%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET617+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 : n014.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 02:14:45 PM UTC 2026
% Result : Theorem 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 22 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 2 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 1 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th92,conjecture,
! [X1] :
( symmetric_difference(empty_set,X1) = X1
& symmetric_difference(X1,empty_set) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th92) ).
fof(union_empty_set,axiom,
! [X1] : union(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(commutativity_of_symmetric_difference,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = symmetric_difference(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
fof(symmetric_difference_defn,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(no_difference_with_empty_set1,axiom,
! [X1] : difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_difference_with_empty_set1) ).
fof(no_difference_with_empty_set2,axiom,
! [X1] : difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_difference_with_empty_set2) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( symmetric_difference(empty_set,X1) = X1
& symmetric_difference(X1,empty_set) = X1 ),
inference(assume_negation,[status(cth)],[prove_th92]) ).
fof(c_0_8,plain,
! [X10] : union(X10,empty_set) = X10,
inference(variable_rename,[status(thm)],[union_empty_set]) ).
fof(c_0_9,plain,
! [X11,X12] : union(X11,X12) = union(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_10,negated_conjecture,
( symmetric_difference(empty_set,esk1_0) != esk1_0
| symmetric_difference(esk1_0,empty_set) != esk1_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_11,plain,
! [X7,X8] : symmetric_difference(X7,X8) = symmetric_difference(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_of_symmetric_difference]) ).
fof(c_0_12,plain,
! [X5,X6] : symmetric_difference(X5,X6) = union(difference(X5,X6),difference(X6,X5)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
fof(c_0_13,plain,
! [X13] : difference(X13,empty_set) = X13,
inference(variable_rename,[status(thm)],[no_difference_with_empty_set1]) ).
fof(c_0_14,plain,
! [X14] : difference(empty_set,X14) = empty_set,
inference(variable_rename,[status(thm)],[no_difference_with_empty_set2]) ).
cnf(c_0_15,plain,
union(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
( symmetric_difference(empty_set,esk1_0) != esk1_0
| symmetric_difference(esk1_0,empty_set) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
symmetric_difference(X1,X2) = symmetric_difference(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
union(empty_set,X1) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,negated_conjecture,
symmetric_difference(empty_set,esk1_0) != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_24,plain,
symmetric_difference(empty_set,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET617+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 05:29:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 0.09/0.44 % Version: 3.5.1
% 0.09/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.44 % Starting sh5l with 300s (1) cores
% 0.09/0.44 % new_bool_3 with pid 3228442 completed with status 0
% 0.09/0.44 % Result found by new_bool_3
% 0.09/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.44 % Search class: FGHSM-FFSF22-SFFFFFNN
% 0.09/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.44 % SubtermCWHack with pid 3228445 completed with status 0
% 0.09/0.44 % Result found by SubtermCWHack
% 0.09/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.44 % Search class: FGHSM-FFSF22-SFFFFFNN
% 0.09/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.44 % Preprocessing time : 0.001 s
% 0.09/0.44
% 0.09/0.44 % Proof found!
% 0.09/0.44 % SZS status Theorem
% 0.09/0.44 % SZS output start CNFRefutation
% See solution above
% 0.09/0.44 % Parsed axioms : 13
% 0.09/0.44 % Removed by relevancy pruning/SinE : 1
% 0.09/0.44 % Initial clauses : 19
% 0.09/0.44 % Removed in clause preprocessing : 2
% 0.09/0.44 % Initial clauses in saturation : 17
% 0.09/0.44 % Processed clauses : 23
% 0.09/0.44 % ...of these trivial : 1
% 0.09/0.44 % ...subsumed : 1
% 0.09/0.44 % ...remaining for further processing : 21
% 0.09/0.44 % Other redundant clauses eliminated : 2
% 0.09/0.44 % Clauses deleted for lack of memory : 0
% 0.09/0.44 % Backward-subsumed : 0
% 0.09/0.44 % Backward-rewritten : 1
% 0.09/0.44 % Generated clauses : 25
% 0.09/0.44 % ...of the previous two non-redundant : 15
% 0.09/0.44 % ...aggressively subsumed : 0
% 0.09/0.44 % Contextual simplify-reflections : 0
% 0.09/0.44 % Paramodulations : 21
% 0.09/0.44 % Factorizations : 2
% 0.09/0.44 % NegExts : 0
% 0.09/0.44 % Equation resolutions : 2
% 0.09/0.44 % Disequality decompositions : 0
% 0.09/0.44 % Total rewrite steps : 18
% 0.09/0.44 % ...of those cached : 9
% 0.09/0.44 % Propositional unsat checks : 0
% 0.09/0.44 % Propositional check models : 0
% 0.09/0.44 % Propositional check unsatisfiable : 0
% 0.09/0.44 % Propositional clauses : 0
% 0.09/0.44 % Propositional clauses after purity: 0
% 0.09/0.44 % Propositional unsat core size : 0
% 0.09/0.44 % Propositional preprocessing time : 0.000
% 0.09/0.44 % Propositional encoding time : 0.000
% 0.09/0.44 % Propositional solver time : 0.000
% 0.09/0.44 % Success case prop preproc time : 0.000
% 0.09/0.44 % Success case prop encoding time : 0.000
% 0.09/0.44 % Success case prop solver time : 0.000
% 0.09/0.44 % Current number of processed clauses : 18
% 0.09/0.44 % Positive orientable unit clauses : 9
% 0.09/0.44 % Positive unorientable unit clauses: 2
% 0.09/0.44 % Negative unit clauses : 1
% 0.09/0.44 % Non-unit-clauses : 6
% 0.09/0.44 % Current number of unprocessed clauses: 9
% 0.09/0.44 % ...number of literals in the above : 13
% 0.09/0.44 % Current number of archived formulas : 0
% 0.09/0.44 % Current number of archived clauses : 1
% 0.09/0.44 % Clause-clause subsumption calls (NU) : 3
% 0.09/0.44 % Rec. Clause-clause subsumption calls : 3
% 0.09/0.44 % Non-unit clause-clause subsumptions : 0
% 0.09/0.44 % Unit Clause-clause subsumption calls : 0
% 0.09/0.44 % Rewrite failures with RHS unbound : 0
% 0.09/0.44 % BW rewrite match attempts : 3
% 0.09/0.44 % BW rewrite match successes : 3
% 0.09/0.44 % Condensation attempts : 0
% 0.09/0.44 % Condensation successes : 0
% 0.09/0.44 % Termbank termtop insertions : 1104
% 0.09/0.44 % Search garbage collected termcells : 252
% 0.09/0.44
% 0.09/0.44 % -------------------------------------------------
% 0.09/0.44 % User time : 0.003 s
% 0.09/0.44 % System time : 0.003 s
% 0.09/0.44 % Total time : 0.006 s
% 0.09/0.44 % Maximum resident set size: 3636 pages
% 0.09/0.44
% 0.09/0.44 % -------------------------------------------------
% 0.09/0.44 % User time : 0.005 s
% 0.09/0.44 % System time : 0.007 s
% 0.09/0.44 % Total time : 0.012 s
% 0.09/0.44 % Maximum resident set size: 4608 pages
% 0.09/0.44 % E exiting
%------------------------------------------------------------------------------