%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET622+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 02:14:46 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th98,conjecture,
! [X1,X2,X3] : difference(X1,symmetric_difference(X2,X3)) = union(difference(X1,union(X2,X3)),intersection(intersection(X1,X2),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th98) ).
fof(associativity_of_intersection,axiom,
! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_intersection) ).
fof(difference_difference_union2,axiom,
! [X1,X2,X3] : difference(X1,difference(X2,X3)) = union(difference(X1,X2),intersection(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_difference_union2) ).
fof(symmetric_difference_and_difference,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = difference(union(X1,X2),intersection(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_and_difference) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] : difference(X1,symmetric_difference(X2,X3)) = union(difference(X1,union(X2,X3)),intersection(intersection(X1,X2),X3)),
inference(assume_negation,[status(cth)],[prove_th98]) ).
fof(c_0_5,negated_conjecture,
difference(esk1_0,symmetric_difference(esk2_0,esk3_0)) != union(difference(esk1_0,union(esk2_0,esk3_0)),intersection(intersection(esk1_0,esk2_0),esk3_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X19,X20,X21] : intersection(intersection(X19,X20),X21) = intersection(X19,intersection(X20,X21)),
inference(variable_rename,[status(thm)],[associativity_of_intersection]) ).
fof(c_0_7,plain,
! [X7,X8,X9] : difference(X7,difference(X8,X9)) = union(difference(X7,X8),intersection(X7,X9)),
inference(variable_rename,[status(thm)],[difference_difference_union2]) ).
fof(c_0_8,plain,
! [X10,X11] : symmetric_difference(X10,X11) = difference(union(X10,X11),intersection(X10,X11)),
inference(variable_rename,[status(thm)],[symmetric_difference_and_difference]) ).
cnf(c_0_9,negated_conjecture,
difference(esk1_0,symmetric_difference(esk2_0,esk3_0)) != union(difference(esk1_0,union(esk2_0,esk3_0)),intersection(intersection(esk1_0,esk2_0),esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
difference(X1,difference(X2,X3)) = union(difference(X1,X2),intersection(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
symmetric_difference(X1,X2) = difference(union(X1,X2),intersection(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET622+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n026.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 05:32:38 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.44 % Version: 3.5.1
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % new_bool_3 with pid 1463874 completed with status 0
% 0.10/0.44 % Result found by new_bool_3
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.44 % Search class: FGHSM-FFSF22-MFFFFFNN
% 0.10/0.44 % partial match(1): FGHSM-FFMF22-MFFFFFNN
% 0.10/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.44 % SubtermCWHack with pid 1463877 completed with status 0
% 0.10/0.45 % Result found by SubtermCWHack
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.45 % Search class: FGHSM-FFSF22-MFFFFFNN
% 0.10/0.45 % partial match(1): FGHSM-FFMF22-MFFFFFNN
% 0.10/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.45 % Preprocessing time : 0.001 s
% 0.10/0.45
% 0.10/0.45 % Proof found!
% 0.10/0.45 % SZS status Theorem
% 0.10/0.45 % SZS output start CNFRefutation
% See solution above
% 0.10/0.45 % Parsed axioms : 15
% 0.10/0.45 % Removed by relevancy pruning/SinE : 3
% 0.10/0.45 % Initial clauses : 21
% 0.10/0.45 % Removed in clause preprocessing : 2
% 0.10/0.45 % Initial clauses in saturation : 19
% 0.10/0.45 % Processed clauses : 88
% 0.10/0.45 % ...of these trivial : 1
% 0.10/0.45 % ...subsumed : 53
% 0.10/0.45 % ...remaining for further processing : 33
% 0.10/0.45 % Other redundant clauses eliminated : 0
% 0.10/0.45 % Clauses deleted for lack of memory : 0
% 0.10/0.45 % Backward-subsumed : 0
% 0.10/0.45 % Backward-rewritten : 0
% 0.10/0.45 % Generated clauses : 242
% 0.10/0.45 % ...of the previous two non-redundant : 228
% 0.10/0.45 % ...aggressively subsumed : 0
% 0.10/0.45 % Contextual simplify-reflections : 0
% 0.10/0.45 % Paramodulations : 240
% 0.10/0.45 % Factorizations : 2
% 0.10/0.45 % NegExts : 0
% 0.10/0.45 % Equation resolutions : 0
% 0.10/0.45 % Disequality decompositions : 0
% 0.10/0.45 % Total rewrite steps : 58
% 0.10/0.45 % ...of those cached : 30
% 0.10/0.45 % Propositional unsat checks : 0
% 0.10/0.45 % Propositional check models : 0
% 0.10/0.45 % Propositional check unsatisfiable : 0
% 0.10/0.45 % Propositional clauses : 0
% 0.10/0.45 % Propositional clauses after purity: 0
% 0.10/0.45 % Propositional unsat core size : 0
% 0.10/0.45 % Propositional preprocessing time : 0.000
% 0.10/0.45 % Propositional encoding time : 0.000
% 0.10/0.45 % Propositional solver time : 0.000
% 0.10/0.45 % Success case prop preproc time : 0.000
% 0.10/0.45 % Success case prop encoding time : 0.000
% 0.10/0.45 % Success case prop solver time : 0.000
% 0.10/0.45 % Current number of processed clauses : 33
% 0.10/0.45 % Positive orientable unit clauses : 5
% 0.10/0.45 % Positive unorientable unit clauses: 5
% 0.10/0.45 % Negative unit clauses : 0
% 0.10/0.45 % Non-unit-clauses : 23
% 0.10/0.45 % Current number of unprocessed clauses: 159
% 0.10/0.45 % ...number of literals in the above : 297
% 0.10/0.45 % Current number of archived formulas : 0
% 0.10/0.45 % Current number of archived clauses : 0
% 0.10/0.45 % Clause-clause subsumption calls (NU) : 209
% 0.10/0.45 % Rec. Clause-clause subsumption calls : 203
% 0.10/0.45 % Non-unit clause-clause subsumptions : 46
% 0.10/0.45 % Unit Clause-clause subsumption calls : 3
% 0.10/0.45 % Rewrite failures with RHS unbound : 0
% 0.10/0.45 % BW rewrite match attempts : 15
% 0.10/0.45 % BW rewrite match successes : 14
% 0.10/0.45 % Condensation attempts : 0
% 0.10/0.45 % Condensation successes : 0
% 0.10/0.45 % Termbank termtop insertions : 3234
% 0.10/0.45 % Search garbage collected termcells : 249
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.007 s
% 0.10/0.45 % System time : 0.002 s
% 0.10/0.45 % Total time : 0.009 s
% 0.10/0.45 % Maximum resident set size: 3644 pages
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.007 s
% 0.10/0.45 % System time : 0.008 s
% 0.10/0.45 % Total time : 0.015 s
% 0.10/0.45 % Maximum resident set size: 4864 pages
% 0.10/0.45 % E exiting
%------------------------------------------------------------------------------