%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU008+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 : n019.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 02:23:40 PM UTC 2026
% Result : Theorem 0.43s 0.55s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 120 ( 37 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 138 ( 52 ~; 54 |; 20 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 66 ( 5 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t38_funct_1,conjecture,
! [X1,X2,X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X2,set_intersection2(relation_dom(X3),X1))
=> apply(X3,X2) = apply(relation_composition(identity_relation(X1),X3),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_1) ).
fof(t34_funct_1,axiom,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( X2 = identity_relation(X1)
<=> ( ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 )
& relation_dom(X2) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( function(identity_relation(X1))
& relation(identity_relation(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t23_funct_1,axiom,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(c_0_7,plain,
! [X35,X36,X37,X38,X39,X40,X41,X42] :
( ( X42 = set_intersection2(X40,X41)
| in(esk5_3(X40,X41,X42),X42)
| in(esk5_3(X40,X41,X42),X41) )
& ( X42 = set_intersection2(X40,X41)
| in(esk5_3(X40,X41,X42),X42)
| in(esk5_3(X40,X41,X42),X40) )
& ( X42 = set_intersection2(X40,X41)
| ~ in(esk5_3(X40,X41,X42),X41)
| ~ in(esk5_3(X40,X41,X42),X40)
| ~ in(esk5_3(X40,X41,X42),X42) )
& ( X37 != set_intersection2(X35,X36)
| in(X39,X37)
| ~ in(X39,X36)
| ~ in(X39,X35) )
& ( X37 != set_intersection2(X35,X36)
| ~ in(X38,X37)
| in(X38,X36) )
& ( X37 != set_intersection2(X35,X36)
| ~ in(X38,X37)
| in(X38,X35) ) ),
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_xboole_0])])])])])])]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X2,set_intersection2(relation_dom(X3),X1))
=> apply(X3,X2) = apply(relation_composition(identity_relation(X1),X3),X2) ) ),
inference(assume_negation,[status(cth)],[t38_funct_1]) ).
fof(c_0_9,plain,
! [X11,X12,X13] :
( ( ~ function(X12)
| ~ relation(X12)
| X12 = identity_relation(X11)
| relation_dom(X12) != X11
| apply(X12,esk4_2(X11,X12)) != esk4_2(X11,X12) )
& ( ~ function(X12)
| ~ relation(X12)
| X12 = identity_relation(X11)
| relation_dom(X12) != X11
| in(esk4_2(X11,X12),X11) )
& ( ~ function(X12)
| ~ relation(X12)
| X12 != identity_relation(X11)
| apply(X12,X13) = X13
| ~ in(X13,X11) )
& ( ~ function(X12)
| ~ relation(X12)
| X12 != identity_relation(X11)
| relation_dom(X12) = X11 ) ),
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)],[t34_funct_1])])])])])]) ).
fof(c_0_10,plain,
! [X23] : relation(identity_relation(X23)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_11,plain,
! [X24] :
( function(identity_relation(X24))
& relation(identity_relation(X24)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
cnf(c_0_12,plain,
( X3 != set_intersection2(X4,X2)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,plain,
! [X33,X34] : set_intersection2(X33,X34) = set_intersection2(X34,X33),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_14,negated_conjecture,
( apply(esk3_0,esk2_0) != apply(relation_composition(identity_relation(esk1_0),esk3_0),esk2_0)
& in(esk2_0,set_intersection2(relation_dom(esk3_0),esk1_0))
& function(esk3_0)
& relation(esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_15,plain,
! [X8,X9,X10] :
( apply(relation_composition(X9,X10),X8) = apply(X10,apply(X9,X8))
| ~ in(X8,relation_dom(X9))
| ~ function(X10)
| ~ relation(X10)
| ~ function(X9)
| ~ relation(X9) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])])]) ).
cnf(c_0_16,plain,
( ~ function(X3)
| ~ relation(X3)
| X3 != identity_relation(X2)
| ~ in(X1,X2)
| apply(X3,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| relation_dom(X1) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,plain,
( ~ in(X1,set_intersection2(X3,X2))
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
in(esk2_0,set_intersection2(relation_dom(esk3_0),esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
( ~ in(X3,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1)
| apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( ~ in(X2,X1)
| apply(identity_relation(X1),X2) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_25,plain,
relation_dom(identity_relation(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_19]),c_0_17]),c_0_18])]) ).
cnf(c_0_26,plain,
( ~ in(X1,set_intersection2(X2,X3))
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
in(esk2_0,set_intersection2(esk1_0,relation_dom(esk3_0))),
inference(rw,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
apply(esk3_0,esk2_0) != apply(relation_composition(identity_relation(esk1_0),esk3_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_29,plain,
( ~ in(X3,X1)
| ~ function(X2)
| ~ relation(X2)
| apply(relation_composition(identity_relation(X1),X2),X3) = apply(X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_17]),c_0_18]),c_0_25])]) ).
cnf(c_0_30,negated_conjecture,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_31,negated_conjecture,
function(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_32,negated_conjecture,
in(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU008+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:46:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.44 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
% 0.43/0.55 % Version: 3.5.1
% 0.43/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.43/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.43/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.43/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.43/0.55 % Starting sh5l with 300s (1) cores
% 0.43/0.55 % new_bool_1 with pid 1810761 completed with status 0
% 0.43/0.55 % Result found by new_bool_1
% 0.43/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.43/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.43/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.43/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.43/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.43/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.43/0.55 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.43/0.55 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.43/0.55 % Starting SubtermCWHack with 28s (1) cores
% 0.43/0.55 % SubtermCWHack with pid 1810764 completed with status 0
% 0.43/0.55 % Result found by SubtermCWHack
% 0.43/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.43/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.43/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.43/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.43/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.43/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.43/0.55 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.43/0.55 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.43/0.55 % Starting SubtermCWHack with 28s (1) cores
% 0.43/0.55 % Preprocessing time : 0.001 s
% 0.43/0.55
% 0.43/0.55 % Proof found!
% 0.43/0.55 % SZS status Theorem
% 0.43/0.55 % SZS output start CNFRefutation
% See solution above
% 0.43/0.55 % Parsed axioms : 41
% 0.43/0.55 % Removed by relevancy pruning/SinE : 4
% 0.43/0.55 % Initial clauses : 59
% 0.43/0.55 % Removed in clause preprocessing : 0
% 0.43/0.55 % Initial clauses in saturation : 59
% 0.43/0.55 % Processed clauses : 825
% 0.43/0.55 % ...of these trivial : 4
% 0.43/0.55 % ...subsumed : 558
% 0.43/0.55 % ...remaining for further processing : 263
% 0.43/0.55 % Other redundant clauses eliminated : 7
% 0.43/0.55 % Clauses deleted for lack of memory : 0
% 0.43/0.55 % Backward-subsumed : 15
% 0.43/0.55 % Backward-rewritten : 12
% 0.43/0.55 % Generated clauses : 3465
% 0.43/0.55 % ...of the previous two non-redundant : 2729
% 0.43/0.55 % ...aggressively subsumed : 0
% 0.43/0.55 % Contextual simplify-reflections : 1
% 0.43/0.55 % Paramodulations : 3454
% 0.43/0.55 % Factorizations : 4
% 0.43/0.55 % NegExts : 0
% 0.43/0.55 % Equation resolutions : 7
% 0.43/0.55 % Disequality decompositions : 0
% 0.43/0.55 % Total rewrite steps : 1237
% 0.43/0.55 % ...of those cached : 1198
% 0.43/0.55 % Propositional unsat checks : 0
% 0.43/0.55 % Propositional check models : 0
% 0.43/0.55 % Propositional check unsatisfiable : 0
% 0.43/0.55 % Propositional clauses : 0
% 0.43/0.55 % Propositional clauses after purity: 0
% 0.43/0.55 % Propositional unsat core size : 0
% 0.43/0.55 % Propositional preprocessing time : 0.000
% 0.43/0.55 % Propositional encoding time : 0.000
% 0.43/0.55 % Propositional solver time : 0.000
% 0.43/0.55 % Success case prop preproc time : 0.000
% 0.43/0.55 % Success case prop encoding time : 0.000
% 0.43/0.55 % Success case prop solver time : 0.000
% 0.43/0.55 % Current number of processed clauses : 229
% 0.43/0.55 % Positive orientable unit clauses : 25
% 0.43/0.55 % Positive unorientable unit clauses: 1
% 0.43/0.55 % Negative unit clauses : 13
% 0.43/0.55 % Non-unit-clauses : 190
% 0.43/0.55 % Current number of unprocessed clauses: 1830
% 0.43/0.55 % ...number of literals in the above : 7852
% 0.43/0.55 % Current number of archived formulas : 0
% 0.43/0.55 % Current number of archived clauses : 27
% 0.43/0.55 % Clause-clause subsumption calls (NU) : 9884
% 0.43/0.55 % Rec. Clause-clause subsumption calls : 7688
% 0.43/0.55 % Non-unit clause-clause subsumptions : 513
% 0.43/0.55 % Unit Clause-clause subsumption calls : 286
% 0.43/0.55 % Rewrite failures with RHS unbound : 0
% 0.43/0.55 % BW rewrite match attempts : 15
% 0.43/0.55 % BW rewrite match successes : 14
% 0.43/0.55 % Condensation attempts : 0
% 0.43/0.55 % Condensation successes : 0
% 0.43/0.55 % Termbank termtop insertions : 36556
% 0.43/0.55 % Search garbage collected termcells : 711
% 0.43/0.55
% 0.43/0.55 % -------------------------------------------------
% 0.43/0.55 % User time : 0.055 s
% 0.43/0.55 % System time : 0.002 s
% 0.43/0.55 % Total time : 0.057 s
% 0.43/0.55 % Maximum resident set size: 3668 pages
% 0.43/0.55
% 0.43/0.55 % -------------------------------------------------
% 0.43/0.55 % User time : 0.059 s
% 0.43/0.55 % System time : 0.008 s
% 0.43/0.55 % Total time : 0.067 s
% 0.43/0.55 % Maximum resident set size: 4608 pages
% 0.43/0.55 % E exiting
%------------------------------------------------------------------------------