%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET621+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 : n016.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 0.18s 0.58s
% Output : CNFRefutation 0.18s
% 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th97,conjecture,
! [X1,X2,X3] : difference(symmetric_difference(X1,X2),X3) = union(difference(X1,union(X2,X3)),difference(X2,union(X1,X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th97) ).
fof(difference_difference_union,axiom,
! [X1,X2,X3] : difference(difference(X1,X2),X3) = difference(X1,union(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_difference_union) ).
fof(difference_distributes_over_union,axiom,
! [X1,X2,X3] : difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_distributes_over_union) ).
fof(symmetric_difference_defn,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] : difference(symmetric_difference(X1,X2),X3) = union(difference(X1,union(X2,X3)),difference(X2,union(X1,X3))),
inference(assume_negation,[status(cth)],[prove_th97]) ).
fof(c_0_5,negated_conjecture,
difference(symmetric_difference(esk1_0,esk2_0),esk3_0) != union(difference(esk1_0,union(esk2_0,esk3_0)),difference(esk2_0,union(esk1_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,
! [X7,X8,X9] : difference(difference(X7,X8),X9) = difference(X7,union(X8,X9)),
inference(variable_rename,[status(thm)],[difference_difference_union]) ).
fof(c_0_7,plain,
! [X10,X11,X12] : difference(union(X10,X11),X12) = union(difference(X10,X12),difference(X11,X12)),
inference(variable_rename,[status(thm)],[difference_distributes_over_union]) ).
fof(c_0_8,plain,
! [X21,X22] : symmetric_difference(X21,X22) = union(difference(X21,X22),difference(X22,X21)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
cnf(c_0_9,negated_conjecture,
difference(symmetric_difference(esk1_0,esk2_0),esk3_0) != union(difference(esk1_0,union(esk2_0,esk3_0)),difference(esk2_0,union(esk1_0,esk3_0))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
difference(difference(X1,X2),X3) = difference(X1,union(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
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)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]),c_0_11]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET621+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.51 % Computer : n016.cluster.edu
% 0.11/0.51 % Model : x86_64 x86_64
% 0.11/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.51 % Memory : 8046.5625MB
% 0.11/0.51 % OS : Linux 6.8.0-71-generic
% 0.11/0.51 % CPULimit : 300
% 0.11/0.51 % WCLimit : 300
% 0.11/0.51 % DateTime : Mon Sep 21 05:34:53 UTC 2026
% 0.11/0.51 % CPUTime :
% 0.11/0.51 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.56 Running first-order theorem proving
% 0.18/0.56 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
% 0.18/0.58 % Version: 3.5.1
% 0.18/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.58 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.58 % Starting sh5l with 300s (1) cores
% 0.18/0.58 % new_bool_3 with pid 1657240 completed with status 0
% 0.18/0.58 % Result found by new_bool_3
% 0.18/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.58 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.18/0.58 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.18/0.58 % Search class: FGHSM-FFSF22-MFFFFFNN
% 0.18/0.58 % partial match(1): FGHSM-FFMF22-MFFFFFNN
% 0.18/0.58 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.58 % Starting SubtermCWHack with 31s (1) cores
% 0.18/0.58 % SubtermCWHack with pid 1657244 completed with status 0
% 0.18/0.58 % Result found by SubtermCWHack
% 0.18/0.58 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.18/0.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.18/0.58 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.58 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.18/0.58 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.18/0.58 % Search class: FGHSM-FFSF22-MFFFFFNN
% 0.18/0.58 % partial match(1): FGHSM-FFMF22-MFFFFFNN
% 0.18/0.58 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.58 % Starting SubtermCWHack with 31s (1) cores
% 0.18/0.58 % Preprocessing time : 0.001 s
% 0.18/0.58
% 0.18/0.58 % Proof found!
% 0.18/0.58 % SZS status Theorem
% 0.18/0.58 % SZS output start CNFRefutation
% See solution above
% 0.18/0.58 % Parsed axioms : 12
% 0.18/0.58 % Removed by relevancy pruning/SinE : 0
% 0.18/0.58 % Initial clauses : 23
% 0.18/0.58 % Removed in clause preprocessing : 2
% 0.18/0.58 % Initial clauses in saturation : 21
% 0.18/0.58 % Processed clauses : 66
% 0.18/0.58 % ...of these trivial : 0
% 0.18/0.58 % ...subsumed : 35
% 0.18/0.58 % ...remaining for further processing : 30
% 0.18/0.58 % Other redundant clauses eliminated : 2
% 0.18/0.58 % Clauses deleted for lack of memory : 0
% 0.18/0.58 % Backward-subsumed : 0
% 0.18/0.58 % Backward-rewritten : 0
% 0.18/0.58 % Generated clauses : 148
% 0.18/0.58 % ...of the previous two non-redundant : 133
% 0.18/0.58 % ...aggressively subsumed : 0
% 0.18/0.58 % Contextual simplify-reflections : 0
% 0.18/0.58 % Paramodulations : 144
% 0.18/0.58 % Factorizations : 2
% 0.18/0.58 % NegExts : 0
% 0.18/0.58 % Equation resolutions : 2
% 0.18/0.58 % Disequality decompositions : 0
% 0.18/0.58 % Total rewrite steps : 29
% 0.18/0.58 % ...of those cached : 9
% 0.18/0.58 % Propositional unsat checks : 0
% 0.18/0.58 % Propositional check models : 0
% 0.18/0.58 % Propositional check unsatisfiable : 0
% 0.18/0.58 % Propositional clauses : 0
% 0.18/0.58 % Propositional clauses after purity: 0
% 0.18/0.58 % Propositional unsat core size : 0
% 0.18/0.58 % Propositional preprocessing time : 0.000
% 0.18/0.58 % Propositional encoding time : 0.000
% 0.18/0.58 % Propositional solver time : 0.000
% 0.18/0.58 % Success case prop preproc time : 0.000
% 0.18/0.58 % Success case prop encoding time : 0.000
% 0.18/0.58 % Success case prop solver time : 0.000
% 0.18/0.58 % Current number of processed clauses : 28
% 0.18/0.58 % Positive orientable unit clauses : 5
% 0.18/0.58 % Positive unorientable unit clauses: 3
% 0.18/0.58 % Negative unit clauses : 0
% 0.18/0.58 % Non-unit-clauses : 20
% 0.18/0.58 % Current number of unprocessed clauses: 88
% 0.18/0.58 % ...number of literals in the above : 180
% 0.18/0.58 % Current number of archived formulas : 0
% 0.18/0.58 % Current number of archived clauses : 0
% 0.18/0.58 % Clause-clause subsumption calls (NU) : 164
% 0.18/0.58 % Rec. Clause-clause subsumption calls : 157
% 0.18/0.58 % Non-unit clause-clause subsumptions : 30
% 0.18/0.58 % Unit Clause-clause subsumption calls : 0
% 0.18/0.58 % Rewrite failures with RHS unbound : 0
% 0.18/0.58 % BW rewrite match attempts : 6
% 0.18/0.58 % BW rewrite match successes : 4
% 0.18/0.58 % Condensation attempts : 0
% 0.18/0.58 % Condensation successes : 0
% 0.18/0.58 % Termbank termtop insertions : 2631
% 0.18/0.58 % Search garbage collected termcells : 306
% 0.18/0.58
% 0.18/0.58 % -------------------------------------------------
% 0.18/0.58 % User time : 0.007 s
% 0.18/0.58 % System time : 0.002 s
% 0.18/0.58 % Total time : 0.009 s
% 0.18/0.58 % Maximum resident set size: 3640 pages
% 0.18/0.58
% 0.18/0.58 % -------------------------------------------------
% 0.18/0.58 % User time : 0.008 s
% 0.18/0.58 % System time : 0.008 s
% 0.18/0.58 % Total time : 0.015 s
% 0.18/0.58 % Maximum resident set size: 4864 pages
% 0.18/0.58 % E exiting
%------------------------------------------------------------------------------