%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET679+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 02:14:58 PM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 92 ( 7 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 107 ( 46 ~; 32 |; 9 &)
% ( 5 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 3 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_relset_1_46,conjecture,
! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> not_equal(identity_relation_of(X1),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_46) ).
fof(p7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( not_equal(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(p22,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X1)
<=> member(ordered_pair(X2,X2),identity_relation_of(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p8,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> not_equal(identity_relation_of(X1),empty_set) ),
inference(assume_negation,[status(cth)],[prove_relset_1_46]) ).
fof(c_0_7,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( not_equal(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[p7]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> not_equal(identity_relation_of(X1),empty_set) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X6,X7] :
( ( ~ ilf_type(X6,set_type)
| ~ ilf_type(X7,set_type)
| not_equal(X6,X7)
| X6 = X7 )
& ( ~ ilf_type(X6,set_type)
| ~ ilf_type(X7,set_type)
| X6 != X7
| ~ not_equal(X6,X7) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
fof(c_0_10,plain,
! [X15] : ilf_type(X15,set_type),
inference(variable_rename,[status(thm)],[p22]) ).
fof(c_0_11,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,empty_set) ),
inference(fof_simplification,[status(thm)],[p2]) ).
fof(c_0_12,plain,
! [X9,X10] :
( ( ~ ilf_type(X9,set_type)
| ~ ilf_type(X10,set_type)
| member(X10,X9)
| ~ member(ordered_pair(X10,X10),identity_relation_of(X9)) )
& ( ~ ilf_type(X9,set_type)
| ~ ilf_type(X10,set_type)
| member(ordered_pair(X10,X10),identity_relation_of(X9))
| ~ member(X10,X9) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])])]) ).
fof(c_0_13,negated_conjecture,
( ~ not_equal(identity_relation_of(esk1_0),empty_set)
& ilf_type(esk1_0,set_type)
& ~ empty(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_14,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| not_equal(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X8] :
( ~ member(X8,empty_set)
| ~ ilf_type(X8,set_type) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_17,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p8]) ).
cnf(c_0_18,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X1,X2)
| member(ordered_pair(X1,X1),identity_relation_of(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
~ not_equal(identity_relation_of(esk1_0),empty_set),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( not_equal(X1,X2)
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15])]) ).
cnf(c_0_21,plain,
( ~ member(X1,empty_set)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X16,X17] :
( ( ~ ilf_type(X16,set_type)
| empty(X16)
| member(esk2_1(X16),X16) )
& ( ~ ilf_type(X16,set_type)
| empty(X16)
| ilf_type(esk2_1(X16),set_type) )
& ( ~ ilf_type(X16,set_type)
| ~ member(X17,X16)
| ~ ilf_type(X17,set_type)
| ~ empty(X16) ) ),
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_17])])])])])]) ).
cnf(c_0_23,plain,
( ~ member(X1,X2)
| member(ordered_pair(X1,X1),identity_relation_of(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_15]),c_0_15])]) ).
cnf(c_0_24,negated_conjecture,
identity_relation_of(esk1_0) = empty_set,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
~ member(X1,empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_15])]) ).
cnf(c_0_26,plain,
( ~ ilf_type(X1,set_type)
| empty(X1)
| member(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
~ member(X1,esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_28,plain,
( member(esk2_1(X1),X1)
| empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_15])]) ).
cnf(c_0_29,negated_conjecture,
~ empty(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET679+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:35:01 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.13/0.44 % Version: 3.5.1
% 0.13/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.44 % Starting sh5l with 300s (1) cores
% 0.13/0.44 % new_bool_3 with pid 2532099 completed with status 0
% 0.13/0.44 % Result found by new_bool_3
% 0.13/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.44 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.13/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.44 % SubtermCWHack with pid 2532110 completed with status 0
% 0.13/0.44 % Result found by SubtermCWHack
% 0.13/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.44 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.13/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.44 % Preprocessing time : 0.002 s
% 0.13/0.44
% 0.13/0.44 % Proof found!
% 0.13/0.44 % SZS status Theorem
% 0.13/0.44 % SZS output start CNFRefutation
% See solution above
% 0.13/0.44 % Parsed axioms : 24
% 0.13/0.44 % Removed by relevancy pruning/SinE : 9
% 0.13/0.44 % Initial clauses : 34
% 0.13/0.44 % Removed in clause preprocessing : 3
% 0.13/0.44 % Initial clauses in saturation : 31
% 0.13/0.44 % Processed clauses : 28
% 0.13/0.44 % ...of these trivial : 4
% 0.13/0.44 % ...subsumed : 2
% 0.13/0.44 % ...remaining for further processing : 22
% 0.13/0.44 % Other redundant clauses eliminated : 1
% 0.13/0.44 % Clauses deleted for lack of memory : 0
% 0.13/0.44 % Backward-subsumed : 0
% 0.13/0.44 % Backward-rewritten : 2
% 0.13/0.44 % Generated clauses : 14
% 0.13/0.44 % ...of the previous two non-redundant : 9
% 0.13/0.44 % ...aggressively subsumed : 0
% 0.13/0.44 % Contextual simplify-reflections : 0
% 0.13/0.44 % Paramodulations : 13
% 0.13/0.44 % Factorizations : 0
% 0.13/0.44 % NegExts : 0
% 0.13/0.44 % Equation resolutions : 1
% 0.13/0.44 % Disequality decompositions : 0
% 0.13/0.44 % Total rewrite steps : 30
% 0.13/0.44 % ...of those cached : 19
% 0.13/0.44 % Propositional unsat checks : 0
% 0.13/0.44 % Propositional check models : 0
% 0.13/0.44 % Propositional check unsatisfiable : 0
% 0.13/0.44 % Propositional clauses : 0
% 0.13/0.44 % Propositional clauses after purity: 0
% 0.13/0.44 % Propositional unsat core size : 0
% 0.13/0.44 % Propositional preprocessing time : 0.000
% 0.13/0.44 % Propositional encoding time : 0.000
% 0.13/0.44 % Propositional solver time : 0.000
% 0.13/0.44 % Success case prop preproc time : 0.000
% 0.13/0.44 % Success case prop encoding time : 0.000
% 0.13/0.44 % Success case prop solver time : 0.000
% 0.13/0.44 % Current number of processed clauses : 19
% 0.13/0.44 % Positive orientable unit clauses : 7
% 0.13/0.44 % Positive unorientable unit clauses: 0
% 0.13/0.44 % Negative unit clauses : 4
% 0.13/0.44 % Non-unit-clauses : 8
% 0.13/0.44 % Current number of unprocessed clauses: 11
% 0.13/0.44 % ...number of literals in the above : 52
% 0.13/0.44 % Current number of archived formulas : 0
% 0.13/0.44 % Current number of archived clauses : 2
% 0.13/0.44 % Clause-clause subsumption calls (NU) : 7
% 0.13/0.44 % Rec. Clause-clause subsumption calls : 7
% 0.13/0.44 % Non-unit clause-clause subsumptions : 1
% 0.13/0.44 % Unit Clause-clause subsumption calls : 12
% 0.13/0.44 % Rewrite failures with RHS unbound : 0
% 0.13/0.44 % BW rewrite match attempts : 2
% 0.13/0.44 % BW rewrite match successes : 2
% 0.13/0.44 % Condensation attempts : 0
% 0.13/0.44 % Condensation successes : 0
% 0.13/0.44 % Termbank termtop insertions : 2830
% 0.13/0.44 % Search garbage collected termcells : 733
% 0.13/0.44
% 0.13/0.44 % -------------------------------------------------
% 0.13/0.44 % User time : 0.006 s
% 0.13/0.44 % System time : 0.003 s
% 0.13/0.44 % Total time : 0.009 s
% 0.13/0.44 % Maximum resident set size: 3656 pages
% 0.13/0.44
% 0.13/0.44 % -------------------------------------------------
% 0.13/0.44 % User time : 0.008 s
% 0.13/0.44 % System time : 0.008 s
% 0.13/0.44 % Total time : 0.016 s
% 0.13/0.44 % Maximum resident set size: 4608 pages
% 0.13/0.44 % E exiting
%------------------------------------------------------------------------------