%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET607+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 : n009.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 02:14:42 PM UTC 2026
% Result : Theorem 25.88s 4.18s
% Output : CNFRefutation 25.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 16 unt; 0 def)
% Number of atoms : 98 ( 14 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 87 ( 31 ~; 39 |; 11 &)
% ( 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 : 104 ( 9 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X2)
| member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(prove_th79,conjecture,
! [X1,X2] : union(X1,difference(X2,X1)) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th79) ).
fof(c_0_6,plain,
! [X6,X7,X8] :
( ( member(X8,union(X6,X7))
| ~ member(X8,X7) )
& ( member(X8,union(X6,X7))
| ~ member(X8,X6) )
& ( member(X8,X7)
| member(X8,X6)
| ~ member(X8,union(X6,X7)) ) ),
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,plain,
! [X14,X15,X16,X17,X18] :
( ( subset(X17,X18)
| ~ member(esk3_2(X17,X18),X18) )
& ( subset(X17,X18)
| member(esk3_2(X17,X18),X17) )
& ( member(X16,X15)
| ~ member(X16,X14)
| ~ subset(X14,X15) ) ),
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,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[difference_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,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X11,X12,X13] :
( ( member(X13,difference(X11,X12))
| member(X13,X12)
| ~ member(X13,X11) )
& ( ~ member(X13,difference(X11,X12))
| ~ member(X13,X12) )
& ( ~ member(X13,difference(X11,X12))
| member(X13,X11) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_12,plain,
( ~ member(esk3_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( member(esk3_2(union(X1,X2),X3),X1)
| member(esk3_2(union(X1,X2),X3),X2)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
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,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( member(esk3_2(union(X1,X2),X1),X2)
| subset(union(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( ~ member(esk3_2(X1,union(X2,X3)),X3)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
fof(c_0_19,plain,
! [X9,X10] : union(X9,X10) = union(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,plain,
( ~ member(esk3_2(X1,union(X2,X3)),X2)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
fof(c_0_22,plain,
! [X27,X28] :
( ( X27 = X28
| ~ subset(X28,X27)
| ~ subset(X27,X28) )
& ( X27 != X28
| subset(X28,X27) )
& ( X27 != X28
| subset(X27,X28) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_23,plain,
( member(esk3_2(union(X1,difference(X2,X3)),X1),X2)
| subset(union(X1,difference(X2,X3)),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_10]) ).
cnf(c_0_25,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( ~ member(esk3_2(X1,union(X2,difference(X3,X4))),X3)
| member(esk3_2(X1,union(X2,difference(X3,X4))),X4)
| subset(X1,union(X2,difference(X3,X4))) ),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_27,plain,
( member(esk3_2(union(X1,X2),union(X1,X3)),X2)
| subset(union(X1,X2),union(X1,X3)) ),
inference(spm,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_28,plain,
( ~ member(esk3_2(X1,union(X2,union(X3,X4))),X4)
| subset(X1,union(X2,union(X3,X4))) ),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_29,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
subset(union(X1,difference(X1,X2)),X1),
inference(spm,[status(thm)],[c_0_12,c_0_23]) ).
cnf(c_0_31,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_32,negated_conjecture,
~ ! [X1,X2] : union(X1,difference(X2,X1)) = union(X1,X2),
inference(assume_negation,[status(cth)],[prove_th79]) ).
cnf(c_0_33,plain,
( member(esk3_2(union(X1,X2),union(X1,difference(X2,X3))),X3)
| subset(union(X1,X2),union(X1,difference(X2,X3))) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
subset(union(X1,X2),union(X1,union(X3,X2))),
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_35,plain,
union(X1,difference(X1,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
fof(c_0_36,negated_conjecture,
union(esk1_0,difference(esk2_0,esk1_0)) != union(esk1_0,esk2_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])]) ).
cnf(c_0_37,plain,
subset(union(X1,X2),union(X1,difference(X2,X1))),
inference(spm,[status(thm)],[c_0_21,c_0_33]) ).
cnf(c_0_38,plain,
subset(union(X1,difference(X2,X3)),union(X1,X2)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
union(esk1_0,difference(esk2_0,esk1_0)) != union(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_40,plain,
union(X1,difference(X2,X1)) = union(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_37]),c_0_38])]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET607+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 05:28:42 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.42 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
% 25.88/4.18 % Version: 3.5.1
% 25.88/4.18 % Preprocessing class: FSMSSMSSSSSNFFN.
% 25.88/4.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.88/4.18 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 25.88/4.18 % Starting new_bool_3 with 300s (1) cores
% 25.88/4.18 % Starting new_bool_1 with 300s (1) cores
% 25.88/4.18 % Starting sh5l with 300s (1) cores
% 25.88/4.18 % sh5l with pid 937689 completed with status 0
% 25.88/4.18 % Result found by sh5l
% 25.88/4.18 % Preprocessing class: FSMSSMSSSSSNFFN.
% 25.88/4.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.88/4.18 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 25.88/4.18 % Starting new_bool_3 with 300s (1) cores
% 25.88/4.18 % Starting new_bool_1 with 300s (1) cores
% 25.88/4.18 % Starting sh5l with 300s (1) cores
% 25.88/4.18 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 25.88/4.18 % SinE strategy is gf500_gu_R04_F100_L20000
% 25.88/4.18 % Search class: FGHSS-FFSF22-SFFFFFNN
% 25.88/4.18 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 25.88/4.18 % Starting SubtermCWHack with 31s (1) cores
% 25.88/4.18 % SubtermCWHack with pid 937697 completed with status 0
% 25.88/4.18 % Result found by SubtermCWHack
% 25.88/4.18 % Preprocessing class: FSMSSMSSSSSNFFN.
% 25.88/4.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.88/4.18 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 25.88/4.18 % Starting new_bool_3 with 300s (1) cores
% 25.88/4.18 % Starting new_bool_1 with 300s (1) cores
% 25.88/4.18 % Starting sh5l with 300s (1) cores
% 25.88/4.18 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 25.88/4.18 % SinE strategy is gf500_gu_R04_F100_L20000
% 25.88/4.18 % Search class: FGHSS-FFSF22-SFFFFFNN
% 25.88/4.18 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 25.88/4.18 % Starting SubtermCWHack with 31s (1) cores
% 25.88/4.18 % Preprocessing time : 0.001 s
% 25.88/4.18
% 25.88/4.18 % Proof found!
% 25.88/4.18 % SZS status Theorem
% 25.88/4.18 % SZS output start CNFRefutation
% See solution above
% 25.88/4.18 % Parsed axioms : 8
% 25.88/4.18 % Removed by relevancy pruning/SinE : 0
% 25.88/4.18 % Initial clauses : 19
% 25.88/4.18 % Removed in clause preprocessing : 2
% 25.88/4.18 % Initial clauses in saturation : 17
% 25.88/4.18 % Processed clauses : 19923
% 25.88/4.18 % ...of these trivial : 1646
% 25.88/4.18 % ...subsumed : 16931
% 25.88/4.18 % ...remaining for further processing : 1346
% 25.88/4.18 % Other redundant clauses eliminated : 2
% 25.88/4.18 % Clauses deleted for lack of memory : 0
% 25.88/4.18 % Backward-subsumed : 9
% 25.88/4.18 % Backward-rewritten : 87
% 25.88/4.18 % Generated clauses : 326417
% 25.88/4.18 % ...of the previous two non-redundant : 236087
% 25.88/4.18 % ...aggressively subsumed : 0
% 25.88/4.18 % Contextual simplify-reflections : 3
% 25.88/4.18 % Paramodulations : 325475
% 25.88/4.18 % Factorizations : 940
% 25.88/4.18 % NegExts : 0
% 25.88/4.18 % Equation resolutions : 2
% 25.88/4.18 % Disequality decompositions : 0
% 25.88/4.18 % Total rewrite steps : 287418
% 25.88/4.18 % ...of those cached : 269670
% 25.88/4.18 % Propositional unsat checks : 0
% 25.88/4.18 % Propositional check models : 0
% 25.88/4.18 % Propositional check unsatisfiable : 0
% 25.88/4.18 % Propositional clauses : 0
% 25.88/4.18 % Propositional clauses after purity: 0
% 25.88/4.18 % Propositional unsat core size : 0
% 25.88/4.18 % Propositional preprocessing time : 0.000
% 25.88/4.18 % Propositional encoding time : 0.000
% 25.88/4.18 % Propositional solver time : 0.000
% 25.88/4.18 % Success case prop preproc time : 0.000
% 25.88/4.18 % Success case prop encoding time : 0.000
% 25.88/4.18 % Success case prop solver time : 0.000
% 25.88/4.18 % Current number of processed clauses : 1248
% 25.88/4.18 % Positive orientable unit clauses : 491
% 25.88/4.18 % Positive unorientable unit clauses: 19
% 25.88/4.18 % Negative unit clauses : 32
% 25.88/4.18 % Non-unit-clauses : 706
% 25.88/4.18 % Current number of unprocessed clauses: 215413
% 25.88/4.18 % ...number of literals in the above : 614367
% 25.88/4.18 % Current number of archived formulas : 0
% 25.88/4.18 % Current number of archived clauses : 96
% 25.88/4.18 % Clause-clause subsumption calls (NU) : 162069
% 25.88/4.18 % Rec. Clause-clause subsumption calls : 80305
% 25.88/4.18 % Non-unit clause-clause subsumptions : 7998
% 25.88/4.18 % Unit Clause-clause subsumption calls : 31705
% 25.88/4.18 % Rewrite failures with RHS unbound : 1487
% 25.88/4.18 % BW rewrite match attempts : 8825
% 25.88/4.18 % BW rewrite match successes : 179
% 25.88/4.18 % Condensation attempts : 0
% 25.88/4.18 % Condensation successes : 0
% 25.88/4.18 % Termbank termtop insertions : 5451204
% 25.88/4.18 % Search garbage collected termcells : 300
% 25.88/4.18
% 25.88/4.18 % -------------------------------------------------
% 25.88/4.18 % User time : 3.462 s
% 25.88/4.18 % System time : 0.179 s
% 25.88/4.18 % Total time : 3.641 s
% 25.88/4.18 % Maximum resident set size: 3632 pages
% 25.88/4.18
% 25.88/4.18 % -------------------------------------------------
% 25.88/4.18 % User time : 3.464 s
% 25.88/4.18 % System time : 0.184 s
% 25.88/4.18 % Total time : 3.648 s
% 25.88/4.18 % Maximum resident set size: 4608 pages
% 25.88/4.18 % E exiting
%------------------------------------------------------------------------------