%------------------------------------------------------------------------------
% File : E-SAT---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 : n019.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 02:16:43 PM UTC 2026
% Result : Theorem 0.15s 5.86s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 22 unt; 0 def)
% Number of atoms : 92 ( 20 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 76 ( 30 ~; 35 |; 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 : 119 ( 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]) ).
fof(c_0_30,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_31,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_32,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_33,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_34,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_30]) ).
cnf(c_0_35,plain,
union(union(X1,X2),X3) = union(X2,union(X1,X3)),
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_36,plain,
subset(union(X1,union(X2,X1)),union(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_16]),c_0_26]) ).
cnf(c_0_37,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_38,plain,
subset(union(X1,union(X2,union(X1,X3))),union(X2,union(X1,X3))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
union(esk5_0,union(esk3_0,esk4_0)) != union(esk3_0,union(esk4_0,esk5_0)),
inference(rw,[status(thm)],[c_0_34,c_0_26]) ).
cnf(c_0_40,plain,
union(X1,union(X2,X3)) = union(X3,union(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_35]),c_0_35]) ).
cnf(c_0_41,plain,
union(X1,union(X2,X1)) = union(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_36]),c_0_37])]) ).
cnf(c_0_42,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_38]),c_0_37])]) ).
cnf(c_0_43,negated_conjecture,
union(esk4_0,union(esk3_0,esk5_0)) != union(esk3_0,union(esk4_0,esk5_0)),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,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_35,c_0_41]),c_0_35]),c_0_35]),c_0_42]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET159+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/5.39 % Computer : n019.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Mon Sep 21 04:57:41 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.46 Running first-order theorem proving
% 0.15/5.46 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
% 0.15/5.86 % Version: 3.5.1
% 0.15/5.86 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.86 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.86 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.86 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.86 % Starting sh5l with 300s (1) cores
% 0.15/5.86 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1733886 completed with status 0
% 0.15/5.86 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.15/5.86 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.86 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.86 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.86 % No SInE strategy applied
% 0.15/5.86 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.15/5.86 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.86 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.86 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.15/5.86 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/5.86 % Starting new_bool_3 with 136s (1) cores
% 0.15/5.86 % Starting new_bool_1 with 136s (1) cores
% 0.15/5.86 % U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 1733893 completed with status 0
% 0.15/5.86 % Result found by U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.15/5.86 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.86 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.86 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.86 % No SInE strategy applied
% 0.15/5.86 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.15/5.86 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.86 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.86 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.15/5.86 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/5.86 % Preprocessing time : 0.002 s
% 0.15/5.86 % Presaturation interreduction done
% 0.15/5.86
% 0.15/5.86 % Proof found!
% 0.15/5.86 % SZS status Theorem
% 0.15/5.86 % SZS output start CNFRefutation
% See solution above
% 0.15/5.86 % Parsed axioms : 7
% 0.15/5.86 % Removed by relevancy pruning/SinE : 0
% 0.15/5.86 % Initial clauses : 16
% 0.15/5.86 % Removed in clause preprocessing : 2
% 0.15/5.86 % Initial clauses in saturation : 14
% 0.15/5.86 % Processed clauses : 1853
% 0.15/5.86 % ...of these trivial : 437
% 0.15/5.86 % ...subsumed : 1090
% 0.15/5.86 % ...remaining for further processing : 326
% 0.15/5.86 % Other redundant clauses eliminated : 2
% 0.15/5.86 % Clauses deleted for lack of memory : 0
% 0.15/5.86 % Backward-subsumed : 0
% 0.15/5.86 % Backward-rewritten : 162
% 0.15/5.86 % Generated clauses : 16935
% 0.15/5.86 % ...of the previous two non-redundant : 12236
% 0.15/5.86 % ...aggressively subsumed : 0
% 0.15/5.86 % Contextual simplify-reflections : 0
% 0.15/5.86 % Paramodulations : 16837
% 0.15/5.86 % Factorizations : 96
% 0.15/5.86 % NegExts : 0
% 0.15/5.86 % Equation resolutions : 2
% 0.15/5.86 % Disequality decompositions : 0
% 0.15/5.86 % Total rewrite steps : 8590
% 0.15/5.86 % ...of those cached : 6995
% 0.15/5.86 % Propositional unsat checks : 0
% 0.15/5.86 % Propositional check models : 0
% 0.15/5.86 % Propositional check unsatisfiable : 0
% 0.15/5.86 % Propositional clauses : 0
% 0.15/5.86 % Propositional clauses after purity: 0
% 0.15/5.86 % Propositional unsat core size : 0
% 0.15/5.86 % Propositional preprocessing time : 0.000
% 0.15/5.86 % Propositional encoding time : 0.000
% 0.15/5.86 % Propositional solver time : 0.000
% 0.15/5.86 % Success case prop preproc time : 0.000
% 0.15/5.86 % Success case prop encoding time : 0.000
% 0.15/5.86 % Success case prop solver time : 0.000
% 0.15/5.86 % Current number of processed clauses : 150
% 0.15/5.86 % Positive orientable unit clauses : 48
% 0.15/5.86 % Positive unorientable unit clauses: 3
% 0.15/5.86 % Negative unit clauses : 0
% 0.15/5.86 % Non-unit-clauses : 99
% 0.15/5.86 % Current number of unprocessed clauses: 10174
% 0.15/5.86 % ...number of literals in the above : 25190
% 0.15/5.86 % Current number of archived formulas : 0
% 0.15/5.86 % Current number of archived clauses : 174
% 0.15/5.86 % Clause-clause subsumption calls (NU) : 14331
% 0.15/5.86 % Rec. Clause-clause subsumption calls : 13664
% 0.15/5.86 % Non-unit clause-clause subsumptions : 1055
% 0.15/5.86 % Unit Clause-clause subsumption calls : 1876
% 0.15/5.86 % Rewrite failures with RHS unbound : 0
% 0.15/5.86 % BW rewrite match attempts : 1795
% 0.15/5.86 % BW rewrite match successes : 379
% 0.15/5.86 % Condensation attempts : 0
% 0.15/5.86 % Condensation successes : 0
% 0.15/5.86 % Termbank termtop insertions : 216721
% 0.15/5.86 % Search garbage collected termcells : 276
% 0.15/5.86
% 0.15/5.86 % -------------------------------------------------
% 0.15/5.86 % User time : 0.359 s
% 0.15/5.86 % System time : 0.015 s
% 0.15/5.86 % Total time : 0.374 s
% 0.15/5.86 % Maximum resident set size: 3632 pages
% 0.15/5.86
% 0.15/5.86 % -------------------------------------------------
% 0.15/5.86 % User time : 1.776 s
% 0.15/5.86 % System time : 0.093 s
% 0.15/5.86 % Total time : 1.869 s
% 0.15/5.86 % Maximum resident set size: 4608 pages
% 0.15/5.86 % E exiting
%------------------------------------------------------------------------------