%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET890+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 69 ( 31 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 76 ( 27 ~; 36 |; 9 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-3 aty)
% Number of variables : 39 ( 0 sgn 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t31_zfmisc_1,conjecture,
! [X1] : union(singleton(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_zfmisc_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
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(c_0_3,negated_conjecture,
~ ! [X1] : union(singleton(X1)) = X1,
inference(assume_negation,[status(cth)],[t31_zfmisc_1]) ).
fof(c_0_4,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( X14 = singleton(X13)
| esk1_2(X13,X14) = X13
| in(esk1_2(X13,X14),X14) )
& ( X14 = singleton(X13)
| esk1_2(X13,X14) != X13
| ~ in(esk1_2(X13,X14),X14) )
& ( X10 != singleton(X9)
| in(X12,X10)
| X12 != X9 )
& ( X10 != singleton(X9)
| 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_tarski])])])])])])]) ).
fof(c_0_5,negated_conjecture,
union(singleton(esk8_0)) != esk8_0,
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
fof(c_0_6,plain,
! [X22,X23,X24,X26,X27,X28,X29,X31] :
( ( X29 = union(X28)
| in(esk4_2(X28,X29),X29)
| in(esk5_2(X28,X29),X28) )
& ( X29 = union(X28)
| in(esk4_2(X28,X29),X29)
| in(esk4_2(X28,X29),esk5_2(X28,X29)) )
& ( X29 = union(X28)
| ~ in(X31,X28)
| ~ in(esk4_2(X28,X29),X31)
| ~ in(esk4_2(X28,X29),X29) )
& ( X23 != union(X22)
| in(X26,X23)
| ~ in(X27,X22)
| ~ in(X26,X27) )
& ( X23 != union(X22)
| ~ in(X24,X23)
| in(esk3_3(X22,X23,X24),X22) )
& ( X23 != union(X22)
| ~ in(X24,X23)
| in(X24,esk3_3(X22,X23,X24)) ) ),
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_7,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
union(singleton(esk8_0)) != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( X2 = union(X1)
| in(esk4_2(X1,X2),X2)
| in(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( in(esk4_2(singleton(esk8_0),esk8_0),esk8_0)
| in(esk5_2(singleton(esk8_0),esk8_0),singleton(esk8_0)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9])]) ).
cnf(c_0_12,plain,
( X3 != singleton(X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,plain,
( ~ in(X3,X1)
| ~ in(esk4_2(X1,X2),X3)
| ~ in(esk4_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
( in(esk4_2(singleton(esk8_0),esk8_0),esk8_0)
| esk5_2(singleton(esk8_0),esk8_0) = esk8_0 ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_12])]) ).
cnf(c_0_16,plain,
( X2 = union(X1)
| in(esk4_2(X1,X2),X2)
| in(esk4_2(X1,X2),esk5_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
esk5_2(singleton(esk8_0),esk8_0) = esk8_0,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),c_0_8]),c_0_14]) ).
cnf(c_0_18,negated_conjecture,
in(esk4_2(singleton(esk8_0),esk8_0),esk8_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_16])]),c_0_17])]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_18]),c_0_18]),c_0_15])]),c_0_8]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET890+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n006.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 05:42:42 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 0.14/0.47 % Version: 3.5.1
% 0.14/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.47 % Starting sh5l with 300s (1) cores
% 0.14/0.47 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2115695 completed with status 0
% 0.14/0.47 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.47 % No SInE strategy applied
% 0.14/0.47 % Search class: FGHSF-FFMF31-SFFFFFNN
% 0.14/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.47 % Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 166s (1) cores
% 0.14/0.47 % Starting new_bool_3 with 162s (1) cores
% 0.14/0.47 % Starting new_bool_1 with 158s (1) cores
% 0.14/0.47 % G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2115701 completed with status 0
% 0.14/0.47 % Result found by G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.47 % No SInE strategy applied
% 0.14/0.47 % Search class: FGHSF-FFMF31-SFFFFFNN
% 0.14/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.47 % Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 166s (1) cores
% 0.14/0.47 % Preprocessing time : 0.001 s
% 0.14/0.47 % Presaturation interreduction done
% 0.14/0.47
% 0.14/0.47 % Proof found!
% 0.14/0.47 % SZS status Theorem
% 0.14/0.47 % SZS output start CNFRefutation
% See solution above
% 0.14/0.47 % Parsed axioms : 10
% 0.14/0.47 % Removed by relevancy pruning/SinE : 0
% 0.14/0.47 % Initial clauses : 22
% 0.14/0.47 % Removed in clause preprocessing : 0
% 0.14/0.47 % Initial clauses in saturation : 22
% 0.14/0.47 % Processed clauses : 84
% 0.14/0.47 % ...of these trivial : 0
% 0.14/0.47 % ...subsumed : 5
% 0.14/0.47 % ...remaining for further processing : 79
% 0.14/0.47 % Other redundant clauses eliminated : 15
% 0.14/0.47 % Clauses deleted for lack of memory : 0
% 0.14/0.47 % Backward-subsumed : 0
% 0.14/0.47 % Backward-rewritten : 3
% 0.14/0.47 % Generated clauses : 875
% 0.14/0.47 % ...of the previous two non-redundant : 855
% 0.14/0.47 % ...aggressively subsumed : 0
% 0.14/0.47 % Contextual simplify-reflections : 1
% 0.14/0.47 % Paramodulations : 861
% 0.14/0.47 % Factorizations : 0
% 0.14/0.47 % NegExts : 0
% 0.14/0.47 % Equation resolutions : 15
% 0.14/0.47 % Disequality decompositions : 0
% 0.14/0.47 % Total rewrite steps : 14
% 0.14/0.47 % ...of those cached : 10
% 0.14/0.47 % Propositional unsat checks : 0
% 0.14/0.47 % Propositional check models : 0
% 0.14/0.47 % Propositional check unsatisfiable : 0
% 0.14/0.47 % Propositional clauses : 0
% 0.14/0.47 % Propositional clauses after purity: 0
% 0.14/0.47 % Propositional unsat core size : 0
% 0.14/0.47 % Propositional preprocessing time : 0.000
% 0.14/0.47 % Propositional encoding time : 0.000
% 0.14/0.47 % Propositional solver time : 0.000
% 0.14/0.47 % Success case prop preproc time : 0.000
% 0.14/0.47 % Success case prop encoding time : 0.000
% 0.14/0.47 % Success case prop solver time : 0.000
% 0.14/0.47 % Current number of processed clauses : 49
% 0.14/0.47 % Positive orientable unit clauses : 5
% 0.14/0.47 % Positive unorientable unit clauses: 0
% 0.14/0.47 % Negative unit clauses : 19
% 0.14/0.47 % Non-unit-clauses : 25
% 0.14/0.47 % Current number of unprocessed clauses: 811
% 0.14/0.47 % ...number of literals in the above : 2637
% 0.14/0.47 % Current number of archived formulas : 0
% 0.14/0.47 % Current number of archived clauses : 23
% 0.14/0.47 % Clause-clause subsumption calls (NU) : 107
% 0.14/0.47 % Rec. Clause-clause subsumption calls : 103
% 0.14/0.47 % Non-unit clause-clause subsumptions : 1
% 0.14/0.47 % Unit Clause-clause subsumption calls : 57
% 0.14/0.47 % Rewrite failures with RHS unbound : 0
% 0.14/0.47 % BW rewrite match attempts : 3
% 0.14/0.47 % BW rewrite match successes : 1
% 0.14/0.47 % Condensation attempts : 0
% 0.14/0.47 % Condensation successes : 0
% 0.14/0.47 % Termbank termtop insertions : 22647
% 0.14/0.47 % Search garbage collected termcells : 441
% 0.14/0.47
% 0.14/0.47 % -------------------------------------------------
% 0.14/0.47 % User time : 0.018 s
% 0.14/0.47 % System time : 0.004 s
% 0.14/0.47 % Total time : 0.022 s
% 0.14/0.47 % Maximum resident set size: 3636 pages
% 0.14/0.47
% 0.14/0.47 % -------------------------------------------------
% 0.14/0.47 % User time : 0.088 s
% 0.14/0.47 % System time : 0.020 s
% 0.14/0.47 % Total time : 0.108 s
% 0.14/0.47 % Maximum resident set size: 4608 pages
% 0.14/0.47 % E exiting
%------------------------------------------------------------------------------