%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET594+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 : n005.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 02:17:25 PM UTC 2026
% Result : Theorem 4.00s 1.01s
% Output : CNFRefutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 6 unt; 0 def)
% Number of atoms : 73 ( 7 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 70 ( 25 ~; 31 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 3 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th53,conjecture,
! [X1,X2,X3] :
( union(intersection(X1,X2),intersection(X1,X3)) = X1
=> subset(X1,union(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th53) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X2)
| member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_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(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(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_5,negated_conjecture,
~ ! [X1,X2,X3] :
( union(intersection(X1,X2),intersection(X1,X3)) = X1
=> subset(X1,union(X2,X3)) ),
inference(assume_negation,[status(cth)],[prove_th53]) ).
fof(c_0_6,plain,
! [X16,X17,X18] :
( ( member(X18,union(X16,X17))
| ~ member(X18,X17) )
& ( member(X18,union(X16,X17))
| ~ member(X18,X16) )
& ( member(X18,X17)
| member(X18,X16)
| ~ member(X18,union(X16,X17)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])]) ).
fof(c_0_7,negated_conjecture,
( ~ subset(esk1_0,union(esk2_0,esk3_0))
& union(intersection(esk1_0,esk2_0),intersection(esk1_0,esk3_0)) = esk1_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_8,plain,
! [X21,X22,X23] :
( ( member(X23,intersection(X21,X22))
| ~ member(X23,X22)
| ~ member(X23,X21) )
& ( ~ member(X23,intersection(X21,X22))
| member(X23,X22) )
& ( ~ member(X23,intersection(X21,X22))
| member(X23,X21) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
cnf(c_0_9,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
union(intersection(esk1_0,esk2_0),intersection(esk1_0,esk3_0)) = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X7,X8,X9,X10,X11] :
( ( subset(X10,X11)
| ~ member(esk4_2(X10,X11),X11) )
& ( subset(X10,X11)
| member(esk4_2(X10,X11),X10) )
& ( member(X9,X8)
| ~ member(X9,X7)
| ~ subset(X7,X8) ) ),
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])])])])])])]) ).
cnf(c_0_12,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( ~ member(X1,esk1_0)
| member(X1,intersection(esk1_0,esk2_0))
| member(X1,intersection(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( ~ member(esk4_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
( ~ member(X1,esk1_0)
| member(X1,esk3_0)
| member(X1,intersection(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,plain,
( ~ member(esk4_2(X1,union(X2,X3)),X2)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( ~ member(X1,esk1_0)
| member(X1,esk2_0)
| member(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
fof(c_0_20,plain,
! [X19,X20] : union(X19,X20) = union(X20,X19),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_21,plain,
( ~ member(esk4_2(X1,union(X2,X3)),X3)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( ~ member(esk4_2(X1,union(esk3_0,X2)),esk1_0)
| subset(X1,union(esk3_0,X2))
| member(esk4_2(X1,union(esk3_0,X2)),esk2_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( ~ member(esk4_2(X1,union(esk2_0,esk3_0)),esk1_0)
| subset(X1,union(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_23]) ).
cnf(c_0_25,plain,
( subset(X1,X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_26,negated_conjecture,
~ subset(esk1_0,union(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET594+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 : n005.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:27:48 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 4.00/1.01 % Version: 3.5.1
% 4.00/1.01 % Preprocessing class: FSMSSMSSSSSNFFN.
% 4.00/1.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.00/1.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.00/1.01 % Starting new_bool_3 with 300s (1) cores
% 4.00/1.01 % Starting new_bool_1 with 300s (1) cores
% 4.00/1.01 % Starting sh5l with 300s (1) cores
% 4.00/1.01 % new_bool_3 with pid 2642122 completed with status 0
% 4.00/1.01 % Result found by new_bool_3
% 4.00/1.01 % Preprocessing class: FSMSSMSSSSSNFFN.
% 4.00/1.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.00/1.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.00/1.01 % Starting new_bool_3 with 300s (1) cores
% 4.00/1.01 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 4.00/1.01 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.00/1.01 % Search class: FGUSS-FFSF22-SFFFFFNN
% 4.00/1.01 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 4.00/1.01 % Starting SubtermCWHack with 31s (1) cores
% 4.00/1.01 % SubtermCWHack with pid 2642128 completed with status 0
% 4.00/1.01 % Result found by SubtermCWHack
% 4.00/1.01 % Preprocessing class: FSMSSMSSSSSNFFN.
% 4.00/1.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.00/1.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.00/1.01 % Starting new_bool_3 with 300s (1) cores
% 4.00/1.01 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 4.00/1.01 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.00/1.01 % Search class: FGUSS-FFSF22-SFFFFFNN
% 4.00/1.01 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 4.00/1.01 % Starting SubtermCWHack with 31s (1) cores
% 4.00/1.01 % Preprocessing time : 0.001 s
% 4.00/1.01
% 4.00/1.01 % Proof found!
% 4.00/1.01 % SZS status Theorem
% 4.00/1.01 % SZS output start CNFRefutation
% See solution above
% 4.00/1.01 % Parsed axioms : 9
% 4.00/1.01 % Removed by relevancy pruning/SinE : 0
% 4.00/1.01 % Initial clauses : 21
% 4.00/1.01 % Removed in clause preprocessing : 2
% 4.00/1.01 % Initial clauses in saturation : 19
% 4.00/1.01 % Processed clauses : 5515
% 4.00/1.01 % ...of these trivial : 2230
% 4.00/1.01 % ...subsumed : 2260
% 4.00/1.01 % ...remaining for further processing : 1025
% 4.00/1.01 % Other redundant clauses eliminated : 2
% 4.00/1.01 % Clauses deleted for lack of memory : 0
% 4.00/1.01 % Backward-subsumed : 4
% 4.00/1.01 % Backward-rewritten : 116
% 4.00/1.01 % Generated clauses : 101317
% 4.00/1.01 % ...of the previous two non-redundant : 80175
% 4.00/1.01 % ...aggressively subsumed : 0
% 4.00/1.01 % Contextual simplify-reflections : 0
% 4.00/1.01 % Paramodulations : 100555
% 4.00/1.01 % Factorizations : 760
% 4.00/1.01 % NegExts : 0
% 4.00/1.01 % Equation resolutions : 2
% 4.00/1.01 % Disequality decompositions : 0
% 4.00/1.01 % Total rewrite steps : 29076
% 4.00/1.01 % ...of those cached : 22122
% 4.00/1.01 % Propositional unsat checks : 0
% 4.00/1.01 % Propositional check models : 0
% 4.00/1.01 % Propositional check unsatisfiable : 0
% 4.00/1.01 % Propositional clauses : 0
% 4.00/1.01 % Propositional clauses after purity: 0
% 4.00/1.01 % Propositional unsat core size : 0
% 4.00/1.01 % Propositional preprocessing time : 0.000
% 4.00/1.01 % Propositional encoding time : 0.000
% 4.00/1.01 % Propositional solver time : 0.000
% 4.00/1.01 % Success case prop preproc time : 0.000
% 4.00/1.01 % Success case prop encoding time : 0.000
% 4.00/1.01 % Success case prop solver time : 0.000
% 4.00/1.01 % Current number of processed clauses : 903
% 4.00/1.01 % Positive orientable unit clauses : 406
% 4.00/1.01 % Positive unorientable unit clauses: 2
% 4.00/1.01 % Negative unit clauses : 1
% 4.00/1.01 % Non-unit-clauses : 494
% 4.00/1.01 % Current number of unprocessed clauses: 74085
% 4.00/1.01 % ...number of literals in the above : 226887
% 4.00/1.01 % Current number of archived formulas : 0
% 4.00/1.01 % Current number of archived clauses : 120
% 4.00/1.01 % Clause-clause subsumption calls (NU) : 57286
% 4.00/1.01 % Rec. Clause-clause subsumption calls : 25450
% 4.00/1.01 % Non-unit clause-clause subsumptions : 2262
% 4.00/1.01 % Unit Clause-clause subsumption calls : 11928
% 4.00/1.01 % Rewrite failures with RHS unbound : 0
% 4.00/1.01 % BW rewrite match attempts : 6111
% 4.00/1.01 % BW rewrite match successes : 117
% 4.00/1.01 % Condensation attempts : 0
% 4.00/1.01 % Condensation successes : 0
% 4.00/1.01 % Termbank termtop insertions : 1595459
% 4.00/1.01 % Search garbage collected termcells : 317
% 4.00/1.01
% 4.00/1.01 % -------------------------------------------------
% 4.00/1.01 % User time : 0.543 s
% 4.00/1.01 % System time : 0.033 s
% 4.00/1.01 % Total time : 0.575 s
% 4.00/1.01 % Maximum resident set size: 3636 pages
% 4.00/1.01
% 4.00/1.01 % -------------------------------------------------
% 4.00/1.01 % User time : 0.543 s
% 4.00/1.01 % System time : 0.039 s
% 4.00/1.01 % Total time : 0.581 s
% 4.00/1.01 % Maximum resident set size: 4864 pages
% 4.00/1.01 % E exiting
%------------------------------------------------------------------------------