%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET619+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 : n006.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 0.15s 5.46s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 29 unt; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 53 ( 2 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th95,conjecture,
! [X1,X2] : union(X1,X2) = union(symmetric_difference(X1,X2),intersection(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th95) ).
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(associativity_of_union,axiom,
! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_union) ).
fof(union_intersection,axiom,
! [X1,X2] : union(X1,intersection(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_intersection) ).
fof(union_intersection_difference,axiom,
! [X1,X2] : union(intersection(X1,X2),difference(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_intersection_difference) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] : union(X1,X2) = union(symmetric_difference(X1,X2),intersection(X1,X2)),
inference(assume_negation,[status(cth)],[prove_th95]) ).
fof(c_0_8,negated_conjecture,
union(esk3_0,esk4_0) != union(symmetric_difference(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_7])])])]) ).
fof(c_0_9,plain,
! [X4,X5] : symmetric_difference(X4,X5) = union(difference(X4,X5),difference(X5,X4)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
fof(c_0_10,plain,
! [X6,X7,X8] : union(union(X6,X7),X8) = union(X6,union(X7,X8)),
inference(variable_rename,[status(thm)],[associativity_of_union]) ).
fof(c_0_11,plain,
! [X9,X10] : union(X9,intersection(X9,X10)) = X9,
inference(variable_rename,[status(thm)],[union_intersection]) ).
fof(c_0_12,plain,
! [X11,X12] : union(intersection(X11,X12),difference(X11,X12)) = X11,
inference(variable_rename,[status(thm)],[union_intersection_difference]) ).
fof(c_0_13,plain,
! [X23,X24] : intersection(X23,X24) = intersection(X24,X23),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_14,negated_conjecture,
union(esk3_0,esk4_0) != union(symmetric_difference(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_16,plain,
! [X21,X22] : union(X21,X22) = union(X22,X21),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_17,plain,
union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
union(X1,intersection(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
union(intersection(X1,X2),difference(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
union(esk3_0,esk4_0) != union(union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)),intersection(esk3_0,esk4_0)),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
union(X1,union(intersection(X1,X2),X3)) = union(X1,X3),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
union(intersection(X1,X2),difference(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
union(intersection(esk3_0,esk4_0),union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))) != union(esk3_0,esk4_0),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
union(intersection(X1,X2),union(difference(X1,X2),X3)) = union(X1,X3),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_27,plain,
union(X1,difference(X2,X1)) = union(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET619+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/5.38 % Computer : n006.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Mon Sep 21 05:29:32 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 0.15/5.46 % Version: 3.5.1
% 0.15/5.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.46 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.46 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.46 % Starting sh5l with 300s (1) cores
% 0.15/5.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2091072 completed with status 0
% 0.15/5.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/5.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.46 % No SInE strategy applied
% 0.15/5.46 % Search class: FGUSM-FFMF22-MFFFFFNN
% 0.15/5.46 % partial match(1): FGUSM-FFMF21-MFFFFFNN
% 0.15/5.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.46 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/5.46 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S0S with 136s (1) cores
% 0.15/5.46 % Starting new_bool_3 with 136s (1) cores
% 0.15/5.46 % Starting new_bool_1 with 136s (1) cores
% 0.15/5.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2091077 completed with status 0
% 0.15/5.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/5.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.46 % No SInE strategy applied
% 0.15/5.46 % Search class: FGUSM-FFMF22-MFFFFFNN
% 0.15/5.46 % partial match(1): FGUSM-FFMF21-MFFFFFNN
% 0.15/5.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.46 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/5.46 % Preprocessing time : 0.001 s
% 0.15/5.46 % Presaturation interreduction done
% 0.15/5.46
% 0.15/5.46 % Proof found!
% 0.15/5.46 % SZS status Theorem
% 0.15/5.46 % SZS output start CNFRefutation
% See solution above
% 0.15/5.46 % Parsed axioms : 14
% 0.15/5.46 % Removed by relevancy pruning/SinE : 0
% 0.15/5.46 % Initial clauses : 25
% 0.15/5.46 % Removed in clause preprocessing : 3
% 0.15/5.46 % Initial clauses in saturation : 22
% 0.15/5.46 % Processed clauses : 105
% 0.15/5.46 % ...of these trivial : 18
% 0.15/5.46 % ...subsumed : 20
% 0.15/5.46 % ...remaining for further processing : 67
% 0.15/5.46 % Other redundant clauses eliminated : 2
% 0.15/5.46 % Clauses deleted for lack of memory : 0
% 0.15/5.46 % Backward-subsumed : 0
% 0.15/5.46 % Backward-rewritten : 2
% 0.15/5.46 % Generated clauses : 420
% 0.15/5.46 % ...of the previous two non-redundant : 309
% 0.15/5.46 % ...aggressively subsumed : 0
% 0.15/5.46 % Contextual simplify-reflections : 0
% 0.15/5.46 % Paramodulations : 416
% 0.15/5.46 % Factorizations : 2
% 0.15/5.46 % NegExts : 0
% 0.15/5.46 % Equation resolutions : 2
% 0.15/5.46 % Disequality decompositions : 0
% 0.15/5.46 % Total rewrite steps : 187
% 0.15/5.46 % ...of those cached : 111
% 0.15/5.46 % Propositional unsat checks : 0
% 0.15/5.46 % Propositional check models : 0
% 0.15/5.46 % Propositional check unsatisfiable : 0
% 0.15/5.46 % Propositional clauses : 0
% 0.15/5.46 % Propositional clauses after purity: 0
% 0.15/5.46 % Propositional unsat core size : 0
% 0.15/5.46 % Propositional preprocessing time : 0.000
% 0.15/5.46 % Propositional encoding time : 0.000
% 0.15/5.46 % Propositional solver time : 0.000
% 0.15/5.46 % Success case prop preproc time : 0.000
% 0.15/5.46 % Success case prop encoding time : 0.000
% 0.15/5.46 % Success case prop solver time : 0.000
% 0.15/5.46 % Current number of processed clauses : 44
% 0.15/5.46 % Positive orientable unit clauses : 22
% 0.15/5.46 % Positive unorientable unit clauses: 3
% 0.15/5.46 % Negative unit clauses : 0
% 0.15/5.46 % Non-unit-clauses : 19
% 0.15/5.46 % Current number of unprocessed clauses: 245
% 0.15/5.46 % ...number of literals in the above : 392
% 0.15/5.46 % Current number of archived formulas : 0
% 0.15/5.46 % Current number of archived clauses : 22
% 0.15/5.46 % Clause-clause subsumption calls (NU) : 174
% 0.15/5.46 % Rec. Clause-clause subsumption calls : 152
% 0.15/5.46 % Non-unit clause-clause subsumptions : 14
% 0.15/5.46 % Unit Clause-clause subsumption calls : 2
% 0.15/5.46 % Rewrite failures with RHS unbound : 0
% 0.15/5.46 % BW rewrite match attempts : 59
% 0.15/5.46 % BW rewrite match successes : 41
% 0.15/5.46 % Condensation attempts : 0
% 0.15/5.46 % Condensation successes : 0
% 0.15/5.46 % Termbank termtop insertions : 4442
% 0.15/5.46 % Search garbage collected termcells : 307
% 0.15/5.46
% 0.15/5.46 % -------------------------------------------------
% 0.15/5.46 % User time : 0.007 s
% 0.15/5.46 % System time : 0.005 s
% 0.15/5.46 % Total time : 0.011 s
% 0.15/5.46 % Maximum resident set size: 3640 pages
% 0.15/5.46
% 0.15/5.46 % -------------------------------------------------
% 0.15/5.46 % User time : 0.027 s
% 0.15/5.46 % System time : 0.017 s
% 0.15/5.46 % Total time : 0.043 s
% 0.15/5.46 % Maximum resident set size: 4864 pages
% 0.15/5.46 % E exiting
%------------------------------------------------------------------------------