%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET620+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 : n007.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 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_into_intersection,axiom,
! [X1,X2] : difference(X1,intersection(X1,X2)) = difference(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_into_intersection) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(prove_th96,conjecture,
! [X1,X2] : symmetric_difference(X1,X2) = difference(union(X1,X2),intersection(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th96) ).
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(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_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_6,plain,
! [X6,X7] : difference(X6,intersection(X6,X7)) = difference(X6,X7),
inference(variable_rename,[status(thm)],[difference_into_intersection]) ).
fof(c_0_7,plain,
! [X24,X25] : intersection(X24,X25) = intersection(X25,X24),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] : symmetric_difference(X1,X2) = difference(union(X1,X2),intersection(X1,X2)),
inference(assume_negation,[status(cth)],[prove_th96]) ).
fof(c_0_9,plain,
! [X8,X9,X10] : difference(union(X8,X9),X10) = union(difference(X8,X10),difference(X9,X10)),
inference(variable_rename,[status(thm)],[difference_distributes_over_union]) ).
cnf(c_0_10,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X22,X23] : union(X22,X23) = union(X23,X22),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_13,negated_conjecture,
symmetric_difference(esk3_0,esk4_0) != difference(union(esk3_0,esk4_0),intersection(esk3_0,esk4_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_14,plain,
! [X4,X5] : symmetric_difference(X4,X5) = union(difference(X4,X5),difference(X5,X4)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
cnf(c_0_15,plain,
difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
difference(X1,intersection(X2,X1)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
symmetric_difference(esk3_0,esk4_0) != difference(union(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
union(difference(X1,X2),difference(X3,intersection(X2,X1))) = difference(union(X3,X1),intersection(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,negated_conjecture,
union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)) != difference(union(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
difference(union(X1,X2),intersection(X1,X2)) = union(difference(X2,X1),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_10]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET620+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:27:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.43 % Version: 3.5.1
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % Starting sh5l with 300s (1) cores
% 0.14/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 264099 completed with status 0
% 0.14/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.43 % No SInE strategy applied
% 0.14/0.43 % Search class: FGHSM-FFMF22-SFFFFFNN
% 0.14/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.43 % Starting G-E--_107_C18_F1_AE_Q4_CS_SP_CO_S0Y with 136s (1) cores
% 0.14/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.43 % new_bool_1 with pid 264107 completed with status 0
% 0.14/0.43 % Result found by new_bool_1
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.43 % No SInE strategy applied
% 0.14/0.43 % Search class: FGHSM-FFMF22-SFFFFFNN
% 0.14/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.43 % Starting G-E--_107_C18_F1_AE_Q4_CS_SP_CO_S0Y with 136s (1) cores
% 0.14/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.43 % Preprocessing time : 0.001 s
% 0.14/0.43 % Presaturation interreduction done
% 0.14/0.43
% 0.14/0.43 % Proof found!
% 0.14/0.43 % SZS status Theorem
% 0.14/0.43 % SZS output start CNFRefutation
% See solution above
% 0.14/0.43 % Parsed axioms : 14
% 0.14/0.43 % Removed by relevancy pruning/SinE : 0
% 0.14/0.43 % Initial clauses : 27
% 0.14/0.43 % Removed in clause preprocessing : 3
% 0.14/0.43 % Initial clauses in saturation : 24
% 0.14/0.43 % Processed clauses : 216
% 0.14/0.43 % ...of these trivial : 15
% 0.14/0.43 % ...subsumed : 95
% 0.14/0.43 % ...remaining for further processing : 106
% 0.14/0.43 % Other redundant clauses eliminated : 2
% 0.14/0.43 % Clauses deleted for lack of memory : 0
% 0.14/0.43 % Backward-subsumed : 4
% 0.14/0.43 % Backward-rewritten : 1
% 0.14/0.43 % Generated clauses : 1016
% 0.14/0.43 % ...of the previous two non-redundant : 835
% 0.14/0.43 % ...aggressively subsumed : 0
% 0.14/0.43 % Contextual simplify-reflections : 0
% 0.14/0.43 % Paramodulations : 1006
% 0.14/0.43 % Factorizations : 8
% 0.14/0.43 % NegExts : 0
% 0.14/0.43 % Equation resolutions : 2
% 0.14/0.43 % Disequality decompositions : 0
% 0.14/0.43 % Total rewrite steps : 258
% 0.14/0.43 % ...of those cached : 171
% 0.14/0.43 % Propositional unsat checks : 0
% 0.14/0.43 % Propositional check models : 0
% 0.14/0.43 % Propositional check unsatisfiable : 0
% 0.14/0.43 % Propositional clauses : 0
% 0.14/0.43 % Propositional clauses after purity: 0
% 0.14/0.43 % Propositional unsat core size : 0
% 0.14/0.43 % Propositional preprocessing time : 0.000
% 0.14/0.43 % Propositional encoding time : 0.000
% 0.14/0.43 % Propositional solver time : 0.000
% 0.14/0.43 % Success case prop preproc time : 0.000
% 0.14/0.43 % Success case prop encoding time : 0.000
% 0.14/0.43 % Success case prop solver time : 0.000
% 0.14/0.43 % Current number of processed clauses : 78
% 0.14/0.43 % Positive orientable unit clauses : 24
% 0.14/0.43 % Positive unorientable unit clauses: 3
% 0.14/0.43 % Negative unit clauses : 0
% 0.14/0.43 % Non-unit-clauses : 51
% 0.14/0.43 % Current number of unprocessed clauses: 661
% 0.14/0.43 % ...number of literals in the above : 1437
% 0.14/0.43 % Current number of archived formulas : 0
% 0.14/0.43 % Current number of archived clauses : 27
% 0.14/0.43 % Clause-clause subsumption calls (NU) : 697
% 0.14/0.43 % Rec. Clause-clause subsumption calls : 630
% 0.14/0.43 % Non-unit clause-clause subsumptions : 88
% 0.14/0.43 % Unit Clause-clause subsumption calls : 19
% 0.14/0.43 % Rewrite failures with RHS unbound : 26
% 0.14/0.43 % BW rewrite match attempts : 58
% 0.14/0.43 % BW rewrite match successes : 21
% 0.14/0.43 % Condensation attempts : 0
% 0.14/0.43 % Condensation successes : 0
% 0.14/0.43 % Termbank termtop insertions : 12534
% 0.14/0.43 % Search garbage collected termcells : 330
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.010 s
% 0.14/0.43 % System time : 0.003 s
% 0.14/0.43 % Total time : 0.013 s
% 0.14/0.43 % Maximum resident set size: 3640 pages
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.053 s
% 0.14/0.43 % System time : 0.013 s
% 0.14/0.43 % Total time : 0.067 s
% 0.14/0.43 % Maximum resident set size: 4608 pages
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------