%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET159+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 : n002.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 02:13:46 PM UTC 2026
% Result : Theorem 0.17s 5.90s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 23 unt; 0 def)
% Number of atoms : 95 ( 21 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 77 ( 30 ~; 36 |; 7 &)
% ( 3 <=>; 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; 3 con; 0-2 aty)
% Number of variables : 124 ( 5 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(prove_associativity_of_union,conjecture,
! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_union) ).
fof(c_0_5,plain,
! [X11,X12,X13,X14,X15] :
( ( subset(X14,X15)
| ~ member(esk1_2(X14,X15),X15) )
& ( subset(X14,X15)
| member(esk1_2(X14,X15),X14) )
& ( member(X13,X12)
| ~ member(X13,X11)
| ~ subset(X11,X12) ) ),
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_6,plain,
! [X4,X5,X6] :
( ( member(X6,union(X4,X5))
| ~ member(X6,X5) )
& ( member(X6,union(X4,X5))
| ~ member(X6,X4) )
& ( member(X6,X5)
| member(X6,X4)
| ~ member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])]) ).
cnf(c_0_7,plain,
( ~ member(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,plain,
( ~ member(esk1_2(X1,union(X2,X3)),X2)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,plain,
( ~ member(esk1_2(X1,union(X2,X3)),X3)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_7,c_0_9]) ).
cnf(c_0_14,plain,
( member(esk1_2(union(X1,X2),X3),X2)
| member(esk1_2(union(X1,X2),X3),X1)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3)
| subset(X1,union(union(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_16,plain,
( member(esk1_2(union(X1,X2),union(X3,X2)),X1)
| subset(union(X1,X2),union(X3,X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,plain,
subset(union(X1,X2),union(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( ~ member(X1,union(X3,X4))
| member(X1,union(union(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
( ~ member(esk1_2(X1,union(union(X2,X3),X4)),X2)
| subset(X1,union(union(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
cnf(c_0_21,plain,
( ~ member(esk1_2(X1,union(union(X2,X3),X4)),union(X3,X4))
| subset(X1,union(union(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_7,c_0_19]) ).
cnf(c_0_22,plain,
( member(esk1_2(union(X1,X2),union(union(X2,X3),X4)),X1)
| subset(union(X1,X2),union(union(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
fof(c_0_23,plain,
! [X9,X10] : union(X9,X10) = union(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_24,plain,
! [X7,X8] :
( ( X7 = X8
| ~ subset(X8,X7)
| ~ subset(X7,X8) )
& ( X7 != X8
| subset(X8,X7) )
& ( X7 != X8
| subset(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_25,plain,
subset(union(union(X1,X2),X3),union(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_27,negated_conjecture,
~ ! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(assume_negation,[status(cth)],[prove_associativity_of_union]) ).
cnf(c_0_28,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
subset(union(union(X1,X2),X3),union(union(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( member(esk1_2(union(X1,X2),union(X2,X3)),X1)
| subset(union(X1,X2),union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
fof(c_0_31,negated_conjecture,
union(union(esk3_0,esk4_0),esk5_0) != union(esk3_0,union(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_27])])])]) ).
cnf(c_0_32,plain,
union(union(X1,X2),X3) = union(union(X1,X3),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_29])]) ).
cnf(c_0_33,plain,
subset(union(X1,union(X1,X2)),union(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_30]),c_0_26]) ).
cnf(c_0_34,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_35,plain,
( ~ member(esk1_2(X1,union(X2,union(X3,X4))),X3)
| subset(X1,union(X2,union(X3,X4))) ),
inference(spm,[status(thm)],[c_0_13,c_0_8]) ).
cnf(c_0_36,plain,
( member(esk1_2(union(X1,X2),X2),X1)
| subset(union(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_14]) ).
cnf(c_0_37,negated_conjecture,
union(union(esk3_0,esk4_0),esk5_0) != union(esk3_0,union(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
union(union(X1,X2),X3) = union(X2,union(X1,X3)),
inference(spm,[status(thm)],[c_0_26,c_0_32]) ).
cnf(c_0_39,plain,
union(X1,union(X1,X2)) = union(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_33]),c_0_34])]) ).
cnf(c_0_40,plain,
subset(union(X1,union(X2,union(X1,X3))),union(X2,union(X1,X3))),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
union(esk5_0,union(esk3_0,esk4_0)) != union(esk3_0,union(esk4_0,esk5_0)),
inference(rw,[status(thm)],[c_0_37,c_0_26]) ).
cnf(c_0_42,plain,
union(X1,union(X2,X3)) = union(X3,union(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_38]),c_0_38]) ).
cnf(c_0_43,plain,
union(X1,union(X2,X1)) = union(X2,X1),
inference(spm,[status(thm)],[c_0_39,c_0_26]) ).
cnf(c_0_44,plain,
union(X1,union(X2,union(X1,X3))) = union(X2,union(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_40]),c_0_34])]) ).
cnf(c_0_45,negated_conjecture,
union(esk4_0,union(esk3_0,esk5_0)) != union(esk3_0,union(esk4_0,esk5_0)),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
union(X1,union(X2,X3)) = union(X2,union(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_43]),c_0_38]),c_0_38]),c_0_44]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET159+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.60 % Computer : n002.cluster.edu
% 0.13/5.60 % Model : x86_64 x86_64
% 0.13/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.60 % Memory : 8046.5625MB
% 0.13/5.60 % OS : Linux 6.8.0-71-generic
% 0.13/5.60 % CPULimit : 300
% 0.13/5.60 % WCLimit : 300
% 0.13/5.60 % DateTime : Mon Sep 21 05:00:10 UTC 2026
% 0.13/5.60 % CPUTime :
% 0.13/5.60 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.65 Running first-order theorem proving
% 0.13/5.65 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
% 0.17/5.90 % Version: 3.5.1
% 0.17/5.90 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.17/5.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/5.90 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.17/5.90 % Starting new_bool_3 with 300s (1) cores
% 0.17/5.90 % Starting new_bool_1 with 300s (1) cores
% 0.17/5.90 % Starting sh5l with 300s (1) cores
% 0.17/5.90 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2481890 completed with status 0
% 0.17/5.90 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.17/5.90 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.17/5.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/5.90 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.17/5.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/5.90 % No SInE strategy applied
% 0.17/5.90 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.17/5.90 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/5.90 % Starting SubtermCWHack with 136s (1) cores
% 0.17/5.90 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.17/5.90 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.17/5.90 % Starting new_bool_3 with 136s (1) cores
% 0.17/5.90 % Starting new_bool_1 with 136s (1) cores
% 0.17/5.90 % U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 2481897 completed with status 0
% 0.17/5.90 % Result found by U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.17/5.90 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.17/5.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/5.90 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.17/5.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/5.90 % No SInE strategy applied
% 0.17/5.90 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.17/5.90 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/5.90 % Starting SubtermCWHack with 136s (1) cores
% 0.17/5.90 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.17/5.90 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.17/5.90 % Preprocessing time : 0.001 s
% 0.17/5.90 % Presaturation interreduction done
% 0.17/5.90
% 0.17/5.90 % Proof found!
% 0.17/5.90 % SZS status Theorem
% 0.17/5.90 % SZS output start CNFRefutation
% See solution above
% 0.17/5.90 % Parsed axioms : 7
% 0.17/5.90 % Removed by relevancy pruning/SinE : 0
% 0.17/5.90 % Initial clauses : 16
% 0.17/5.90 % Removed in clause preprocessing : 2
% 0.17/5.90 % Initial clauses in saturation : 14
% 0.17/5.90 % Processed clauses : 1853
% 0.17/5.90 % ...of these trivial : 447
% 0.17/5.90 % ...subsumed : 1080
% 0.17/5.90 % ...remaining for further processing : 326
% 0.17/5.90 % Other redundant clauses eliminated : 2
% 0.17/5.90 % Clauses deleted for lack of memory : 0
% 0.17/5.90 % Backward-subsumed : 0
% 0.17/5.90 % Backward-rewritten : 162
% 0.17/5.90 % Generated clauses : 18328
% 0.17/5.90 % ...of the previous two non-redundant : 13369
% 0.17/5.90 % ...aggressively subsumed : 0
% 0.17/5.90 % Contextual simplify-reflections : 0
% 0.17/5.90 % Paramodulations : 18230
% 0.17/5.90 % Factorizations : 96
% 0.17/5.90 % NegExts : 0
% 0.17/5.90 % Equation resolutions : 2
% 0.17/5.90 % Disequality decompositions : 0
% 0.17/5.90 % Total rewrite steps : 9044
% 0.17/5.90 % ...of those cached : 7410
% 0.17/5.90 % Propositional unsat checks : 0
% 0.17/5.90 % Propositional check models : 0
% 0.17/5.90 % Propositional check unsatisfiable : 0
% 0.17/5.90 % Propositional clauses : 0
% 0.17/5.90 % Propositional clauses after purity: 0
% 0.17/5.90 % Propositional unsat core size : 0
% 0.17/5.90 % Propositional preprocessing time : 0.000
% 0.17/5.90 % Propositional encoding time : 0.000
% 0.17/5.90 % Propositional solver time : 0.000
% 0.17/5.90 % Success case prop preproc time : 0.000
% 0.17/5.90 % Success case prop encoding time : 0.000
% 0.17/5.90 % Success case prop solver time : 0.000
% 0.17/5.90 % Current number of processed clauses : 150
% 0.17/5.90 % Positive orientable unit clauses : 48
% 0.17/5.90 % Positive unorientable unit clauses: 3
% 0.17/5.90 % Negative unit clauses : 0
% 0.17/5.90 % Non-unit-clauses : 99
% 0.17/5.90 % Current number of unprocessed clauses: 11272
% 0.17/5.90 % ...number of literals in the above : 27095
% 0.17/5.90 % Current number of archived formulas : 0
% 0.17/5.90 % Current number of archived clauses : 174
% 0.17/5.90 % Clause-clause subsumption calls (NU) : 14324
% 0.17/5.90 % Rec. Clause-clause subsumption calls : 13657
% 0.17/5.90 % Non-unit clause-clause subsumptions : 1042
% 0.17/5.90 % Unit Clause-clause subsumption calls : 2036
% 0.17/5.90 % Rewrite failures with RHS unbound : 0
% 0.17/5.90 % BW rewrite match attempts : 1922
% 0.17/5.90 % BW rewrite match successes : 497
% 0.17/5.90 % Condensation attempts : 0
% 0.17/5.90 % Condensation successes : 0
% 0.17/5.90 % Termbank termtop insertions : 226723
% 0.17/5.90 % Search garbage collected termcells : 276
% 0.17/5.90
% 0.17/5.90 % -------------------------------------------------
% 0.17/5.90 % User time : 0.218 s
% 0.17/5.90 % System time : 0.010 s
% 0.17/5.90 % Total time : 0.228 s
% 0.17/5.90 % Maximum resident set size: 3632 pages
% 0.17/5.90
% 0.17/5.90 % -------------------------------------------------
% 0.17/5.90 % User time : 1.081 s
% 0.17/5.90 % System time : 0.058 s
% 0.17/5.90 % Total time : 1.138 s
% 0.17/5.90 % Maximum resident set size: 4608 pages
% 0.17/5.90 % E exiting
%------------------------------------------------------------------------------