%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET662+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 : n012.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 02:17:53 PM UTC 2026
% Result : Theorem 0.06s 0.34s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 9 unt; 0 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 179 ( 71 ~; 65 |; 13 &)
% ( 6 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 7 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p11,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).
fof(p14,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
fof(p20,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
fof(p4,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(p7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,subset_type(X1))
<=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(p12,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X1,power_set(X2))
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(prove_relset_1_25,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ilf_type(empty_set,relation_type(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_25) ).
fof(c_0_8,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p11]) ).
fof(c_0_9,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p14]) ).
fof(c_0_10,plain,
! [X12,X13] :
( ( ~ ilf_type(X12,set_type)
| empty(X12)
| member(esk4_1(X12),X12) )
& ( ~ ilf_type(X12,set_type)
| empty(X12)
| ilf_type(esk4_1(X12),set_type) )
& ( ~ ilf_type(X12,set_type)
| ~ member(X13,X12)
| ~ ilf_type(X13,set_type)
| ~ empty(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(fof_nnf,[status(thm)],[c_0_8])])])])])]) ).
fof(c_0_11,plain,
! [X15] : ilf_type(X15,set_type),
inference(variable_rename,[status(thm)],[p20]) ).
fof(c_0_12,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,empty_set) ),
inference(fof_simplification,[status(thm)],[p4]) ).
fof(c_0_13,plain,
! [X45,X46] :
( ( ~ ilf_type(X45,set_type)
| ~ ilf_type(X46,set_type)
| ilf_type(X46,subset_type(X45))
| ~ ilf_type(X46,member_type(power_set(X45))) )
& ( ~ ilf_type(X45,set_type)
| ~ ilf_type(X46,set_type)
| ilf_type(X46,member_type(power_set(X45)))
| ~ ilf_type(X46,subset_type(X45)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])])]) ).
fof(c_0_14,plain,
! [X33,X34] :
( ( ~ ilf_type(X33,set_type)
| ~ ilf_type(X34,set_type)
| empty(X34)
| ilf_type(X33,member_type(X34))
| ~ member(X33,X34) )
& ( ~ ilf_type(X33,set_type)
| ~ ilf_type(X34,set_type)
| empty(X34)
| member(X33,X34)
| ~ ilf_type(X33,member_type(X34)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])]) ).
cnf(c_0_15,plain,
( ~ ilf_type(X1,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X7] :
( ~ member(X7,empty_set)
| ~ ilf_type(X7,set_type) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_18,plain,
! [X29,X30,X31] :
( ( ~ ilf_type(X29,set_type)
| ~ ilf_type(X30,set_type)
| member(X29,power_set(X30))
| ~ member(esk7_2(X29,X30),X30) )
& ( ~ ilf_type(X29,set_type)
| ~ ilf_type(X30,set_type)
| member(X29,power_set(X30))
| member(esk7_2(X29,X30),X29) )
& ( ~ ilf_type(X29,set_type)
| ~ ilf_type(X30,set_type)
| member(X29,power_set(X30))
| ilf_type(esk7_2(X29,X30),set_type) )
& ( ~ ilf_type(X29,set_type)
| ~ ilf_type(X30,set_type)
| member(X31,X30)
| ~ member(X31,X29)
| ~ ilf_type(X31,set_type)
| ~ member(X29,power_set(X30)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p12])])])])])]) ).
cnf(c_0_19,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(power_set(X2)))
| ilf_type(X1,subset_type(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,X2)
| empty(X2)
| ilf_type(X1,member_type(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( ~ member(X2,X1)
| ~ empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16])]) ).
cnf(c_0_22,plain,
( ~ member(X1,empty_set)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X1,power_set(X2))
| member(esk7_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,plain,
! [X16,X17,X18,X19] :
( ( ~ ilf_type(X16,set_type)
| ~ ilf_type(X17,set_type)
| ilf_type(X19,subset_type(cross_product(X16,X17)))
| ~ ilf_type(X19,relation_type(X16,X17)) )
& ( ~ ilf_type(X16,set_type)
| ~ ilf_type(X17,set_type)
| ilf_type(X18,relation_type(X16,X17))
| ~ ilf_type(X18,subset_type(cross_product(X16,X17))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])])]) ).
cnf(c_0_25,plain,
( ~ ilf_type(X1,member_type(power_set(X2)))
| ilf_type(X1,subset_type(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_16]),c_0_16])]) ).
cnf(c_0_26,plain,
( ~ member(X1,X2)
| ilf_type(X1,member_type(X2)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_16]),c_0_16])]),c_0_21]) ).
cnf(c_0_27,plain,
~ member(X1,empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_16])]) ).
cnf(c_0_28,plain,
( member(X1,power_set(X2))
| member(esk7_2(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_16]),c_0_16])]) ).
fof(c_0_29,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ilf_type(empty_set,relation_type(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_25]) ).
cnf(c_0_30,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ilf_type(X1,relation_type(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( ~ member(X1,power_set(X2))
| ilf_type(X1,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
member(empty_set,power_set(X1)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_33,negated_conjecture,
( ~ ilf_type(empty_set,relation_type(esk1_0,esk2_0))
& ilf_type(esk2_0,set_type)
& ilf_type(esk1_0,set_type) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).
cnf(c_0_34,plain,
( ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ilf_type(X1,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_16]),c_0_16])]) ).
cnf(c_0_35,plain,
ilf_type(empty_set,subset_type(X1)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
~ ilf_type(empty_set,relation_type(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
ilf_type(empty_set,relation_type(X1,X2)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET662+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 05:31:37 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.06/0.34 % Version: 3.5.1
% 0.06/0.34 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.06/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.06/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.06/0.34 % Starting new_bool_1 with 300s (1) cores
% 0.06/0.34 % Starting sh5l with 300s (1) cores
% 0.06/0.34 % sh5l with pid 1648544 completed with status 0
% 0.06/0.34 % Result found by sh5l
% 0.06/0.34 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.06/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.06/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.06/0.34 % Starting new_bool_1 with 300s (1) cores
% 0.06/0.34 % Starting sh5l with 300s (1) cores
% 0.06/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.06/0.34 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.06/0.34 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.06/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.06/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.06/0.34 % SubtermCWHack with pid 1648551 completed with status 0
% 0.06/0.34 % Result found by SubtermCWHack
% 0.06/0.34 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.06/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.06/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.06/0.34 % Starting new_bool_1 with 300s (1) cores
% 0.06/0.34 % Starting sh5l with 300s (1) cores
% 0.06/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.06/0.34 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.06/0.34 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.06/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.06/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.06/0.34 % Preprocessing time : 0.001 s
% 0.06/0.34
% 0.06/0.34 % Proof found!
% 0.06/0.34 % SZS status Theorem
% 0.06/0.34 % SZS output start CNFRefutation
% See solution above
% 0.06/0.34 % Parsed axioms : 22
% 0.06/0.34 % Removed by relevancy pruning/SinE : 0
% 0.06/0.34 % Initial clauses : 41
% 0.06/0.34 % Removed in clause preprocessing : 0
% 0.06/0.34 % Initial clauses in saturation : 41
% 0.06/0.34 % Processed clauses : 81
% 0.06/0.34 % ...of these trivial : 9
% 0.06/0.34 % ...subsumed : 10
% 0.06/0.34 % ...remaining for further processing : 62
% 0.06/0.34 % Other redundant clauses eliminated : 0
% 0.06/0.34 % Clauses deleted for lack of memory : 0
% 0.06/0.34 % Backward-subsumed : 0
% 0.06/0.34 % Backward-rewritten : 4
% 0.06/0.34 % Generated clauses : 66
% 0.06/0.34 % ...of the previous two non-redundant : 51
% 0.06/0.34 % ...aggressively subsumed : 0
% 0.06/0.34 % Contextual simplify-reflections : 1
% 0.06/0.34 % Paramodulations : 66
% 0.06/0.34 % Factorizations : 0
% 0.06/0.34 % NegExts : 0
% 0.06/0.34 % Equation resolutions : 0
% 0.06/0.34 % Disequality decompositions : 0
% 0.06/0.34 % Total rewrite steps : 77
% 0.06/0.34 % ...of those cached : 55
% 0.06/0.34 % Propositional unsat checks : 0
% 0.06/0.34 % Propositional check models : 0
% 0.06/0.34 % Propositional check unsatisfiable : 0
% 0.06/0.34 % Propositional clauses : 0
% 0.06/0.34 % Propositional clauses after purity: 0
% 0.06/0.34 % Propositional unsat core size : 0
% 0.06/0.34 % Propositional preprocessing time : 0.000
% 0.06/0.34 % Propositional encoding time : 0.000
% 0.06/0.34 % Propositional solver time : 0.000
% 0.06/0.34 % Success case prop preproc time : 0.000
% 0.06/0.34 % Success case prop encoding time : 0.000
% 0.06/0.34 % Success case prop solver time : 0.000
% 0.06/0.34 % Current number of processed clauses : 58
% 0.06/0.34 % Positive orientable unit clauses : 20
% 0.06/0.34 % Positive unorientable unit clauses: 0
% 0.06/0.34 % Negative unit clauses : 2
% 0.06/0.34 % Non-unit-clauses : 36
% 0.06/0.34 % Current number of unprocessed clauses: 11
% 0.06/0.34 % ...number of literals in the above : 25
% 0.06/0.34 % Current number of archived formulas : 0
% 0.06/0.34 % Current number of archived clauses : 4
% 0.06/0.34 % Clause-clause subsumption calls (NU) : 86
% 0.06/0.34 % Rec. Clause-clause subsumption calls : 80
% 0.06/0.34 % Non-unit clause-clause subsumptions : 6
% 0.06/0.34 % Unit Clause-clause subsumption calls : 24
% 0.06/0.34 % Rewrite failures with RHS unbound : 0
% 0.06/0.34 % BW rewrite match attempts : 18
% 0.06/0.34 % BW rewrite match successes : 4
% 0.06/0.34 % Condensation attempts : 0
% 0.06/0.34 % Condensation successes : 0
% 0.06/0.34 % Termbank termtop insertions : 4376
% 0.06/0.34 % Search garbage collected termcells : 789
% 0.06/0.34
% 0.06/0.34 % -------------------------------------------------
% 0.06/0.34 % User time : 0.006 s
% 0.06/0.34 % System time : 0.002 s
% 0.06/0.34 % Total time : 0.007 s
% 0.06/0.34 % Maximum resident set size: 3656 pages
% 0.06/0.34
% 0.06/0.34 % -------------------------------------------------
% 0.06/0.34 % User time : 0.008 s
% 0.06/0.34 % System time : 0.003 s
% 0.06/0.34 % Total time : 0.011 s
% 0.06/0.34 % Maximum resident set size: 4608 pages
% 0.06/0.34 % E exiting
%------------------------------------------------------------------------------