%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET606+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 : n017.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 02:14:41 PM UTC 2026
% Result : Theorem 6.89s 1.45s
% Output : CNFRefutation 6.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 20 unt; 0 def)
% Number of atoms : 115 ( 17 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 103 ( 40 ~; 45 |; 12 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 129 ( 10 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
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_difference_into_intersection,conjecture,
! [X1,X2] : difference(X1,intersection(X1,X2)) = difference(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_into_intersection) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_7,plain,
! [X24,X25,X26,X27,X28] :
( ( subset(X27,X28)
| ~ member(esk3_2(X27,X28),X28) )
& ( subset(X27,X28)
| member(esk3_2(X27,X28),X27) )
& ( member(X26,X25)
| ~ member(X26,X24)
| ~ subset(X24,X25) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_defn])])])])])])]) ).
fof(c_0_8,plain,
! [X10,X11,X12] :
( ( member(X12,difference(X10,X11))
| member(X12,X11)
| ~ member(X12,X10) )
& ( ~ member(X12,difference(X10,X11))
| ~ member(X12,X11) )
& ( ~ member(X12,difference(X10,X11))
| member(X12,X10) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_9,plain,
( ~ member(esk3_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X7,X8,X9] :
( ( member(X9,intersection(X7,X8))
| ~ member(X9,X8)
| ~ member(X9,X7) )
& ( ~ member(X9,intersection(X7,X8))
| member(X9,X8) )
& ( ~ member(X9,intersection(X7,X8))
| member(X9,X7) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
cnf(c_0_12,plain,
( ~ member(esk3_2(X1,difference(X2,X3)),X2)
| member(esk3_2(X1,difference(X2,X3)),X3)
| subset(X1,difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( member(esk3_2(X1,difference(X1,X2)),X2)
| subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
( ~ member(esk3_2(difference(X1,X2),X3),X2)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_21,plain,
( member(esk3_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_22,plain,
( member(esk3_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
fof(c_0_23,plain,
! [X13,X14] :
( ( X13 = X14
| ~ subset(X14,X13)
| ~ subset(X13,X14) )
& ( X13 != X14
| subset(X14,X13) )
& ( X13 != X14
| subset(X13,X14) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_24,plain,
( ~ member(esk3_2(X1,difference(X1,difference(X2,X3))),X3)
| subset(X1,difference(X1,difference(X2,X3))) ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_25,plain,
( member(esk3_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_26,plain,
( ~ member(esk3_2(X1,intersection(X2,X3)),X2)
| ~ member(esk3_2(X1,intersection(X2,X3)),X3)
| subset(X1,intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_9,c_0_19]) ).
cnf(c_0_27,plain,
( ~ member(esk3_2(difference(X1,difference(X2,X3)),X4),X2)
| member(esk3_2(difference(X1,difference(X2,X3)),X4),X3)
| subset(difference(X1,difference(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_20,c_0_10]) ).
cnf(c_0_28,plain,
( ~ member(esk3_2(intersection(difference(X1,X2),X3),X4),X2)
| subset(intersection(difference(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_29,plain,
( member(esk3_2(intersection(X1,X2),difference(X2,X3)),X3)
| subset(intersection(X1,X2),difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_22]) ).
cnf(c_0_30,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
subset(X1,difference(X1,difference(X2,X1))),
inference(spm,[status(thm)],[c_0_24,c_0_13]) ).
cnf(c_0_32,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_9,c_0_25]) ).
cnf(c_0_33,plain,
( ~ member(esk3_2(difference(X1,X2),intersection(X3,X1)),X3)
| subset(difference(X1,X2),intersection(X3,X1)) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_34,plain,
( member(esk3_2(difference(X1,difference(X1,X2)),X3),X2)
| subset(difference(X1,difference(X1,X2)),X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_35,plain,
subset(intersection(difference(X1,X2),X3),difference(X3,X2)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
difference(X1,difference(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_37,plain,
( ~ member(esk3_2(X1,intersection(X2,X1)),X2)
| subset(X1,intersection(X2,X1)) ),
inference(spm,[status(thm)],[c_0_26,c_0_13]) ).
cnf(c_0_38,plain,
subset(difference(X1,difference(X1,X2)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
subset(intersection(X1,X2),difference(X2,difference(X3,X1))),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_40,plain,
! [X15,X16] : intersection(X15,X16) = intersection(X16,X15),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_41,plain,
subset(difference(X1,X2),intersection(X1,difference(X1,X2))),
inference(spm,[status(thm)],[c_0_37,c_0_25]) ).
cnf(c_0_42,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_9,c_0_22]) ).
fof(c_0_43,negated_conjecture,
~ ! [X1,X2] : difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(assume_negation,[status(cth)],[prove_difference_into_intersection]) ).
cnf(c_0_44,plain,
difference(X1,difference(X1,X2)) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_38]),c_0_39])]) ).
cnf(c_0_45,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
intersection(X1,difference(X1,X2)) = difference(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_41]),c_0_42])]) ).
fof(c_0_47,negated_conjecture,
difference(esk4_0,intersection(esk4_0,esk5_0)) != difference(esk4_0,esk5_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])]) ).
cnf(c_0_48,plain,
difference(X1,intersection(X2,X1)) = difference(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_44]),c_0_45]),c_0_46]) ).
cnf(c_0_49,negated_conjecture,
difference(esk4_0,intersection(esk4_0,esk5_0)) != difference(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_50,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_48,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET606+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 05:23:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 6.89/1.45 % Version: 3.5.1
% 6.89/1.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 6.89/1.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.89/1.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.89/1.45 % Starting new_bool_3 with 300s (1) cores
% 6.89/1.45 % Starting new_bool_1 with 300s (1) cores
% 6.89/1.45 % Starting sh5l with 300s (1) cores
% 6.89/1.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1515620 completed with status 0
% 6.89/1.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 6.89/1.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 6.89/1.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.89/1.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.89/1.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.89/1.45 % No SInE strategy applied
% 6.89/1.45 % Search class: FGHSS-FFSF22-SFFFFFNN
% 6.89/1.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.89/1.45 % Starting SubtermCWHack with 136s (1) cores
% 6.89/1.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 6.89/1.45 % Starting G----_0010_evo with 136s (1) cores
% 6.89/1.45 % Starting new_bool_3 with 136s (1) cores
% 6.89/1.45 % Starting new_bool_1 with 136s (1) cores
% 6.89/1.45 % SubtermCWHack with pid 1515625 completed with status 0
% 6.89/1.45 % Result found by SubtermCWHack
% 6.89/1.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 6.89/1.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.89/1.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.89/1.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.89/1.45 % No SInE strategy applied
% 6.89/1.45 % Search class: FGHSS-FFSF22-SFFFFFNN
% 6.89/1.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.89/1.45 % Starting SubtermCWHack with 136s (1) cores
% 6.89/1.45 % Preprocessing time : 0.001 s
% 6.89/1.45
% 6.89/1.45 % Proof found!
% 6.89/1.45 % SZS status Theorem
% 6.89/1.45 % SZS output start CNFRefutation
% See solution above
% 6.89/1.45 % Parsed axioms : 9
% 6.89/1.45 % Removed by relevancy pruning/SinE : 0
% 6.89/1.45 % Initial clauses : 21
% 6.89/1.45 % Removed in clause preprocessing : 2
% 6.89/1.45 % Initial clauses in saturation : 19
% 6.89/1.45 % Processed clauses : 10656
% 6.89/1.45 % ...of these trivial : 427
% 6.89/1.45 % ...subsumed : 9510
% 6.89/1.45 % ...remaining for further processing : 719
% 6.89/1.45 % Other redundant clauses eliminated : 2
% 6.89/1.45 % Clauses deleted for lack of memory : 0
% 6.89/1.45 % Backward-subsumed : 5
% 6.89/1.45 % Backward-rewritten : 65
% 6.89/1.45 % Generated clauses : 122086
% 6.89/1.45 % ...of the previous two non-redundant : 88370
% 6.89/1.45 % ...aggressively subsumed : 0
% 6.89/1.45 % Contextual simplify-reflections : 5
% 6.89/1.45 % Paramodulations : 121892
% 6.89/1.45 % Factorizations : 192
% 6.89/1.45 % NegExts : 0
% 6.89/1.45 % Equation resolutions : 2
% 6.89/1.45 % Disequality decompositions : 0
% 6.89/1.45 % Total rewrite steps : 96156
% 6.89/1.45 % ...of those cached : 89810
% 6.89/1.45 % Propositional unsat checks : 0
% 6.89/1.45 % Propositional check models : 0
% 6.89/1.45 % Propositional check unsatisfiable : 0
% 6.89/1.45 % Propositional clauses : 0
% 6.89/1.45 % Propositional clauses after purity: 0
% 6.89/1.45 % Propositional unsat core size : 0
% 6.89/1.45 % Propositional preprocessing time : 0.000
% 6.89/1.45 % Propositional encoding time : 0.000
% 6.89/1.45 % Propositional solver time : 0.000
% 6.89/1.45 % Success case prop preproc time : 0.000
% 6.89/1.45 % Success case prop encoding time : 0.000
% 6.89/1.45 % Success case prop solver time : 0.000
% 6.89/1.45 % Current number of processed clauses : 647
% 6.89/1.45 % Positive orientable unit clauses : 189
% 6.89/1.45 % Positive unorientable unit clauses: 23
% 6.89/1.45 % Negative unit clauses : 47
% 6.89/1.45 % Non-unit-clauses : 388
% 6.89/1.45 % Current number of unprocessed clauses: 77362
% 6.89/1.45 % ...number of literals in the above : 158370
% 6.89/1.45 % Current number of archived formulas : 0
% 6.89/1.45 % Current number of archived clauses : 70
% 6.89/1.45 % Clause-clause subsumption calls (NU) : 34185
% 6.89/1.45 % Rec. Clause-clause subsumption calls : 20401
% 6.89/1.45 % Non-unit clause-clause subsumptions : 1345
% 6.89/1.45 % Unit Clause-clause subsumption calls : 19086
% 6.89/1.45 % Rewrite failures with RHS unbound : 2009
% 6.89/1.45 % BW rewrite match attempts : 3802
% 6.89/1.45 % BW rewrite match successes : 221
% 6.89/1.45 % Condensation attempts : 0
% 6.89/1.45 % Condensation successes : 0
% 6.89/1.45 % Termbank termtop insertions : 1269247
% 6.89/1.45 % Search garbage collected termcells : 346
% 6.89/1.45
% 6.89/1.45 % -------------------------------------------------
% 6.89/1.45 % User time : 0.952 s
% 6.89/1.45 % System time : 0.043 s
% 6.89/1.45 % Total time : 0.995 s
% 6.89/1.45 % Maximum resident set size: 3636 pages
% 6.89/1.45
% 6.89/1.45 % -------------------------------------------------
% 6.89/1.45 % User time : 4.780 s
% 6.89/1.45 % System time : 0.237 s
% 6.89/1.45 % Total time : 5.017 s
% 6.89/1.45 % Maximum resident set size: 4608 pages
% 6.89/1.45 % E exiting
%------------------------------------------------------------------------------