%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET635+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 02:14:50 PM UTC 2026
% Result : Theorem 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 26 unt; 0 def)
% Number of atoms : 34 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 3 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_empty_set,axiom,
! [X1,X2] :
( difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_empty_set) ).
fof(reflexivity_of_subset,axiom,
! [X1] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(difference_and_intersection_and_union,axiom,
! [X1,X2,X3] : difference(X1,intersection(X2,X3)) = union(difference(X1,X2),difference(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection_and_union) ).
fof(union_empty_set,axiom,
! [X1] : union(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).
fof(prove_th117,conjecture,
! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),intersection(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th117) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(difference_and_intersection,axiom,
! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection) ).
fof(c_0_7,plain,
! [X6,X7] :
( ( difference(X6,X7) = empty_set
| ~ subset(X6,X7) )
& ( subset(X6,X7)
| difference(X6,X7) != empty_set ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[difference_empty_set])])]) ).
fof(c_0_8,plain,
! [X34] : subset(X34,X34),
inference(variable_rename,[status(thm)],[reflexivity_of_subset]) ).
fof(c_0_9,plain,
! [X9,X10,X11] : difference(X9,intersection(X10,X11)) = union(difference(X9,X10),difference(X9,X11)),
inference(variable_rename,[status(thm)],[difference_and_intersection_and_union]) ).
cnf(c_0_10,plain,
( ~ subset(X1,X2)
| difference(X1,X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X8] : union(X8,empty_set) = X8,
inference(variable_rename,[status(thm)],[union_empty_set]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),intersection(X1,X3)),
inference(assume_negation,[status(cth)],[prove_th117]) ).
cnf(c_0_14,plain,
difference(X1,intersection(X2,X3)) = union(difference(X1,X2),difference(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
difference(X1,X1) = empty_set,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
union(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X26,X27] : intersection(X26,X27) = intersection(X27,X26),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_18,negated_conjecture,
intersection(esk4_0,difference(esk5_0,esk6_0)) != difference(intersection(esk4_0,esk5_0),intersection(esk4_0,esk6_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_19,plain,
! [X12,X13,X14] : intersection(X12,difference(X13,X14)) = difference(intersection(X12,X13),X14),
inference(variable_rename,[status(thm)],[difference_and_intersection]) ).
cnf(c_0_20,plain,
difference(X1,intersection(X2,X1)) = difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_21,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
intersection(esk4_0,difference(esk5_0,esk6_0)) != difference(intersection(esk4_0,esk5_0),intersection(esk4_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
difference(X1,intersection(intersection(X2,X1),X3)) = difference(X1,intersection(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_20]),c_0_14]) ).
cnf(c_0_26,negated_conjecture,
intersection(esk4_0,difference(esk5_0,intersection(esk4_0,esk6_0))) != intersection(esk4_0,difference(esk5_0,esk6_0)),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
intersection(X1,difference(X2,intersection(X1,X3))) = intersection(X1,difference(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_23]),c_0_25]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET635+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:30:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.47 % Version: 3.5.1
% 0.14/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.47 % Starting sh5l with 300s (1) cores
% 0.14/0.47 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3231607 completed with status 0
% 0.14/0.47 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.47 % No SInE strategy applied
% 0.14/0.47 % Search class: FGHSM-FFMF21-SFFFFFNN
% 0.14/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.47 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.47 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.47 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.47 % new_bool_3 with pid 3231617 completed with status 0
% 0.14/0.47 % Result found by new_bool_3
% 0.14/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.47 % No SInE strategy applied
% 0.14/0.47 % Search class: FGHSM-FFMF21-SFFFFFNN
% 0.14/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.47 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.47 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.47 % Preprocessing time : 0.002 s
% 0.14/0.47 % Presaturation interreduction done
% 0.14/0.47
% 0.14/0.47 % Proof found!
% 0.14/0.47 % SZS status Theorem
% 0.14/0.47 % SZS output start CNFRefutation
% See solution above
% 0.14/0.47 % Parsed axioms : 16
% 0.14/0.47 % Removed by relevancy pruning/SinE : 0
% 0.14/0.47 % Initial clauses : 29
% 0.14/0.47 % Removed in clause preprocessing : 2
% 0.14/0.47 % Initial clauses in saturation : 27
% 0.14/0.47 % Processed clauses : 479
% 0.14/0.47 % ...of these trivial : 26
% 0.14/0.47 % ...subsumed : 313
% 0.14/0.47 % ...remaining for further processing : 140
% 0.14/0.47 % Other redundant clauses eliminated : 19
% 0.14/0.47 % Clauses deleted for lack of memory : 0
% 0.14/0.47 % Backward-subsumed : 1
% 0.14/0.47 % Backward-rewritten : 9
% 0.14/0.47 % Generated clauses : 2181
% 0.14/0.47 % ...of the previous two non-redundant : 1603
% 0.14/0.47 % ...aggressively subsumed : 0
% 0.14/0.47 % Contextual simplify-reflections : 2
% 0.14/0.47 % Paramodulations : 2160
% 0.14/0.47 % Factorizations : 2
% 0.14/0.47 % NegExts : 0
% 0.14/0.47 % Equation resolutions : 19
% 0.14/0.47 % Disequality decompositions : 0
% 0.14/0.47 % Total rewrite steps : 1150
% 0.14/0.47 % ...of those cached : 911
% 0.14/0.47 % Propositional unsat checks : 0
% 0.14/0.47 % Propositional check models : 0
% 0.14/0.47 % Propositional check unsatisfiable : 0
% 0.14/0.47 % Propositional clauses : 0
% 0.14/0.47 % Propositional clauses after purity: 0
% 0.14/0.47 % Propositional unsat core size : 0
% 0.14/0.47 % Propositional preprocessing time : 0.000
% 0.14/0.47 % Propositional encoding time : 0.000
% 0.14/0.47 % Propositional solver time : 0.000
% 0.14/0.47 % Success case prop preproc time : 0.000
% 0.14/0.47 % Success case prop encoding time : 0.000
% 0.14/0.47 % Success case prop solver time : 0.000
% 0.14/0.47 % Current number of processed clauses : 103
% 0.14/0.47 % Positive orientable unit clauses : 30
% 0.14/0.47 % Positive unorientable unit clauses: 4
% 0.14/0.47 % Negative unit clauses : 3
% 0.14/0.47 % Non-unit-clauses : 66
% 0.14/0.47 % Current number of unprocessed clauses: 1161
% 0.14/0.47 % ...number of literals in the above : 2523
% 0.14/0.47 % Current number of archived formulas : 0
% 0.14/0.47 % Current number of archived clauses : 35
% 0.14/0.47 % Clause-clause subsumption calls (NU) : 1264
% 0.14/0.47 % Rec. Clause-clause subsumption calls : 1227
% 0.14/0.47 % Non-unit clause-clause subsumptions : 226
% 0.14/0.47 % Unit Clause-clause subsumption calls : 29
% 0.14/0.47 % Rewrite failures with RHS unbound : 0
% 0.14/0.47 % BW rewrite match attempts : 73
% 0.14/0.47 % BW rewrite match successes : 26
% 0.14/0.47 % Condensation attempts : 0
% 0.14/0.47 % Condensation successes : 0
% 0.14/0.47 % Termbank termtop insertions : 17730
% 0.14/0.47 % Search garbage collected termcells : 368
% 0.14/0.47
% 0.14/0.47 % -------------------------------------------------
% 0.14/0.47 % User time : 0.034 s
% 0.14/0.47 % System time : 0.006 s
% 0.14/0.47 % Total time : 0.040 s
% 0.14/0.47 % Maximum resident set size: 3640 pages
% 0.14/0.47
% 0.14/0.47 % -------------------------------------------------
% 0.14/0.47 % User time : 0.161 s
% 0.14/0.47 % System time : 0.022 s
% 0.14/0.47 % Total time : 0.182 s
% 0.14/0.47 % Maximum resident set size: 4864 pages
% 0.14/0.47 % E exiting
%------------------------------------------------------------------------------