%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET889+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 02:15:42 PM UTC 2026
% Result : Theorem 0.04s 0.44s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 106 ( 67 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 105 ( 33 ~; 57 |; 10 &)
% ( 5 <=>; 0 =>; 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 : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 75 ( 7 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X2
| X4 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(l4_zfmisc_1,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = singleton(X2)
| X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t30_zfmisc_1,conjecture,
! [X1] : powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_zfmisc_1) ).
fof(c_0_6,plain,
! [X16,X17,X18,X19,X20,X21,X22,X23] :
( ( X23 = unordered_pair(X21,X22)
| esk2_3(X21,X22,X23) = X22
| esk2_3(X21,X22,X23) = X21
| in(esk2_3(X21,X22,X23),X23) )
& ( X23 = unordered_pair(X21,X22)
| ~ in(esk2_3(X21,X22,X23),X23)
| esk2_3(X21,X22,X23) != X22 )
& ( X23 = unordered_pair(X21,X22)
| ~ in(esk2_3(X21,X22,X23),X23)
| esk2_3(X21,X22,X23) != X21 )
& ( X18 != unordered_pair(X16,X17)
| in(X20,X18)
| X20 != X17 )
& ( X18 != unordered_pair(X16,X17)
| in(X20,X18)
| X20 != X16 )
& ( X18 != unordered_pair(X16,X17)
| X19 = X17
| X19 = X16
| ~ in(X19,X18) ) ),
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)],[d2_tarski])])])])])])]) ).
fof(c_0_7,plain,
! [X25,X26] :
( ( subset(X25,singleton(X26))
| X25 != singleton(X26) )
& ( subset(X25,singleton(X26))
| X25 != empty_set )
& ( X25 = singleton(X26)
| X25 = empty_set
| ~ subset(X25,singleton(X26)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])])]) ).
fof(c_0_8,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( X14 = powerset(X13)
| subset(esk1_2(X13,X14),X13)
| in(esk1_2(X13,X14),X14) )
& ( X14 = powerset(X13)
| ~ subset(esk1_2(X13,X14),X13)
| ~ in(esk1_2(X13,X14),X14) )
& ( X10 != powerset(X9)
| in(X12,X10)
| ~ subset(X12,X9) )
& ( X10 != powerset(X9)
| subset(X11,X9)
| ~ in(X11,X10) ) ),
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])])])])])])]) ).
cnf(c_0_9,plain,
( X2 != unordered_pair(X3,X4)
| ~ in(X1,X2)
| X1 = X4
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ subset(X1,singleton(X2))
| X1 = singleton(X2)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( X2 = powerset(X1)
| subset(esk1_2(X1,X2),X1)
| in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( ~ in(X1,unordered_pair(X3,X2))
| X1 = X3
| X1 = X2 ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( in(esk1_2(singleton(X1),X2),X2)
| X2 = powerset(singleton(X1))
| esk1_2(singleton(X1),X2) = empty_set
| esk1_2(singleton(X1),X2) = singleton(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( unordered_pair(X2,X3) = powerset(singleton(X1))
| esk1_2(singleton(X1),unordered_pair(X2,X3)) = X2
| esk1_2(singleton(X1),unordered_pair(X2,X3)) = X3
| esk1_2(singleton(X1),unordered_pair(X2,X3)) = empty_set
| esk1_2(singleton(X1),unordered_pair(X2,X3)) = singleton(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_15,plain,
! [X7,X8] : unordered_pair(X7,X8) = unordered_pair(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_16,plain,
( unordered_pair(X2,empty_set) = powerset(singleton(X1))
| esk1_2(singleton(X1),unordered_pair(X2,empty_set)) = X2
| esk1_2(singleton(X1),unordered_pair(X2,empty_set)) = empty_set
| esk1_2(singleton(X1),unordered_pair(X2,empty_set)) = singleton(X1) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_14])]) ).
cnf(c_0_17,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X29] : subset(X29,X29),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_19,plain,
( X3 != unordered_pair(X4,X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] : powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)),
inference(assume_negation,[status(cth)],[t30_zfmisc_1]) ).
cnf(c_0_21,plain,
( ~ subset(esk1_2(X1,X2),X1)
| ~ in(esk1_2(X1,X2),X2)
| X2 = powerset(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,plain,
( powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1))
| esk1_2(singleton(X1),unordered_pair(empty_set,singleton(X1))) = empty_set
| esk1_2(singleton(X1),unordered_pair(empty_set,singleton(X1))) = singleton(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_16])]),c_0_17]),c_0_17]),c_0_17]) ).
cnf(c_0_23,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_19])]) ).
cnf(c_0_25,plain,
( X1 != empty_set
| subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,plain,
( X3 != unordered_pair(X2,X4)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_27,negated_conjecture,
powerset(singleton(esk6_0)) != unordered_pair(empty_set,singleton(esk6_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_28,plain,
( powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1))
| esk1_2(singleton(X1),unordered_pair(empty_set,singleton(X1))) = empty_set ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]) ).
cnf(c_0_29,plain,
subset(empty_set,singleton(X1)),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_26])]) ).
cnf(c_0_31,negated_conjecture,
powerset(singleton(esk6_0)) != unordered_pair(empty_set,singleton(esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
powerset(singleton(X1)) = unordered_pair(empty_set,singleton(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET889+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n013.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 05:42:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.40 Running first-order theorem proving
% 0.04/0.40 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
% 0.04/0.44 % Version: 3.5.1
% 0.04/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.04/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.04/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.04/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.04/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.04/0.44 % Starting sh5l with 300s (1) cores
% 0.04/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 50753 completed with status 0
% 0.04/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.04/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.04/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.04/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.04/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.04/0.44 % No SInE strategy applied
% 0.04/0.44 % Search class: FGHSS-FFMF31-SFFFFFNN
% 0.04/0.44 % partial match(1): FGHSS-FFMF32-SFFFFFNN
% 0.04/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.04/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.04/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.04/0.44 % Starting G-E--_207_B07_F1_AE_CS_SP_PS_S0Y with 253s (1) cores
% 0.04/0.44 % Starting new_bool_3 with 248s (1) cores
% 0.04/0.44 % Starting new_bool_1 with 241s (1) cores
% 0.04/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 50760 completed with status 0
% 0.04/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.04/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.04/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.04/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.04/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.04/0.44 % No SInE strategy applied
% 0.04/0.44 % Search class: FGHSS-FFMF31-SFFFFFNN
% 0.04/0.44 % partial match(1): FGHSS-FFMF32-SFFFFFNN
% 0.04/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.04/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.04/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.04/0.44 % Preprocessing time : 0.001 s
% 0.04/0.44 % Presaturation interreduction done
% 0.04/0.44
% 0.04/0.44 % Proof found!
% 0.04/0.44 % SZS status Theorem
% 0.04/0.44 % SZS output start CNFRefutation
% See solution above
% 0.04/0.44 % Parsed axioms : 11
% 0.04/0.44 % Removed by relevancy pruning/SinE : 0
% 0.04/0.44 % Initial clauses : 22
% 0.04/0.44 % Removed in clause preprocessing : 0
% 0.04/0.44 % Initial clauses in saturation : 22
% 0.04/0.44 % Processed clauses : 184
% 0.04/0.44 % ...of these trivial : 6
% 0.04/0.44 % ...subsumed : 52
% 0.04/0.44 % ...remaining for further processing : 126
% 0.04/0.44 % Other redundant clauses eliminated : 38
% 0.04/0.44 % Clauses deleted for lack of memory : 0
% 0.04/0.44 % Backward-subsumed : 5
% 0.04/0.44 % Backward-rewritten : 42
% 0.04/0.44 % Generated clauses : 377
% 0.04/0.44 % ...of the previous two non-redundant : 304
% 0.04/0.44 % ...aggressively subsumed : 0
% 0.04/0.44 % Contextual simplify-reflections : 5
% 0.04/0.44 % Paramodulations : 299
% 0.04/0.44 % Factorizations : 42
% 0.04/0.44 % NegExts : 0
% 0.04/0.44 % Equation resolutions : 38
% 0.04/0.44 % Disequality decompositions : 0
% 0.04/0.44 % Total rewrite steps : 239
% 0.04/0.44 % ...of those cached : 219
% 0.04/0.44 % Propositional unsat checks : 0
% 0.04/0.44 % Propositional check models : 0
% 0.04/0.44 % Propositional check unsatisfiable : 0
% 0.04/0.44 % Propositional clauses : 0
% 0.04/0.44 % Propositional clauses after purity: 0
% 0.04/0.44 % Propositional unsat core size : 0
% 0.04/0.44 % Propositional preprocessing time : 0.000
% 0.04/0.44 % Propositional encoding time : 0.000
% 0.04/0.44 % Propositional solver time : 0.000
% 0.04/0.44 % Success case prop preproc time : 0.000
% 0.04/0.44 % Success case prop encoding time : 0.000
% 0.04/0.44 % Success case prop solver time : 0.000
% 0.04/0.44 % Current number of processed clauses : 51
% 0.04/0.44 % Positive orientable unit clauses : 7
% 0.04/0.44 % Positive unorientable unit clauses: 1
% 0.04/0.44 % Negative unit clauses : 6
% 0.04/0.44 % Non-unit-clauses : 37
% 0.04/0.44 % Current number of unprocessed clauses: 127
% 0.04/0.44 % ...number of literals in the above : 642
% 0.04/0.44 % Current number of archived formulas : 0
% 0.04/0.44 % Current number of archived clauses : 68
% 0.04/0.44 % Clause-clause subsumption calls (NU) : 592
% 0.04/0.44 % Rec. Clause-clause subsumption calls : 255
% 0.04/0.44 % Non-unit clause-clause subsumptions : 52
% 0.04/0.44 % Unit Clause-clause subsumption calls : 30
% 0.04/0.44 % Rewrite failures with RHS unbound : 0
% 0.04/0.44 % BW rewrite match attempts : 9
% 0.04/0.44 % BW rewrite match successes : 7
% 0.04/0.44 % Condensation attempts : 0
% 0.04/0.44 % Condensation successes : 0
% 0.04/0.44 % Termbank termtop insertions : 10406
% 0.04/0.44 % Search garbage collected termcells : 388
% 0.04/0.44
% 0.04/0.44 % -------------------------------------------------
% 0.04/0.44 % User time : 0.011 s
% 0.04/0.44 % System time : 0.004 s
% 0.04/0.44 % Total time : 0.015 s
% 0.04/0.44 % Maximum resident set size: 3636 pages
% 0.04/0.44
% 0.04/0.44 % -------------------------------------------------
% 0.04/0.44 % User time : 0.056 s
% 0.04/0.44 % System time : 0.016 s
% 0.04/0.44 % Total time : 0.072 s
% 0.04/0.44 % Maximum resident set size: 4864 pages
% 0.04/0.44 % E exiting
%------------------------------------------------------------------------------