%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET595+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 : n015.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 02:14:28 PM UTC 2026
% Result : Theorem 4.50s 1.09s
% Output : CNFRefutation 4.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 8 unt; 0 def)
% Number of atoms : 101 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 96 ( 34 ~; 42 |; 12 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 86 ( 4 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th54,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> X2 = union(X1,difference(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th54) ).
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(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(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> X2 = union(X1,difference(X2,X1)) ),
inference(assume_negation,[status(cth)],[prove_th54]) ).
fof(c_0_7,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_8,plain,
! [X13,X14,X15,X16,X17] :
( ( subset(X16,X17)
| ~ member(esk2_2(X16,X17),X17) )
& ( subset(X16,X17)
| member(esk2_2(X16,X17),X16) )
& ( member(X15,X14)
| ~ member(X15,X13)
| ~ subset(X13,X14) ) ),
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_9,negated_conjecture,
( esk5_0 != union(esk4_0,difference(esk5_0,esk4_0))
& subset(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_6])])])]) ).
fof(c_0_10,plain,
! [X7,X8,X9] :
( ( member(X9,union(X7,X8))
| ~ member(X9,X8) )
& ( member(X9,union(X7,X8))
| ~ member(X9,X7) )
& ( member(X9,X8)
| member(X9,X7)
| ~ member(X9,union(X7,X8)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])]) ).
fof(c_0_11,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_7])])])]) ).
cnf(c_0_12,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ member(esk2_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| member(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,negated_conjecture,
( ~ member(X1,esk4_0)
| member(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,plain,
( ~ member(esk2_2(X1,union(X2,X3)),X2)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( member(esk2_2(X1,X2),X3)
| member(esk2_2(X1,X2),difference(X1,X3))
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_23,plain,
! [X21,X22] : union(X21,X22) = union(X22,X21),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_24,negated_conjecture,
( ~ member(esk2_2(X1,esk5_0),esk4_0)
| subset(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_25,plain,
( member(esk2_2(union(X1,X2),X3),X2)
| member(esk2_2(union(X1,X2),X3),X1)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
fof(c_0_26,plain,
! [X19,X20] :
( ( X19 = X20
| ~ subset(X20,X19)
| ~ subset(X19,X20) )
& ( X19 != X20
| subset(X20,X19) )
& ( X19 != X20
| subset(X19,X20) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_27,plain,
( ~ member(esk2_2(X1,union(X2,X3)),X3)
| subset(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_14,c_0_20]) ).
cnf(c_0_28,plain,
( member(esk2_2(X1,union(difference(X1,X2),X3)),X2)
| subset(X1,union(difference(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_31,negated_conjecture,
( member(esk2_2(union(X1,esk4_0),esk5_0),X1)
| subset(union(X1,esk4_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
subset(X1,union(X2,difference(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( member(esk2_2(union(esk4_0,difference(X1,X2)),esk5_0),X1)
| subset(union(esk4_0,difference(X1,X2)),esk5_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_29]),c_0_29]) ).
cnf(c_0_35,plain,
( ~ subset(union(X1,difference(X2,X1)),X2)
| union(X1,difference(X2,X1)) = X2 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
subset(union(esk4_0,difference(esk5_0,X1)),esk5_0),
inference(spm,[status(thm)],[c_0_14,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
esk5_0 != union(esk4_0,difference(esk5_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET595+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 05:31:06 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 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
% 4.50/1.09 % Version: 3.5.1
% 4.50/1.09 % Preprocessing class: FSMSSMSSSSSNFFN.
% 4.50/1.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.50/1.09 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.50/1.09 % Starting new_bool_3 with 300s (1) cores
% 4.50/1.09 % Starting new_bool_1 with 300s (1) cores
% 4.50/1.09 % Starting sh5l with 300s (1) cores
% 4.50/1.09 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 651028 completed with status 0
% 4.50/1.09 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 4.50/1.09 % Preprocessing class: FSMSSMSSSSSNFFN.
% 4.50/1.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.50/1.09 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.50/1.09 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.50/1.09 % No SInE strategy applied
% 4.50/1.09 % Search class: FGHSS-FFSF22-SFFFFFNN
% 4.50/1.09 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.50/1.09 % Starting SubtermCWHack with 136s (1) cores
% 4.50/1.09 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 4.50/1.09 % Starting G----_0010_evo with 136s (1) cores
% 4.50/1.09 % Starting new_bool_3 with 136s (1) cores
% 4.50/1.09 % Starting new_bool_1 with 136s (1) cores
% 4.50/1.09 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 651033 completed with status 0
% 4.50/1.09 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 4.50/1.09 % Preprocessing class: FSMSSMSSSSSNFFN.
% 4.50/1.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.50/1.09 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.50/1.09 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.50/1.09 % No SInE strategy applied
% 4.50/1.09 % Search class: FGHSS-FFSF22-SFFFFFNN
% 4.50/1.09 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.50/1.09 % Starting SubtermCWHack with 136s (1) cores
% 4.50/1.09 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 4.50/1.09 % Preprocessing time : 0.002 s
% 4.50/1.09 % Presaturation interreduction done
% 4.50/1.09
% 4.50/1.09 % Proof found!
% 4.50/1.09 % SZS status Theorem
% 4.50/1.09 % SZS output start CNFRefutation
% See solution above
% 4.50/1.09 % Parsed axioms : 9
% 4.50/1.09 % Removed by relevancy pruning/SinE : 0
% 4.50/1.09 % Initial clauses : 22
% 4.50/1.09 % Removed in clause preprocessing : 2
% 4.50/1.09 % Initial clauses in saturation : 20
% 4.50/1.09 % Processed clauses : 3483
% 4.50/1.09 % ...of these trivial : 338
% 4.50/1.09 % ...subsumed : 2532
% 4.50/1.09 % ...remaining for further processing : 613
% 4.50/1.09 % Other redundant clauses eliminated : 2
% 4.50/1.09 % Clauses deleted for lack of memory : 0
% 4.50/1.09 % Backward-subsumed : 5
% 4.50/1.09 % Backward-rewritten : 68
% 4.50/1.09 % Generated clauses : 33293
% 4.50/1.09 % ...of the previous two non-redundant : 29688
% 4.50/1.09 % ...aggressively subsumed : 0
% 4.50/1.09 % Contextual simplify-reflections : 8
% 4.50/1.09 % Paramodulations : 32845
% 4.50/1.09 % Factorizations : 446
% 4.50/1.09 % NegExts : 0
% 4.50/1.09 % Equation resolutions : 2
% 4.50/1.09 % Disequality decompositions : 0
% 4.50/1.09 % Total rewrite steps : 21311
% 4.50/1.09 % ...of those cached : 20194
% 4.50/1.09 % Propositional unsat checks : 0
% 4.50/1.09 % Propositional check models : 0
% 4.50/1.09 % Propositional check unsatisfiable : 0
% 4.50/1.09 % Propositional clauses : 0
% 4.50/1.09 % Propositional clauses after purity: 0
% 4.50/1.09 % Propositional unsat core size : 0
% 4.50/1.09 % Propositional preprocessing time : 0.000
% 4.50/1.09 % Propositional encoding time : 0.000
% 4.50/1.09 % Propositional solver time : 0.000
% 4.50/1.09 % Success case prop preproc time : 0.000
% 4.50/1.09 % Success case prop encoding time : 0.000
% 4.50/1.09 % Success case prop solver time : 0.000
% 4.50/1.09 % Current number of processed clauses : 520
% 4.50/1.09 % Positive orientable unit clauses : 104
% 4.50/1.09 % Positive unorientable unit clauses: 15
% 4.50/1.09 % Negative unit clauses : 2
% 4.50/1.09 % Non-unit-clauses : 399
% 4.50/1.09 % Current number of unprocessed clauses: 26133
% 4.50/1.09 % ...number of literals in the above : 92240
% 4.50/1.09 % Current number of archived formulas : 0
% 4.50/1.09 % Current number of archived clauses : 91
% 4.50/1.09 % Clause-clause subsumption calls (NU) : 37544
% 4.50/1.09 % Rec. Clause-clause subsumption calls : 15662
% 4.50/1.09 % Non-unit clause-clause subsumptions : 1496
% 4.50/1.09 % Unit Clause-clause subsumption calls : 5685
% 4.50/1.09 % Rewrite failures with RHS unbound : 0
% 4.50/1.09 % BW rewrite match attempts : 1082
% 4.50/1.09 % BW rewrite match successes : 94
% 4.50/1.09 % Condensation attempts : 0
% 4.50/1.09 % Condensation successes : 0
% 4.50/1.09 % Termbank termtop insertions : 561243
% 4.50/1.09 % Search garbage collected termcells : 358
% 4.50/1.09
% 4.50/1.09 % -------------------------------------------------
% 4.50/1.09 % User time : 0.560 s
% 4.50/1.09 % System time : 0.032 s
% 4.50/1.09 % Total time : 0.592 s
% 4.50/1.09 % Maximum resident set size: 3380 pages
% 4.50/1.09
% 4.50/1.09 % -------------------------------------------------
% 4.50/1.09 % User time : 2.675 s
% 4.50/1.09 % System time : 0.146 s
% 4.50/1.09 % Total time : 2.820 s
% 4.50/1.09 % Maximum resident set size: 4608 pages
% 4.50/1.09 % E exiting
%------------------------------------------------------------------------------