%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET700+4 : 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 02:15:01 PM UTC 2026
% Result : Theorem 0.23s 0.67s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 4 unt; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 108 ( 42 ~; 41 |; 15 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 2 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI34,conjecture,
! [X1,X2,X4] :
( ( subset(X2,X4)
& subset(X1,X4) )
=> ( subset(X1,X2)
<=> subset(intersection(X1,difference(X4,X2)),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI34) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( ~ member(X2,X1)
& member(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',difference) ).
fof(intersection,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X4] :
( ( subset(X2,X4)
& subset(X1,X4) )
=> ( subset(X1,X2)
<=> subset(intersection(X1,difference(X4,X2)),X2) ) ),
inference(assume_negation,[status(cth)],[thI34]) ).
fof(c_0_6,plain,
! [X6,X7,X8,X9,X10] :
( ( subset(X9,X10)
| ~ member(esk1_2(X9,X10),X10) )
& ( subset(X9,X10)
| member(esk1_2(X9,X10),X9) )
& ( member(X8,X7)
| ~ member(X8,X6)
| ~ subset(X6,X7) ) ),
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])])])])])])]) ).
fof(c_0_7,negated_conjecture,
( ( subset(intersection(esk4_0,difference(esk6_0,esk5_0)),esk5_0)
| subset(esk4_0,esk5_0) )
& ( ~ subset(intersection(esk4_0,difference(esk6_0,esk5_0)),esk5_0)
| ~ subset(esk4_0,esk5_0) )
& subset(esk5_0,esk6_0)
& subset(esk4_0,esk6_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,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( ~ member(X2,X1)
& member(X2,X4) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
cnf(c_0_9,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( subset(intersection(esk4_0,difference(esk6_0,esk5_0)),esk5_0)
| subset(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X16,X17,X18] :
( ( member(X16,intersection(X17,X18))
| ~ member(X16,X18)
| ~ member(X16,X17) )
& ( ~ member(X16,intersection(X17,X18))
| member(X16,X18) )
& ( ~ member(X16,intersection(X17,X18))
| member(X16,X17) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])])]) ).
fof(c_0_12,plain,
! [X23,X24,X25] :
( ( member(X23,difference(X25,X24))
| member(X23,X24)
| ~ member(X23,X25) )
& ( ~ member(X23,difference(X25,X24))
| ~ member(X23,X24) )
& ( ~ member(X23,difference(X25,X24))
| member(X23,X25) ) ),
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_13,negated_conjecture,
( ~ member(X1,intersection(esk4_0,difference(esk6_0,esk5_0)))
| subset(esk4_0,esk5_0)
| member(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
subset(esk4_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_17,plain,
! [X14,X15] :
( ( member(X14,power_set(X15))
| ~ subset(X14,X15) )
& ( subset(X14,X15)
| ~ member(X14,power_set(X15)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])])]) ).
cnf(c_0_18,negated_conjecture,
( ~ subset(intersection(esk4_0,difference(esk6_0,esk5_0)),esk5_0)
| ~ subset(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
( ~ member(X1,esk4_0)
| ~ member(X1,difference(esk6_0,esk5_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_9]),c_0_15]) ).
cnf(c_0_21,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,negated_conjecture,
( ~ member(X1,esk4_0)
| member(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_16]) ).
cnf(c_0_23,plain,
( ~ subset(X1,X2)
| member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| member(esk1_2(intersection(esk4_0,difference(esk6_0,esk5_0)),esk5_0),intersection(esk4_0,difference(esk6_0,esk5_0))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
( ~ member(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,negated_conjecture,
( ~ member(X1,esk4_0)
| member(X1,esk5_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_28,plain,
( member(X1,power_set(X2))
| member(esk1_2(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_29,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| member(esk1_2(intersection(esk4_0,difference(esk6_0,esk5_0)),esk5_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ member(esk1_2(intersection(esk4_0,difference(esk6_0,esk5_0)),esk5_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_31,plain,
( ~ member(esk1_2(X1,X2),X2)
| member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( member(esk4_0,power_set(X1))
| member(esk1_2(esk4_0,X1),esk5_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
~ subset(esk4_0,esk5_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_29]),c_0_30]) ).
cnf(c_0_34,plain,
( ~ member(X1,power_set(X2))
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_35,negated_conjecture,
member(esk4_0,power_set(esk5_0)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET700+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n015.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 21 05:36:06 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.48 Running first-order theorem proving
% 0.17/0.48 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
% 0.23/0.67 % Version: 3.5.1
% 0.23/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.67 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.67 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.67 % Starting sh5l with 300s (1) cores
% 0.23/0.67 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 664273 completed with status 0
% 0.23/0.67 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.23/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.67 % No SInE strategy applied
% 0.23/0.67 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.23/0.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.67 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.67 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.23/0.67 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.23/0.67 % Starting new_bool_3 with 136s (1) cores
% 0.23/0.67 % G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with pid 664283 completed with status 0
% 0.23/0.67 % Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y
% 0.23/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.67 % No SInE strategy applied
% 0.23/0.67 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.23/0.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.67 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.67 % Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.23/0.67 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 0.23/0.67 % Preprocessing time : 0.002 s
% 0.23/0.67 % Presaturation interreduction done
% 0.23/0.67
% 0.23/0.67 % Proof found!
% 0.23/0.67 % SZS status Theorem
% 0.23/0.67 % SZS output start CNFRefutation
% See solution above
% 0.23/0.67 % Parsed axioms : 12
% 0.23/0.67 % Removed by relevancy pruning/SinE : 0
% 0.23/0.67 % Initial clauses : 33
% 0.23/0.67 % Removed in clause preprocessing : 0
% 0.23/0.67 % Initial clauses in saturation : 33
% 0.23/0.67 % Processed clauses : 320
% 0.23/0.67 % ...of these trivial : 17
% 0.23/0.67 % ...subsumed : 31
% 0.23/0.67 % ...remaining for further processing : 272
% 0.23/0.67 % Other redundant clauses eliminated : 5
% 0.23/0.67 % Clauses deleted for lack of memory : 0
% 0.23/0.67 % Backward-subsumed : 14
% 0.23/0.67 % Backward-rewritten : 12
% 0.23/0.67 % Generated clauses : 2092
% 0.23/0.67 % ...of the previous two non-redundant : 1826
% 0.23/0.67 % ...aggressively subsumed : 0
% 0.23/0.67 % Contextual simplify-reflections : 5
% 0.23/0.67 % Paramodulations : 2083
% 0.23/0.67 % Factorizations : 2
% 0.23/0.67 % NegExts : 0
% 0.23/0.67 % Equation resolutions : 5
% 0.23/0.67 % Disequality decompositions : 0
% 0.23/0.67 % Total rewrite steps : 270
% 0.23/0.67 % ...of those cached : 130
% 0.23/0.67 % Propositional unsat checks : 0
% 0.23/0.67 % Propositional check models : 0
% 0.23/0.67 % Propositional check unsatisfiable : 0
% 0.23/0.67 % Propositional clauses : 0
% 0.23/0.67 % Propositional clauses after purity: 0
% 0.23/0.67 % Propositional unsat core size : 0
% 0.23/0.67 % Propositional preprocessing time : 0.000
% 0.23/0.67 % Propositional encoding time : 0.000
% 0.23/0.67 % Propositional solver time : 0.000
% 0.23/0.67 % Success case prop preproc time : 0.000
% 0.23/0.67 % Success case prop encoding time : 0.000
% 0.23/0.67 % Success case prop solver time : 0.000
% 0.23/0.67 % Current number of processed clauses : 208
% 0.23/0.67 % Positive orientable unit clauses : 68
% 0.23/0.67 % Positive unorientable unit clauses: 0
% 0.23/0.67 % Negative unit clauses : 6
% 0.23/0.67 % Non-unit-clauses : 134
% 0.23/0.67 % Current number of unprocessed clauses: 1568
% 0.23/0.67 % ...number of literals in the above : 3054
% 0.23/0.67 % Current number of archived formulas : 0
% 0.23/0.67 % Current number of archived clauses : 61
% 0.23/0.67 % Clause-clause subsumption calls (NU) : 5449
% 0.23/0.67 % Rec. Clause-clause subsumption calls : 4751
% 0.23/0.67 % Non-unit clause-clause subsumptions : 30
% 0.23/0.67 % Unit Clause-clause subsumption calls : 1170
% 0.23/0.67 % Rewrite failures with RHS unbound : 0
% 0.23/0.67 % BW rewrite match attempts : 149
% 0.23/0.67 % BW rewrite match successes : 11
% 0.23/0.67 % Condensation attempts : 0
% 0.23/0.67 % Condensation successes : 0
% 0.23/0.67 % Termbank termtop insertions : 25790
% 0.23/0.67 % Search garbage collected termcells : 501
% 0.23/0.67
% 0.23/0.67 % -------------------------------------------------
% 0.23/0.67 % User time : 0.069 s
% 0.23/0.67 % System time : 0.009 s
% 0.23/0.67 % Total time : 0.078 s
% 0.23/0.67 % Maximum resident set size: 3648 pages
% 0.23/0.67
% 0.23/0.67 % -------------------------------------------------
% 0.23/0.67 % User time : 0.560 s
% 0.23/0.67 % System time : 0.056 s
% 0.23/0.67 % Total time : 0.617 s
% 0.23/0.67 % Maximum resident set size: 4864 pages
% 0.23/0.67 % E exiting
%------------------------------------------------------------------------------