%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET664+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 : n010.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 02:14:55 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 11 unt; 0 def)
% Number of atoms : 128 ( 18 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 145 ( 56 ~; 53 |; 12 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 6 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(range_of(X3),X2)
& subset(domain_of(X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(p33,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(prove_relset_1_27,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ( ilf_type(X3,relation_type(X2,empty_set))
=> X3 = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_27) ).
fof(p28,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> relation_like(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p28) ).
fof(p6,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',p6) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X1,empty_set)
=> X1 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(p13,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( ilf_type(X1,set_type)
& relation_like(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( ( range_of(X1) = empty_set
| domain_of(X1) = empty_set )
=> X1 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(c_0_8,plain,
! [X19,X20,X21] :
( ( ~ ilf_type(X19,set_type)
| ~ ilf_type(X20,set_type)
| ~ ilf_type(X21,relation_type(X19,X20))
| subset(range_of(X21),X20) )
& ( ~ ilf_type(X19,set_type)
| ~ ilf_type(X20,set_type)
| ~ ilf_type(X21,relation_type(X19,X20))
| subset(domain_of(X21),X19) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])])]) ).
fof(c_0_9,plain,
! [X18] : ilf_type(X18,set_type),
inference(variable_rename,[status(thm)],[p33]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ( ilf_type(X3,relation_type(X2,empty_set))
=> X3 = empty_set ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_27]) ).
fof(c_0_11,plain,
! [X76,X77,X78] :
( relation_like(X78)
| ~ ilf_type(X78,subset_type(cross_product(X76,X77)))
| ~ ilf_type(X77,set_type)
| ~ ilf_type(X76,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p28])])])]) ).
fof(c_0_12,plain,
! [X22,X23,X24,X25] :
( ( ~ ilf_type(X22,set_type)
| ~ ilf_type(X23,set_type)
| ilf_type(X25,subset_type(cross_product(X22,X23)))
| ~ ilf_type(X25,relation_type(X22,X23)) )
& ( ~ ilf_type(X22,set_type)
| ~ ilf_type(X23,set_type)
| ilf_type(X24,relation_type(X22,X23))
| ~ ilf_type(X24,subset_type(cross_product(X22,X23))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])])]) ).
fof(c_0_13,plain,
! [X8] :
( X8 = empty_set
| ~ subset(X8,empty_set)
| ~ ilf_type(X8,set_type) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
cnf(c_0_14,plain,
( ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,relation_type(X3,X2))
| subset(range_of(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_16,negated_conjecture,
( esk3_0 != empty_set
& ilf_type(esk3_0,relation_type(esk2_0,empty_set))
& ilf_type(esk3_0,relation_type(esk2_0,esk1_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_10])])])]) ).
fof(c_0_17,plain,
! [X56] :
( ( ~ ilf_type(X56,set_type)
| ilf_type(X56,binary_relation_type)
| ~ ilf_type(X56,set_type)
| ~ relation_like(X56) )
& ( ~ ilf_type(X56,set_type)
| ~ ilf_type(X56,binary_relation_type)
| ilf_type(X56,set_type) )
& ( ~ ilf_type(X56,set_type)
| ~ ilf_type(X56,binary_relation_type)
| relation_like(X56) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])])]) ).
cnf(c_0_18,plain,
( ~ ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,relation_type(X2,X3))
| ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( ~ subset(X1,empty_set)
| ~ ilf_type(X1,set_type)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( ~ ilf_type(X1,relation_type(X3,X2))
| subset(range_of(X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15])]) ).
cnf(c_0_22,negated_conjecture,
ilf_type(esk3_0,relation_type(esk2_0,empty_set)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_15]),c_0_15])]) ).
cnf(c_0_25,plain,
( ~ ilf_type(X1,relation_type(X2,X3))
| ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_15]),c_0_15])]) ).
fof(c_0_26,plain,
! [X9] :
( ( ~ ilf_type(X9,binary_relation_type)
| X9 = empty_set
| range_of(X9) != empty_set )
& ( ~ ilf_type(X9,binary_relation_type)
| X9 = empty_set
| domain_of(X9) != empty_set ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
cnf(c_0_27,plain,
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_15])]) ).
cnf(c_0_28,negated_conjecture,
subset(range_of(esk3_0),empty_set),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( ~ ilf_type(X1,relation_type(X2,X3))
| relation_like(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
ilf_type(esk3_0,relation_type(esk2_0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_32,plain,
( ~ ilf_type(X1,binary_relation_type)
| range_of(X1) != empty_set
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
range_of(esk3_0) = empty_set,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
esk3_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_35,plain,
( ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_15])]) ).
cnf(c_0_36,negated_conjecture,
relation_like(esk3_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
~ ilf_type(esk3_0,binary_relation_type),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
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
% 0.00/0.02 % Problem : SET664+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:32:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.44 % Version: 3.5.1
% 0.10/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % sh5l with pid 116582 completed with status 0
% 0.10/0.44 % Result found by sh5l
% 0.10/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.44 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.10/0.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.44 % SubtermCWHack with pid 116583 completed with status 0
% 0.10/0.44 % Result found by SubtermCWHack
% 0.10/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.44 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.10/0.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.44 % Preprocessing time : 0.002 s
% 0.10/0.44
% 0.10/0.44 % Proof found!
% 0.10/0.44 % SZS status Theorem
% 0.10/0.44 % SZS output start CNFRefutation
% See solution above
% 0.10/0.44 % Parsed axioms : 35
% 0.10/0.44 % Removed by relevancy pruning/SinE : 1
% 0.10/0.44 % Initial clauses : 64
% 0.10/0.44 % Removed in clause preprocessing : 5
% 0.10/0.44 % Initial clauses in saturation : 59
% 0.10/0.44 % Processed clauses : 157
% 0.10/0.44 % ...of these trivial : 16
% 0.10/0.44 % ...subsumed : 21
% 0.10/0.44 % ...remaining for further processing : 120
% 0.10/0.44 % Other redundant clauses eliminated : 1
% 0.10/0.44 % Clauses deleted for lack of memory : 0
% 0.10/0.44 % Backward-subsumed : 0
% 0.10/0.44 % Backward-rewritten : 9
% 0.10/0.44 % Generated clauses : 203
% 0.10/0.44 % ...of the previous two non-redundant : 158
% 0.10/0.44 % ...aggressively subsumed : 0
% 0.10/0.44 % Contextual simplify-reflections : 1
% 0.10/0.44 % Paramodulations : 202
% 0.10/0.44 % Factorizations : 0
% 0.10/0.44 % NegExts : 0
% 0.10/0.44 % Equation resolutions : 1
% 0.10/0.44 % Disequality decompositions : 0
% 0.10/0.44 % Total rewrite steps : 134
% 0.10/0.44 % ...of those cached : 99
% 0.10/0.44 % Propositional unsat checks : 0
% 0.10/0.44 % Propositional check models : 0
% 0.10/0.44 % Propositional check unsatisfiable : 0
% 0.10/0.44 % Propositional clauses : 0
% 0.10/0.44 % Propositional clauses after purity: 0
% 0.10/0.44 % Propositional unsat core size : 0
% 0.10/0.44 % Propositional preprocessing time : 0.000
% 0.10/0.44 % Propositional encoding time : 0.000
% 0.10/0.44 % Propositional solver time : 0.000
% 0.10/0.44 % Success case prop preproc time : 0.000
% 0.10/0.44 % Success case prop encoding time : 0.000
% 0.10/0.44 % Success case prop solver time : 0.000
% 0.10/0.44 % Current number of processed clauses : 111
% 0.10/0.44 % Positive orientable unit clauses : 33
% 0.10/0.44 % Positive unorientable unit clauses: 0
% 0.10/0.44 % Negative unit clauses : 4
% 0.10/0.44 % Non-unit-clauses : 74
% 0.10/0.44 % Current number of unprocessed clauses: 54
% 0.10/0.44 % ...number of literals in the above : 128
% 0.10/0.44 % Current number of archived formulas : 0
% 0.10/0.44 % Current number of archived clauses : 9
% 0.10/0.44 % Clause-clause subsumption calls (NU) : 1386
% 0.10/0.44 % Rec. Clause-clause subsumption calls : 1204
% 0.10/0.44 % Non-unit clause-clause subsumptions : 12
% 0.10/0.44 % Unit Clause-clause subsumption calls : 675
% 0.10/0.44 % Rewrite failures with RHS unbound : 0
% 0.10/0.44 % BW rewrite match attempts : 18
% 0.10/0.44 % BW rewrite match successes : 4
% 0.10/0.44 % Condensation attempts : 0
% 0.10/0.44 % Condensation successes : 0
% 0.10/0.44 % Termbank termtop insertions : 7775
% 0.10/0.44 % Search garbage collected termcells : 1293
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.011 s
% 0.10/0.44 % System time : 0.004 s
% 0.10/0.44 % Total time : 0.015 s
% 0.10/0.44 % Maximum resident set size: 3928 pages
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.014 s
% 0.10/0.44 % System time : 0.008 s
% 0.10/0.44 % Total time : 0.022 s
% 0.10/0.44 % Maximum resident set size: 4608 pages
% 0.10/0.44 % E exiting
%------------------------------------------------------------------------------