%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU147+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 02:23:58 PM UTC 2026
% Result : Theorem 0.16s 0.78s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 17 unt; 0 def)
% Number of atoms : 120 ( 45 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 123 ( 47 ~; 53 |; 14 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-3 aty)
% Number of variables : 80 ( 6 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(t3_xboole_1,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(t1_zfmisc_1,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
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(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(c_0_9,plain,
! [X28,X29,X30,X31,X32,X33] :
( ( X33 = powerset(X32)
| subset(esk3_2(X32,X33),X32)
| in(esk3_2(X32,X33),X33) )
& ( X33 = powerset(X32)
| ~ subset(esk3_2(X32,X33),X32)
| ~ in(esk3_2(X32,X33),X33) )
& ( X29 != powerset(X28)
| in(X31,X29)
| ~ subset(X31,X28) )
& ( X29 != powerset(X28)
| subset(X30,X28)
| ~ in(X30,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)],[d1_zfmisc_1])])])])])])]) ).
cnf(c_0_10,plain,
( X2 != powerset(X3)
| ~ in(X1,X2)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_11,plain,
! [X53,X54,X55,X56,X57] :
( ( subset(X56,X57)
| ~ in(esk6_2(X56,X57),X57) )
& ( subset(X56,X57)
| in(esk6_2(X56,X57),X56) )
& ( in(X55,X54)
| ~ in(X55,X53)
| ~ subset(X53,X54) ) ),
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])])])])])])]) ).
fof(c_0_12,lemma,
! [X89,X90] :
( ( subset(singleton(X89),X90)
| ~ in(X89,X90) )
& ( in(X89,X90)
| ~ subset(singleton(X89),X90) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])])]) ).
fof(c_0_13,lemma,
! [X159] : unordered_pair(X159,X159) = singleton(X159),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
cnf(c_0_14,plain,
( X3 != powerset(X2)
| ~ subset(X1,X2)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,lemma,
! [X123] : subset(empty_set,X123),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(c_0_16,lemma,
! [X140] :
( X140 = empty_set
| ~ subset(X140,empty_set) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])])]) ).
cnf(c_0_17,plain,
( ~ in(X1,powerset(X2))
| subset(X1,X2) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( subset(X1,X2)
| in(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_19,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(assume_negation,[status(cth)],[t1_zfmisc_1]) ).
cnf(c_0_20,lemma,
( ~ in(X1,X2)
| subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( ~ subset(X1,X2)
| in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_23,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,lemma,
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( subset(powerset(X1),X2)
| subset(esk6_2(powerset(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_26,plain,
! [X35,X36,X37,X38,X39,X40,X41,X42] :
( ( X42 = unordered_pair(X40,X41)
| esk4_3(X40,X41,X42) = X41
| esk4_3(X40,X41,X42) = X40
| in(esk4_3(X40,X41,X42),X42) )
& ( X42 = unordered_pair(X40,X41)
| ~ in(esk4_3(X40,X41,X42),X42)
| esk4_3(X40,X41,X42) != X41 )
& ( X42 = unordered_pair(X40,X41)
| ~ in(esk4_3(X40,X41,X42),X42)
| esk4_3(X40,X41,X42) != X40 )
& ( X37 != unordered_pair(X35,X36)
| in(X39,X37)
| X39 != X36 )
& ( X37 != unordered_pair(X35,X36)
| in(X39,X37)
| X39 != X35 )
& ( X37 != unordered_pair(X35,X36)
| X38 = X36
| X38 = X35
| ~ in(X38,X37) ) ),
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_27,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_28,plain,
! [X15,X16] :
( ( X15 = X16
| ~ subset(X16,X15)
| ~ subset(X15,X16) )
& ( X15 != X16
| subset(X16,X15) )
& ( X15 != X16
| subset(X15,X16) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])]) ).
cnf(c_0_29,lemma,
( ~ in(X1,X2)
| subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_30,lemma,
in(empty_set,powerset(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,plain,
( ~ in(esk6_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_32,lemma,
( subset(powerset(empty_set),X1)
| esk6_2(powerset(empty_set),X1) = empty_set ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,plain,
( X3 != unordered_pair(X2,X4)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_34,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(fof_nnf,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,lemma,
subset(unordered_pair(empty_set,empty_set),powerset(X1)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,lemma,
( ~ in(empty_set,X1)
| subset(powerset(empty_set),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_33])]) ).
cnf(c_0_39,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,lemma,
( ~ subset(powerset(X1),unordered_pair(empty_set,empty_set))
| powerset(X1) = unordered_pair(empty_set,empty_set) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,lemma,
subset(powerset(empty_set),unordered_pair(empty_set,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
powerset(empty_set) != unordered_pair(empty_set,empty_set),
inference(rw,[status(thm)],[c_0_39,c_0_21]) ).
cnf(c_0_43,lemma,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU147+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.53 % Computer : n004.cluster.edu
% 0.11/0.53 % Model : x86_64 x86_64
% 0.11/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.53 % Memory : 8046.5625MB
% 0.11/0.53 % OS : Linux 6.8.0-71-generic
% 0.11/0.53 % CPULimit : 300
% 0.11/0.54 % WCLimit : 300
% 0.11/0.54 % DateTime : Mon Sep 21 05:52:50 UTC 2026
% 0.11/0.54 % CPUTime :
% 0.11/0.54 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.57 Running first-order theorem proving
% 0.11/0.57 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
% 0.16/0.78 % Version: 3.5.1
% 0.16/0.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.78 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.78 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.78 % Starting sh5l with 300s (1) cores
% 0.16/0.78 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2385702 completed with status 0
% 0.16/0.78 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.16/0.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.78 % No SInE strategy applied
% 0.16/0.78 % Search class: FGHSM-FFMF32-SFFFFFNN
% 0.16/0.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.78 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/0.78 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 164s (1) cores
% 0.16/0.78 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.16/0.78 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S022A with 136s (1) cores
% 0.16/0.78 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2385709 completed with status 0
% 0.16/0.78 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.16/0.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.78 % No SInE strategy applied
% 0.16/0.78 % Search class: FGHSM-FFMF32-SFFFFFNN
% 0.16/0.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.78 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/0.78 % Preprocessing time : 0.003 s
% 0.16/0.78 % Presaturation interreduction done
% 0.16/0.78
% 0.16/0.78 % Proof found!
% 0.16/0.78 % SZS status Theorem
% 0.16/0.78 % SZS output start CNFRefutation
% See solution above
% 0.16/0.78 % Parsed axioms : 70
% 0.16/0.78 % Removed by relevancy pruning/SinE : 0
% 0.16/0.78 % Initial clauses : 114
% 0.16/0.78 % Removed in clause preprocessing : 9
% 0.16/0.78 % Initial clauses in saturation : 105
% 0.16/0.78 % Processed clauses : 2042
% 0.16/0.78 % ...of these trivial : 59
% 0.16/0.78 % ...subsumed : 1526
% 0.16/0.78 % ...remaining for further processing : 457
% 0.16/0.78 % Other redundant clauses eliminated : 185
% 0.16/0.78 % Clauses deleted for lack of memory : 0
% 0.16/0.78 % Backward-subsumed : 13
% 0.16/0.78 % Backward-rewritten : 8
% 0.16/0.78 % Generated clauses : 7789
% 0.16/0.78 % ...of the previous two non-redundant : 6494
% 0.16/0.78 % ...aggressively subsumed : 0
% 0.16/0.78 % Contextual simplify-reflections : 0
% 0.16/0.78 % Paramodulations : 7588
% 0.16/0.78 % Factorizations : 19
% 0.16/0.78 % NegExts : 0
% 0.16/0.78 % Equation resolutions : 185
% 0.16/0.78 % Disequality decompositions : 0
% 0.16/0.78 % Total rewrite steps : 2951
% 0.16/0.78 % ...of those cached : 2615
% 0.16/0.78 % Propositional unsat checks : 0
% 0.16/0.78 % Propositional check models : 0
% 0.16/0.78 % Propositional check unsatisfiable : 0
% 0.16/0.78 % Propositional clauses : 0
% 0.16/0.78 % Propositional clauses after purity: 0
% 0.16/0.78 % Propositional unsat core size : 0
% 0.16/0.78 % Propositional preprocessing time : 0.000
% 0.16/0.78 % Propositional encoding time : 0.000
% 0.16/0.78 % Propositional solver time : 0.000
% 0.16/0.78 % Success case prop preproc time : 0.000
% 0.16/0.78 % Success case prop encoding time : 0.000
% 0.16/0.78 % Success case prop solver time : 0.000
% 0.16/0.78 % Current number of processed clauses : 321
% 0.16/0.78 % Positive orientable unit clauses : 74
% 0.16/0.78 % Positive unorientable unit clauses: 3
% 0.16/0.78 % Negative unit clauses : 47
% 0.16/0.78 % Non-unit-clauses : 197
% 0.16/0.78 % Current number of unprocessed clauses: 4582
% 0.16/0.78 % ...number of literals in the above : 13641
% 0.16/0.78 % Current number of archived formulas : 0
% 0.16/0.78 % Current number of archived clauses : 116
% 0.16/0.78 % Clause-clause subsumption calls (NU) : 6385
% 0.16/0.78 % Rec. Clause-clause subsumption calls : 5254
% 0.16/0.78 % Non-unit clause-clause subsumptions : 585
% 0.16/0.78 % Unit Clause-clause subsumption calls : 1907
% 0.16/0.78 % Rewrite failures with RHS unbound : 0
% 0.16/0.78 % BW rewrite match attempts : 86
% 0.16/0.78 % BW rewrite match successes : 39
% 0.16/0.78 % Condensation attempts : 0
% 0.16/0.78 % Condensation successes : 0
% 0.16/0.78 % Termbank termtop insertions : 76124
% 0.16/0.78 % Search garbage collected termcells : 1590
% 0.16/0.78
% 0.16/0.78 % -------------------------------------------------
% 0.16/0.78 % User time : 0.168 s
% 0.16/0.78 % System time : 0.012 s
% 0.16/0.78 % Total time : 0.180 s
% 0.16/0.78 % Maximum resident set size: 3944 pages
% 0.16/0.78
% 0.16/0.78 % -------------------------------------------------
% 0.16/0.78 % User time : 0.819 s
% 0.16/0.78 % System time : 0.054 s
% 0.16/0.78 % Total time : 0.873 s
% 0.16/0.78 % Maximum resident set size: 4864 pages
% 0.16/0.78 % E exiting
%------------------------------------------------------------------------------