%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU164+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 02:28:21 PM UTC 2026
% Result : Theorem 119.10s 17.70s
% Output : CNFRefutation 119.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 8 unt; 0 def)
% Number of atoms : 120 ( 28 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 138 ( 54 ~; 64 |; 12 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-3 aty)
% Number of variables : 90 ( 1 sgn 38 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(X3,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(t99_zfmisc_1,conjecture,
! [X1] : union(powerset(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(c_0_6,plain,
! [X14,X15,X16,X17,X18,X19] :
( ( X19 = powerset(X18)
| subset(esk2_2(X18,X19),X18)
| in(esk2_2(X18,X19),X19) )
& ( X19 = powerset(X18)
| ~ subset(esk2_2(X18,X19),X18)
| ~ in(esk2_2(X18,X19),X19) )
& ( X15 != powerset(X14)
| in(X17,X15)
| ~ subset(X17,X14) )
& ( X15 != powerset(X14)
| subset(X16,X14)
| ~ in(X16,X15) ) ),
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)],[d1_zfmisc_1])])])])])])]) ).
fof(c_0_7,plain,
! [X27,X28,X29,X31,X32,X33,X34,X36] :
( ( X34 = union(X33)
| in(esk5_2(X33,X34),X34)
| in(esk6_2(X33,X34),X33) )
& ( X34 = union(X33)
| in(esk5_2(X33,X34),X34)
| in(esk5_2(X33,X34),esk6_2(X33,X34)) )
& ( X34 = union(X33)
| ~ in(X36,X33)
| ~ in(esk5_2(X33,X34),X36)
| ~ in(esk5_2(X33,X34),X34) )
& ( X28 != union(X27)
| in(X31,X28)
| ~ in(X32,X27)
| ~ in(X31,X32) )
& ( X28 != union(X27)
| ~ in(X29,X28)
| in(esk4_3(X27,X28,X29),X27) )
& ( X28 != union(X27)
| ~ in(X29,X28)
| in(X29,esk4_3(X27,X28,X29)) ) ),
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)],[d4_tarski])])])])])])]) ).
cnf(c_0_8,plain,
( X2 != powerset(X3)
| ~ in(X1,X2)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( X2 != union(X1)
| ~ in(X3,X2)
| in(esk4_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X21,X22,X23,X24,X25] :
( ( subset(X24,X25)
| ~ in(esk3_2(X24,X25),X25) )
& ( subset(X24,X25)
| in(esk3_2(X24,X25),X24) )
& ( in(X23,X22)
| ~ in(X23,X21)
| ~ subset(X21,X22) ) ),
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)],[d3_tarski])])])])])])]) ).
cnf(c_0_11,plain,
( ~ in(X1,powerset(X2))
| subset(X1,X2) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( ~ in(X2,union(X1))
| in(esk4_3(X1,union(X1),X2),X1) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( X4 != union(X3)
| ~ in(X2,X3)
| ~ in(X1,X2)
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( X3 != powerset(X2)
| ~ subset(X1,X2)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,plain,
( ~ in(X3,X1)
| ~ subset(X1,X2)
| in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ~ in(X2,union(powerset(X1)))
| subset(esk4_3(powerset(X1),union(powerset(X1)),X2),X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( X3 != union(X2)
| ~ in(X1,X3)
| in(X1,esk4_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,plain,
( ~ in(X1,X3)
| ~ in(X3,X2)
| in(X1,union(X2)) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( ~ subset(X1,X2)
| in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
! [X42] : subset(X42,X42),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_21,plain,
( ~ in(X3,union(powerset(X2)))
| ~ in(X1,esk4_3(powerset(X2),union(powerset(X2)),X3))
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( ~ in(X1,union(X2))
| in(X1,esk4_3(X2,union(X2),X1)) ),
inference(er,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X43,X44] :
( ( X43 = X44
| in(esk9_2(X43,X44),X44)
| in(esk9_2(X43,X44),X43) )
& ( X43 = X44
| ~ in(esk9_2(X43,X44),X44)
| ~ in(esk9_2(X43,X44),X43) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])])]) ).
cnf(c_0_24,plain,
( ~ in(X1,X3)
| ~ subset(X3,X2)
| in(X1,union(powerset(X2))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,negated_conjecture,
~ ! [X1] : union(powerset(X1)) = X1,
inference(assume_negation,[status(cth)],[t99_zfmisc_1]) ).
cnf(c_0_27,plain,
( ~ in(X1,union(powerset(X2)))
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( X1 = X2
| in(esk9_2(X1,X2),X2)
| in(esk9_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( ~ in(esk9_2(X1,X2),X2)
| ~ in(esk9_2(X1,X2),X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( ~ in(X1,X2)
| in(X1,union(powerset(X2))) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_31,negated_conjecture,
union(powerset(esk10_0)) != esk10_0,
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).
cnf(c_0_32,plain,
( in(esk9_2(X1,union(powerset(X2))),X1)
| X1 = union(powerset(X2))
| in(esk9_2(X1,union(powerset(X2))),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
( ~ in(esk9_2(X1,union(powerset(X2))),X2)
| ~ in(esk9_2(X1,union(powerset(X2))),X1)
| X1 = union(powerset(X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
union(powerset(esk10_0)) != esk10_0,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_32,c_0_33,c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU164+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:53:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 119.10/17.70 % Version: 3.5.1
% 119.10/17.70 % Preprocessing class: FSMSSMSSSSSNFFN.
% 119.10/17.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 119.10/17.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 119.10/17.70 % Starting new_bool_3 with 300s (1) cores
% 119.10/17.70 % Starting new_bool_1 with 300s (1) cores
% 119.10/17.70 % Starting sh5l with 300s (1) cores
% 119.10/17.70 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 991880 completed with status 0
% 119.10/17.70 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 119.10/17.70 % Preprocessing class: FSMSSMSSSSSNFFN.
% 119.10/17.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 119.10/17.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 119.10/17.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 119.10/17.70 % No SInE strategy applied
% 119.10/17.70 % Search class: FGHSF-FFMF31-SFFFFFNN
% 119.10/17.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 119.10/17.70 % Starting SubtermCWHack with 136s (1) cores
% 119.10/17.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 119.10/17.70 % Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 166s (1) cores
% 119.10/17.70 % Starting new_bool_3 with 162s (1) cores
% 119.10/17.70 % Starting new_bool_1 with 158s (1) cores
% 119.10/17.70 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 991885 completed with status 0
% 119.10/17.70 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 119.10/17.70 % Preprocessing class: FSMSSMSSSSSNFFN.
% 119.10/17.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 119.10/17.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 119.10/17.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 119.10/17.70 % No SInE strategy applied
% 119.10/17.70 % Search class: FGHSF-FFMF31-SFFFFFNN
% 119.10/17.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 119.10/17.70 % Starting SubtermCWHack with 136s (1) cores
% 119.10/17.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 119.10/17.70 % Preprocessing time : 0.002 s
% 119.10/17.70 % Presaturation interreduction done
% 119.10/17.70 % SatCheck found unsatisfiable ground set
% 119.10/17.70
% 119.10/17.70 % Proof found!
% 119.10/17.70 % SZS status Theorem
% 119.10/17.70 % SZS output start CNFRefutation
% See solution above
% 119.10/17.71 % Parsed axioms : 11
% 119.10/17.71 % Removed by relevancy pruning/SinE : 0
% 119.10/17.71 % Initial clauses : 26
% 119.10/17.71 % Removed in clause preprocessing : 0
% 119.10/17.71 % Initial clauses in saturation : 26
% 119.10/17.71 % Processed clauses : 23931
% 119.10/17.71 % ...of these trivial : 463
% 119.10/17.71 % ...subsumed : 18468
% 119.10/17.71 % ...remaining for further processing : 5000
% 119.10/17.71 % Other redundant clauses eliminated : 13
% 119.10/17.71 % Clauses deleted for lack of memory : 0
% 119.10/17.71 % Backward-subsumed : 11
% 119.10/17.71 % Backward-rewritten : 66
% 119.10/17.71 % Generated clauses : 1060140
% 119.10/17.71 % ...of the previous two non-redundant : 1057893
% 119.10/17.71 % ...aggressively subsumed : 0
% 119.10/17.71 % Contextual simplify-reflections : 3
% 119.10/17.71 % Paramodulations : 1060084
% 119.10/17.71 % Factorizations : 44
% 119.10/17.71 % NegExts : 0
% 119.10/17.71 % Equation resolutions : 13
% 119.10/17.71 % Disequality decompositions : 0
% 119.10/17.71 % Total rewrite steps : 78405
% 119.10/17.71 % ...of those cached : 71109
% 119.10/17.71 % Propositional unsat checks : 1
% 119.10/17.71 % Propositional check models : 0
% 119.10/17.71 % Propositional check unsatisfiable : 1
% 119.10/17.71 % Propositional clauses : 1037876
% 119.10/17.71 % Propositional clauses after purity: 118
% 119.10/17.71 % Propositional unsat core size : 3
% 119.10/17.71 % Propositional preprocessing time : 0.000
% 119.10/17.71 % Propositional encoding time : 4.262
% 119.10/17.71 % Propositional solver time : 0.061
% 119.10/17.71 % Success case prop preproc time : 0.000
% 119.10/17.71 % Success case prop encoding time : 4.262
% 119.10/17.71 % Success case prop solver time : 0.061
% 119.10/17.71 % Current number of processed clauses : 4890
% 119.10/17.71 % Positive orientable unit clauses : 772
% 119.10/17.71 % Positive unorientable unit clauses: 0
% 119.10/17.71 % Negative unit clauses : 1880
% 119.10/17.71 % Non-unit-clauses : 2238
% 119.10/17.71 % Current number of unprocessed clauses: 1032986
% 119.10/17.71 % ...number of literals in the above : 1631736
% 119.10/17.71 % Current number of archived formulas : 0
% 119.10/17.71 % Current number of archived clauses : 103
% 119.10/17.71 % Clause-clause subsumption calls (NU) : 2469404
% 119.10/17.71 % Rec. Clause-clause subsumption calls : 1601447
% 119.10/17.71 % Non-unit clause-clause subsumptions : 4155
% 119.10/17.71 % Unit Clause-clause subsumption calls : 2248844
% 119.10/17.71 % Rewrite failures with RHS unbound : 0
% 119.10/17.71 % BW rewrite match attempts : 87577
% 119.10/17.71 % BW rewrite match successes : 35
% 119.10/17.71 % Condensation attempts : 0
% 119.10/17.71 % Condensation successes : 0
% 119.10/17.71 % Termbank termtop insertions : 40895165
% 119.10/17.71 % Search garbage collected termcells : 584
% 119.10/17.71
% 119.10/17.71 % -------------------------------------------------
% 119.10/17.71 % User time : 15.962 s
% 119.10/17.71 % System time : 0.791 s
% 119.10/17.71 % Total time : 16.753 s
% 119.10/17.71 % Maximum resident set size: 3636 pages
% 119.10/17.71
% 119.10/17.71 % -------------------------------------------------
% 119.10/17.71 % User time : 81.253 s
% 119.10/17.71 % System time : 3.295 s
% 119.10/17.71 % Total time : 84.547 s
% 119.10/17.71 % Maximum resident set size: 4864 pages
% 119.10/17.71 % E exiting
%------------------------------------------------------------------------------