%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET663+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 0.28s 0.62s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 12 unt; 0 def)
% Number of atoms : 127 ( 18 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 143 ( 55 ~; 52 |; 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 : 59 ( 4 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/sandbox/benchmark/theBenchmark.p',p3) ).
fof(p33,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).
fof(prove_relset_1_26,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( ilf_type(X3,relation_type(empty_set,X2))
=> X3 = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_26) ).
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/sandbox/benchmark/theBenchmark.p',p6) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X1,empty_set)
=> X1 = empty_set ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',p13) ).
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/sandbox/benchmark/theBenchmark.p',p28) ).
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/sandbox/benchmark/theBenchmark.p',p2) ).
fof(c_0_8,plain,
! [X7,X8,X9] :
( ( ~ ilf_type(X7,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X9,relation_type(X7,X8))
| subset(range_of(X9),X8) )
& ( ~ ilf_type(X7,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X9,relation_type(X7,X8))
| subset(domain_of(X9),X7) ) ),
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,
! [X79] : ilf_type(X79,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(X1,X2))
=> ( ilf_type(X3,relation_type(empty_set,X2))
=> X3 = empty_set ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_26]) ).
fof(c_0_11,plain,
! [X11,X12,X13,X14] :
( ( ~ ilf_type(X11,set_type)
| ~ ilf_type(X12,set_type)
| ilf_type(X14,subset_type(cross_product(X11,X12)))
| ~ ilf_type(X14,relation_type(X11,X12)) )
& ( ~ ilf_type(X11,set_type)
| ~ ilf_type(X12,set_type)
| ilf_type(X13,relation_type(X11,X12))
| ~ ilf_type(X13,subset_type(cross_product(X11,X12))) ) ),
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_12,plain,
! [X5] :
( X5 = empty_set
| ~ subset(X5,empty_set)
| ~ ilf_type(X5,set_type) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
cnf(c_0_13,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,relation_type(X2,X3))
| subset(domain_of(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,negated_conjecture,
( esk15_0 != empty_set
& ilf_type(esk15_0,relation_type(empty_set,esk14_0))
& ilf_type(esk15_0,relation_type(esk13_0,esk14_0))
& ilf_type(esk14_0,set_type)
& ilf_type(esk13_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_16,plain,
! [X30] :
( ( ~ ilf_type(X30,set_type)
| ilf_type(X30,binary_relation_type)
| ~ ilf_type(X30,set_type)
| ~ relation_like(X30) )
& ( ~ ilf_type(X30,set_type)
| ~ ilf_type(X30,binary_relation_type)
| ilf_type(X30,set_type) )
& ( ~ ilf_type(X30,set_type)
| ~ ilf_type(X30,binary_relation_type)
| relation_like(X30) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])])]) ).
fof(c_0_17,plain,
! [X64,X65,X66] :
( relation_like(X66)
| ~ ilf_type(X66,subset_type(cross_product(X64,X65)))
| ~ ilf_type(X65,set_type)
| ~ ilf_type(X64,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p28])])])]) ).
cnf(c_0_18,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_11]) ).
cnf(c_0_19,plain,
( ~ subset(X1,empty_set)
| ~ ilf_type(X1,set_type)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( ~ ilf_type(X1,relation_type(X2,X3))
| subset(domain_of(X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14])]) ).
cnf(c_0_21,negated_conjecture,
ilf_type(esk15_0,relation_type(empty_set,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,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_16]) ).
cnf(c_0_23,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_17]) ).
cnf(c_0_24,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_18,c_0_14]),c_0_14])]) ).
cnf(c_0_25,negated_conjecture,
ilf_type(esk15_0,relation_type(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_26,plain,
! [X6] :
( ( ~ ilf_type(X6,binary_relation_type)
| X6 = empty_set
| range_of(X6) != empty_set )
& ( ~ ilf_type(X6,binary_relation_type)
| X6 = empty_set
| domain_of(X6) != 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_19,c_0_14])]) ).
cnf(c_0_28,negated_conjecture,
subset(domain_of(esk15_0),empty_set),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
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_22]) ).
cnf(c_0_30,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_23,c_0_14]),c_0_14])]) ).
cnf(c_0_31,negated_conjecture,
ilf_type(esk15_0,subset_type(cross_product(esk13_0,esk14_0))),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( ~ ilf_type(X1,binary_relation_type)
| domain_of(X1) != empty_set
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
domain_of(esk15_0) = empty_set,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
esk15_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
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_14])]) ).
cnf(c_0_36,negated_conjecture,
relation_like(esk15_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
~ ilf_type(esk15_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
% 0.00/0.05 % Problem : SET663+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n004.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 05:31:49 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.28/0.53 Running first-order theorem proving
% 0.28/0.53 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.28/0.62 % Version: 3.5.1
% 0.28/0.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.28/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.28/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.62 % Starting sh5l with 300s (1) cores
% 0.28/0.62 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2343805 completed with status 0
% 0.28/0.62 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.28/0.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.28/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.28/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.62 % No SInE strategy applied
% 0.28/0.62 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.28/0.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.28/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.28/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.28/0.62 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 0.28/0.62 % Starting new_bool_3 with 136s (1) cores
% 0.28/0.62 % Starting new_bool_1 with 136s (1) cores
% 0.28/0.62 % new_bool_1 with pid 2343813 completed with status 0
% 0.28/0.62 % Result found by new_bool_1
% 0.28/0.62 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.28/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.28/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.62 % No SInE strategy applied
% 0.28/0.62 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.28/0.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.28/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.28/0.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.28/0.62 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 0.28/0.62 % Starting new_bool_3 with 136s (1) cores
% 0.28/0.62 % Starting new_bool_1 with 136s (1) cores
% 0.28/0.62 % Preprocessing time : 0.003 s
% 0.28/0.62 % Presaturation interreduction done
% 0.28/0.62
% 0.28/0.62 % Proof found!
% 0.28/0.62 % SZS status Theorem
% 0.28/0.62 % SZS output start CNFRefutation
% See solution above
% 0.28/0.62 % Parsed axioms : 35
% 0.28/0.62 % Removed by relevancy pruning/SinE : 0
% 0.28/0.62 % Initial clauses : 65
% 0.28/0.62 % Removed in clause preprocessing : 5
% 0.28/0.62 % Initial clauses in saturation : 60
% 0.28/0.62 % Processed clauses : 200
% 0.28/0.62 % ...of these trivial : 14
% 0.28/0.62 % ...subsumed : 22
% 0.28/0.62 % ...remaining for further processing : 164
% 0.28/0.62 % Other redundant clauses eliminated : 0
% 0.28/0.62 % Clauses deleted for lack of memory : 0
% 0.28/0.62 % Backward-subsumed : 1
% 0.28/0.62 % Backward-rewritten : 9
% 0.28/0.62 % Generated clauses : 181
% 0.28/0.62 % ...of the previous two non-redundant : 145
% 0.28/0.62 % ...aggressively subsumed : 0
% 0.28/0.62 % Contextual simplify-reflections : 1
% 0.28/0.62 % Paramodulations : 181
% 0.28/0.62 % Factorizations : 0
% 0.28/0.62 % NegExts : 0
% 0.28/0.62 % Equation resolutions : 0
% 0.28/0.62 % Disequality decompositions : 0
% 0.28/0.62 % Total rewrite steps : 142
% 0.28/0.62 % ...of those cached : 95
% 0.28/0.62 % Propositional unsat checks : 0
% 0.28/0.62 % Propositional check models : 0
% 0.28/0.62 % Propositional check unsatisfiable : 0
% 0.28/0.62 % Propositional clauses : 0
% 0.28/0.62 % Propositional clauses after purity: 0
% 0.28/0.62 % Propositional unsat core size : 0
% 0.28/0.62 % Propositional preprocessing time : 0.000
% 0.28/0.62 % Propositional encoding time : 0.000
% 0.28/0.62 % Propositional solver time : 0.000
% 0.28/0.62 % Success case prop preproc time : 0.000
% 0.28/0.62 % Success case prop encoding time : 0.000
% 0.28/0.62 % Success case prop solver time : 0.000
% 0.28/0.62 % Current number of processed clauses : 109
% 0.28/0.62 % Positive orientable unit clauses : 48
% 0.28/0.62 % Positive unorientable unit clauses: 0
% 0.28/0.62 % Negative unit clauses : 4
% 0.28/0.62 % Non-unit-clauses : 57
% 0.28/0.62 % Current number of unprocessed clauses: 50
% 0.28/0.62 % ...number of literals in the above : 119
% 0.28/0.62 % Current number of archived formulas : 0
% 0.28/0.62 % Current number of archived clauses : 55
% 0.28/0.62 % Clause-clause subsumption calls (NU) : 689
% 0.28/0.62 % Rec. Clause-clause subsumption calls : 456
% 0.28/0.62 % Non-unit clause-clause subsumptions : 13
% 0.28/0.62 % Unit Clause-clause subsumption calls : 322
% 0.28/0.62 % Rewrite failures with RHS unbound : 0
% 0.28/0.62 % BW rewrite match attempts : 28
% 0.28/0.62 % BW rewrite match successes : 7
% 0.28/0.62 % Condensation attempts : 0
% 0.28/0.62 % Condensation successes : 0
% 0.28/0.62 % Termbank termtop insertions : 8016
% 0.28/0.62 % Search garbage collected termcells : 1266
% 0.28/0.62
% 0.28/0.62 % -------------------------------------------------
% 0.28/0.62 % User time : 0.024 s
% 0.28/0.62 % System time : 0.007 s
% 0.28/0.62 % Total time : 0.031 s
% 0.28/0.62 % Maximum resident set size: 3672 pages
% 0.28/0.62
% 0.28/0.62 % -------------------------------------------------
% 0.28/0.62 % User time : 0.060 s
% 0.28/0.62 % System time : 0.019 s
% 0.28/0.62 % Total time : 0.078 s
% 0.28/0.62 % Maximum resident set size: 4864 pages
% 0.28/0.62 % E exiting
%------------------------------------------------------------------------------