| ~ sdtlseqdt0(xj,xi) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3786_02])])])]) ).
fof(c_0_11,negated_conjecture,
~ ( sdtlseqdt0(xj,xi)
=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_12,hypothesis,
( ~ sdtlseqdt0(xj,xi)
| szszuzczcdt0(X1) != xi
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(xj,xi)
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,negated_conjecture,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
& sdtlseqdt0(xj,xi) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
cnf(c_0_14,hypothesis,
( ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(X1,szNzAzT0)
| szszuzczcdt0(X1) != xi
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
inference(cn,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
sdtlseqdt0(xj,xi),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X61] :
( ( ~ aElementOf0(X61,szNzAzT0)
| X61 = sz00
| X61 = szszuzczcdt0(esk5_1(X61)) )
& ( ~ aElementOf0(X61,szNzAzT0)
| X61 = sz00
| aElementOf0(esk5_1(X61),szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNatExtra])])])])]) ).
fof(c_0_18,plain,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ~ sdtlseqdt0(szszuzczcdt0(X1),sz00) ),
inference(fof_simplification,[status(thm)],[mNoScLessZr]) ).
cnf(c_0_19,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| szszuzczcdt0(X1) != xi ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]),c_0_16]) ).
cnf(c_0_20,plain,
( ~ aElementOf0(X1,szNzAzT0)
| X1 = sz00
| X1 = szszuzczcdt0(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3786]) ).
fof(c_0_22,plain,
! [X67] :
( ~ sdtlseqdt0(szszuzczcdt0(X67),sz00)
| ~ aElementOf0(X67,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_23,hypothesis,
( ~ aElementOf0(esk5_1(xi),szNzAzT0)
| xi = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20])]),c_0_21])]) ).
cnf(c_0_24,plain,
( ~ aElementOf0(X1,szNzAzT0)
| X1 = sz00
| aElementOf0(esk5_1(X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( ~ sdtlseqdt0(szszuzczcdt0(X1),sz00)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,hypothesis,
xi = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21])]) ).
cnf(c_0_27,plain,
( ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X1,sz00)
| X1 = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_20]),c_0_24]) ).
cnf(c_0_28,negated_conjecture,
sdtlseqdt0(xj,sz00),
inference(rw,[status(thm)],[c_0_15,c_0_26]) ).
cnf(c_0_29,hypothesis,
aElementOf0(xj,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3786]) ).
fof(c_0_30,hypothesis,
! [X183] :
( ( ~ aElementOf0(X183,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X183))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X183),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X183))) )
& ( ~ aElementOf0(X183,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X183))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X183),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X183)),sdtmndt0(sdtlpdtrp0(xN,X183),szmzizndt0(sdtlpdtrp0(xN,X183)))) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3623])])])])]) ).
fof(c_0_31,plain,
! [X19,X20,X21,X22] :
( ( ~ aSet0(X19)
| aSubsetOf0(X22,X19)
| ~ aSet0(X22)
| ~ aElementOf0(esk2_2(X19,X22),X19) )
& ( ~ aSet0(X19)
| aSubsetOf0(X22,X19)
| ~ aSet0(X22)
| aElementOf0(esk2_2(X19,X22),X22) )
& ( ~ aSet0(X19)
| ~ aSubsetOf0(X20,X19)
| aElementOf0(X21,X19)
| ~ aElementOf0(X21,X20) )
& ( ~ aSet0(X19)
| ~ aSubsetOf0(X20,X19)
| aSet0(X20) ) ),
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)],[mDefSub])])])])])])]) ).
cnf(c_0_32,negated_conjecture,
xj = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_33,hypothesis,
sdtlpdtrp0(xN,sz00) = xS,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_34,plain,
! [X26] :
( aSubsetOf0(X26,X26)
| ~ aSet0(X26) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])])]) ).
cnf(c_0_35,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_37,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_38,negated_conjecture,
~ aSubsetOf0(xS,xS),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_32]),c_0_26]),c_0_33]),c_0_33]) ).
cnf(c_0_39,plain,
( ~ aSet0(X1)
| aSubsetOf0(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM574+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/10.38 % Computer : n008.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Mon Sep 21 02:42:10 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/10.42 Running first-order theorem proving
% 0.15/10.42 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
% 0.15/10.49 % Version: 3.5.1
% 0.15/10.49 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/10.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/10.49 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/10.49 % Starting new_bool_3 with 300s (1) cores
% 0.15/10.49 % Starting new_bool_1 with 300s (1) cores
% 0.15/10.49 % Starting sh5l with 300s (1) cores
% 0.15/10.49 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 4168459 completed with status 0
% 0.15/10.49 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.15/10.49 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/10.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/10.49 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/10.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/10.49 % No SInE strategy applied
% 0.15/10.49 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.15/10.49 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/10.49 % Starting SubtermCWHack with 151s (1) cores
% 0.15/10.49 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 901s (1) cores
% 0.15/10.49 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.15/10.49 % Starting G-E--_302_C18_F1_URBAN_S0Y with 151s (1) cores
% 0.15/10.49 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0U with 146s (1) cores
% 0.15/10.49 % G-E--_300_C18_F1_SE_CS_SP_S0Y with pid 4168475 completed with status 0
% 0.15/10.49 % Result found by G-E--_300_C18_F1_SE_CS_SP_S0Y
% 0.15/10.49 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/10.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/10.49 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/10.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/10.49 % No SInE strategy applied
% 0.15/10.49 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.15/10.49 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/10.49 % Starting SubtermCWHack with 151s (1) cores
% 0.15/10.49 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 901s (1) cores
% 0.15/10.49 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.15/10.49 % Preprocessing time : 0.004 s
% 0.15/10.49
% 0.15/10.49 % Proof found!
% 0.15/10.49 % SZS status Theorem
% 0.15/10.49 % SZS output start CNFRefutation
% See solution above
% 0.15/10.49 % Parsed axioms : 86
% 0.15/10.49 % Removed by relevancy pruning/SinE : 0
% 0.15/10.49 % Initial clauses : 173
% 0.15/10.49 % Removed in clause preprocessing : 7
% 0.15/10.49 % Initial clauses in saturation : 166
% 0.15/10.49 % Processed clauses : 124
% 0.15/10.49 % ...of these trivial : 0
% 0.15/10.49 % ...subsumed : 10
% 0.15/10.49 % ...remaining for further processing : 114
% 0.15/10.49 % Other redundant clauses eliminated : 11
% 0.15/10.49 % Clauses deleted for lack of memory : 0
% 0.15/10.49 % Backward-subsumed : 2
% 0.15/10.49 % Backward-rewritten : 10
% 0.15/10.49 % Generated clauses : 101
% 0.15/10.49 % ...of the previous two non-redundant : 76
% 0.15/10.49 % ...aggressively subsumed : 0
% 0.15/10.49 % Contextual simplify-reflections : 5
% 0.15/10.49 % Paramodulations : 91
% 0.15/10.49 % Factorizations : 0
% 0.15/10.49 % NegExts : 0
% 0.15/10.49 % Equation resolutions : 11
% 0.15/10.49 % Disequality decompositions : 0
% 0.15/10.49 % Total rewrite steps : 103
% 0.15/10.49 % ...of those cached : 79
% 0.15/10.49 % Propositional unsat checks : 0
% 0.15/10.49 % Propositional check models : 0
% 0.15/10.49 % Propositional check unsatisfiable : 0
% 0.15/10.49 % Propositional clauses : 0
% 0.15/10.49 % Propositional clauses after purity: 0
% 0.15/10.49 % Propositional unsat core size : 0
% 0.15/10.49 % Propositional preprocessing time : 0.000
% 0.15/10.49 % Propositional encoding time : 0.000
% 0.15/10.49 % Propositional solver time : 0.000
% 0.15/10.49 % Success case prop preproc time : 0.000
% 0.15/10.49 % Success case prop encoding time : 0.000
% 0.15/10.49 % Success case prop solver time : 0.000
% 0.15/10.49 % Current number of processed clauses : 94
% 0.15/10.49 % Positive orientable unit clauses : 31
% 0.15/10.49 % Positive unorientable unit clauses: 0
% 0.15/10.49 % Negative unit clauses : 11
% 0.15/10.49 % Non-unit-clauses : 52
% 0.15/10.49 % Current number of unprocessed clauses: 118
% 0.15/10.49 % ...number of literals in the above : 591
% 0.15/10.49 % Current number of archived formulas : 0
% 0.15/10.49 % Current number of archived clauses : 12
% 0.15/10.49 % Clause-clause subsumption calls (NU) : 373
% 0.15/10.49 % Rec. Clause-clause subsumption calls : 289
% 0.15/10.49 % Non-unit clause-clause subsumptions : 10
% 0.15/10.49 % Unit Clause-clause subsumption calls : 237
% 0.15/10.49 % Rewrite failures with RHS unbound : 0
% 0.15/10.49 % BW rewrite match attempts : 3
% 0.15/10.49 % BW rewrite match successes : 3
% 0.15/10.49 % Condensation attempts : 0
% 0.15/10.49 % Condensation successes : 0
% 0.15/10.49 % Termbank termtop insertions : 15623
% 0.15/10.49 % Search garbage collected termcells : 3478
% 0.15/10.49
% 0.15/10.49 % -------------------------------------------------
% 0.15/10.49 % User time : 0.024 s
% 0.15/10.49 % System time : 0.008 s
% 0.15/10.49 % Total time : 0.032 s
% 0.15/10.49 % Maximum resident set size: 4000 pages
% 0.15/10.49
% 0.15/10.49 % -------------------------------------------------
% 0.15/10.49 % User time : 0.103 s
% 0.15/10.49 % System time : 0.035 s
% 0.15/10.49 % Total time : 0.138 s
% 0.15/10.49 % Maximum resident set size: 4608 pages
% 0.15/10.49 % E exiting
%------------------------------------------------------------------------------