%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM566+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 : n017.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 01:55:31 PM UTC 2026
% Result : Theorem 0.09s 0.46s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 16 unt; 0 def)
% Number of atoms : 118 ( 13 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 126 ( 53 ~; 48 |; 16 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 19 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( ? [X2] :
( ! [X3] :
( aElementOf0(X3,slbdtsldtrb0(X2,xK))
=> sdtlpdtrp0(xc,X3) = X1 )
& isCountable0(X2)
& aSubsetOf0(X2,xS) )
& aElementOf0(X1,xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__3507,hypothesis,
! [X1] :
( aElementOf0(X1,slbdtsldtrb0(xS,sz00))
=> sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3507) ).
fof(m__3453,hypothesis,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).
fof(m__3462,hypothesis,
xK = sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).
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(m__3435,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(m__3291,hypothesis,
( isFinite0(xT)
& aSet0(xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).
fof(mImgRng,axiom,
! [X1] :
( aFunction0(X1)
=> ! [X2] :
( aElementOf0(X2,szDzozmdt0(X1))
=> aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgRng) ).
fof(m__3476,hypothesis,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3476) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(c_0_11,negated_conjecture,
~ ? [X1] :
( ? [X2] :
( ! [X3] :
( aElementOf0(X3,slbdtsldtrb0(X2,xK))
=> sdtlpdtrp0(xc,X3) = X1 )
& isCountable0(X2)
& aSubsetOf0(X2,xS) )
& aElementOf0(X1,xT) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,hypothesis,
! [X183] :
( sdtlpdtrp0(xc,X183) = sdtlpdtrp0(xc,slcrc0)
| ~ aElementOf0(X183,slbdtsldtrb0(xS,sz00)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3507])])]) ).
cnf(c_0_13,hypothesis,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_14,hypothesis,
xK = sz00,
inference(split_conjunct,[status(thm)],[m__3462]) ).
fof(c_0_15,negated_conjecture,
! [X184,X185] :
( ( ~ aElementOf0(X184,xT)
| ~ isCountable0(X185)
| ~ aSubsetOf0(X185,xS)
| sdtlpdtrp0(xc,esk22_2(X184,X185)) != X184 )
& ( ~ aElementOf0(X184,xT)
| ~ isCountable0(X185)
| ~ aSubsetOf0(X185,xS)
| aElementOf0(esk22_2(X184,X185),slbdtsldtrb0(X185,xK)) ) ),
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)],[c_0_11])])])])])]) ).
cnf(c_0_16,hypothesis,
( ~ aElementOf0(X1,slbdtsldtrb0(xS,sz00))
| sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,hypothesis,
slbdtsldtrb0(xS,sz00) = szDzozmdt0(xc),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( ~ aElementOf0(X1,xT)
| ~ isCountable0(X2)
| ~ aSubsetOf0(X2,xS)
| aElementOf0(esk22_2(X1,X2),slbdtsldtrb0(X2,xK)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,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_20,negated_conjecture,
( ~ aElementOf0(X1,xT)
| ~ isCountable0(X2)
| ~ aSubsetOf0(X2,xS)
| sdtlpdtrp0(xc,esk22_2(X1,X2)) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0) ),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( ~ aElementOf0(X1,xT)
| ~ isCountable0(X2)
| ~ aSubsetOf0(X2,xS)
| aElementOf0(esk22_2(X1,X2),slbdtsldtrb0(X2,sz00)) ),
inference(rw,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_23,hypothesis,
isCountable0(xS),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_24,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,hypothesis,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_26,hypothesis,
aSet0(xT),
inference(split_conjunct,[status(thm)],[m__3291]) ).
fof(c_0_27,plain,
! [X164,X165] :
( aElementOf0(sdtlpdtrp0(X164,X165),sdtlcdtrc0(X164,szDzozmdt0(X164)))
| ~ aElementOf0(X165,szDzozmdt0(X164))
| ~ aFunction0(X164) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mImgRng])])])]) ).
cnf(c_0_28,negated_conjecture,
( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ~ aElementOf0(esk22_2(sdtlpdtrp0(xc,slcrc0),X1),szDzozmdt0(xc))
| ~ isCountable0(X1)
| ~ aSubsetOf0(X1,xS) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21])]) ).
cnf(c_0_29,hypothesis,
( ~ aElementOf0(X1,xT)
| ~ aSubsetOf0(xS,xS)
| aElementOf0(esk22_2(X1,xS),szDzozmdt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_17]),c_0_23])]) ).
cnf(c_0_30,hypothesis,
( ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X1,xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_31,plain,
( ~ aElementOf0(X2,szDzozmdt0(X1))
| ~ aFunction0(X1)
| aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,hypothesis,
aFunction0(xc),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_33,hypothesis,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(split_conjunct,[status(thm)],[m__3476]) ).
cnf(c_0_34,hypothesis,
( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ~ aSubsetOf0(xS,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_23])]) ).
cnf(c_0_35,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,X1),xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_36,hypothesis,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(rw,[status(thm)],[c_0_33,c_0_17]) ).
fof(c_0_37,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_38,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_39,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_40,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_41,hypothesis,
~ aSubsetOf0(xS,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_42,plain,
( ~ aSet0(X1)
| aSubsetOf0(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_44,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM566+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n017.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 02:35:11 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
% 0.09/0.46 % Version: 3.5.1
% 0.09/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.46 % Starting sh5l with 300s (1) cores
% 0.09/0.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1239519 completed with status 0
% 0.09/0.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.09/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.46 % No SInE strategy applied
% 0.09/0.46 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.09/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.09/0.46 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.09/0.46 % Starting G-E--_302_C18_F1_URBAN_S0Y with 136s (1) cores
% 0.09/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0U with 136s (1) cores
% 0.09/0.46 % G-E--_300_C18_F1_SE_CS_SP_S0Y with pid 1239525 completed with status 0
% 0.09/0.46 % Result found by G-E--_300_C18_F1_SE_CS_SP_S0Y
% 0.09/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.09/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.09/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.46 % No SInE strategy applied
% 0.09/0.46 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.09/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.09/0.46 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.09/0.46 % Preprocessing time : 0.004 s
% 0.09/0.46
% 0.09/0.46 % Proof found!
% 0.09/0.46 % SZS status Theorem
% 0.09/0.46 % SZS output start CNFRefutation
% See solution above
% 0.09/0.46 % Parsed axioms : 81
% 0.09/0.46 % Removed by relevancy pruning/SinE : 0
% 0.09/0.46 % Initial clauses : 161
% 0.09/0.46 % Removed in clause preprocessing : 7
% 0.09/0.46 % Initial clauses in saturation : 154
% 0.09/0.46 % Processed clauses : 188
% 0.09/0.46 % ...of these trivial : 2
% 0.09/0.46 % ...subsumed : 46
% 0.09/0.46 % ...remaining for further processing : 140
% 0.09/0.46 % Other redundant clauses eliminated : 17
% 0.09/0.46 % Clauses deleted for lack of memory : 0
% 0.09/0.46 % Backward-subsumed : 5
% 0.09/0.46 % Backward-rewritten : 3
% 0.09/0.46 % Generated clauses : 195
% 0.09/0.46 % ...of the previous two non-redundant : 164
% 0.09/0.46 % ...aggressively subsumed : 0
% 0.09/0.46 % Contextual simplify-reflections : 5
% 0.09/0.46 % Paramodulations : 179
% 0.09/0.46 % Factorizations : 0
% 0.09/0.46 % NegExts : 0
% 0.09/0.46 % Equation resolutions : 17
% 0.09/0.46 % Disequality decompositions : 0
% 0.09/0.46 % Total rewrite steps : 117
% 0.09/0.46 % ...of those cached : 96
% 0.09/0.46 % Propositional unsat checks : 0
% 0.09/0.46 % Propositional check models : 0
% 0.09/0.46 % Propositional check unsatisfiable : 0
% 0.09/0.46 % Propositional clauses : 0
% 0.09/0.46 % Propositional clauses after purity: 0
% 0.09/0.46 % Propositional unsat core size : 0
% 0.09/0.46 % Propositional preprocessing time : 0.000
% 0.09/0.46 % Propositional encoding time : 0.000
% 0.09/0.46 % Propositional solver time : 0.000
% 0.09/0.46 % Success case prop preproc time : 0.000
% 0.09/0.46 % Success case prop encoding time : 0.000
% 0.09/0.46 % Success case prop solver time : 0.000
% 0.09/0.46 % Current number of processed clauses : 120
% 0.09/0.46 % Positive orientable unit clauses : 24
% 0.09/0.46 % Positive unorientable unit clauses: 0
% 0.09/0.46 % Negative unit clauses : 6
% 0.09/0.46 % Non-unit-clauses : 90
% 0.09/0.46 % Current number of unprocessed clauses: 127
% 0.09/0.46 % ...number of literals in the above : 648
% 0.09/0.46 % Current number of archived formulas : 0
% 0.09/0.46 % Current number of archived clauses : 8
% 0.09/0.46 % Clause-clause subsumption calls (NU) : 1806
% 0.09/0.46 % Rec. Clause-clause subsumption calls : 942
% 0.09/0.46 % Non-unit clause-clause subsumptions : 48
% 0.09/0.46 % Unit Clause-clause subsumption calls : 91
% 0.09/0.46 % Rewrite failures with RHS unbound : 0
% 0.09/0.46 % BW rewrite match attempts : 4
% 0.09/0.46 % BW rewrite match successes : 4
% 0.09/0.46 % Condensation attempts : 0
% 0.09/0.46 % Condensation successes : 0
% 0.09/0.46 % Termbank termtop insertions : 16794
% 0.09/0.46 % Search garbage collected termcells : 3446
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.015 s
% 0.09/0.46 % System time : 0.009 s
% 0.09/0.46 % Total time : 0.024 s
% 0.09/0.46 % Maximum resident set size: 4196 pages
% 0.09/0.46
% 0.09/0.46 % -------------------------------------------------
% 0.09/0.46 % User time : 0.061 s
% 0.09/0.46 % System time : 0.024 s
% 0.09/0.46 % Total time : 0.084 s
% 0.09/0.46 % Maximum resident set size: 4864 pages
% 0.09/0.46 % E exiting
%------------------------------------------------------------------------------