%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 02:24:30 PM UTC 2026
% Result : Theorem 0.19s 5.62s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 12 unt; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 80 ( 31 ~; 28 |; 9 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 3 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t14_relset_1,conjecture,
! [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
=> ( subset(relation_rng(X4),X2)
=> relation_of2_as_subset(X4,X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(t119_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( ( subset(X3,X4)
& subset(X1,X2) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(t12_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( subset(relation_rng(X3),X2)
& subset(relation_dom(X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
fof(d1_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
<=> subset(X3,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(t1_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X2,X3)
& subset(X1,X2) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(t21_relat_1,axiom,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
=> ( subset(relation_rng(X4),X2)
=> relation_of2_as_subset(X4,X3,X2) ) ),
inference(assume_negation,[status(cth)],[t14_relset_1]) ).
fof(c_0_10,plain,
! [X22,X23,X24] :
( ( relation_of2_as_subset(X24,X22,X23)
| ~ relation_of2(X24,X22,X23) )
& ( relation_of2(X24,X22,X23)
| ~ relation_of2_as_subset(X24,X22,X23) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])]) ).
fof(c_0_11,negated_conjecture,
( ~ relation_of2_as_subset(esk7_0,esk6_0,esk5_0)
& subset(relation_rng(esk7_0),esk5_0)
& relation_of2_as_subset(esk7_0,esk6_0,esk4_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_12,plain,
! [X26,X27,X28,X29] :
( subset(cartesian_product2(X26,X28),cartesian_product2(X27,X29))
| ~ subset(X28,X29)
| ~ subset(X26,X27) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t119_zfmisc_1])])]) ).
fof(c_0_13,plain,
! [X30,X31,X32] :
( ( ~ relation_of2_as_subset(X32,X30,X31)
| subset(relation_rng(X32),X31) )
& ( ~ relation_of2_as_subset(X32,X30,X31)
| subset(relation_dom(X32),X30) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_relset_1])])])]) ).
fof(c_0_14,plain,
! [X8,X9,X10] :
( ( relation_of2(X10,X8,X9)
| ~ subset(X10,cartesian_product2(X8,X9)) )
& ( subset(X10,cartesian_product2(X8,X9))
| ~ relation_of2(X10,X8,X9) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_relset_1])])]) ).
cnf(c_0_15,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
relation_of2_as_subset(esk7_0,esk6_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( ~ subset(X3,X4)
| ~ subset(X1,X2)
| subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
subset(relation_rng(esk7_0),esk5_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| subset(relation_dom(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X41,X42] :
( ( element(X41,powerset(X42))
| ~ subset(X41,X42) )
& ( subset(X41,X42)
| ~ element(X41,powerset(X42)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
cnf(c_0_21,plain,
( ~ relation_of2(X1,X2,X3)
| subset(X1,cartesian_product2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
relation_of2(esk7_0,esk6_0,esk4_0),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_23,plain,
! [X37,X38,X39] :
( subset(X37,X39)
| ~ subset(X38,X39)
| ~ subset(X37,X38) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])])]) ).
cnf(c_0_24,negated_conjecture,
( ~ subset(X1,X2)
| subset(cartesian_product2(X1,relation_rng(esk7_0)),cartesian_product2(X2,esk5_0)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,negated_conjecture,
subset(relation_dom(esk7_0),esk6_0),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
fof(c_0_26,plain,
! [X5,X6,X7] :
( relation(X7)
| ~ element(X7,powerset(cartesian_product2(X5,X6))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])]) ).
cnf(c_0_27,plain,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
subset(esk7_0,cartesian_product2(esk6_0,esk4_0)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( ~ subset(X2,X3)
| ~ subset(X1,X2)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,negated_conjecture,
subset(cartesian_product2(relation_dom(esk7_0),relation_rng(esk7_0)),cartesian_product2(esk6_0,esk5_0)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_31,plain,
! [X40] :
( subset(X40,cartesian_product2(relation_dom(X40),relation_rng(X40)))
| ~ relation(X40) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_relat_1])])]) ).
cnf(c_0_32,plain,
( ~ element(X1,powerset(cartesian_product2(X2,X3)))
| relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
element(esk7_0,powerset(cartesian_product2(esk6_0,esk4_0))),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
( ~ subset(X1,cartesian_product2(relation_dom(esk7_0),relation_rng(esk7_0)))
| subset(X1,cartesian_product2(esk6_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( ~ relation(X1)
| subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
relation(esk7_0),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
( ~ subset(X1,cartesian_product2(X2,X3))
| relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_38,negated_conjecture,
subset(esk7_0,cartesian_product2(esk6_0,esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_39,plain,
( ~ relation_of2(X1,X2,X3)
| relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_40,negated_conjecture,
relation_of2(esk7_0,esk6_0,esk5_0),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
~ relation_of2_as_subset(esk7_0,esk6_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.40 % Computer : n005.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Mon Sep 21 06:04:38 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.48 Running first-order theorem proving
% 0.13/5.48 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
% 0.19/5.62 % Version: 3.5.1
% 0.19/5.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/5.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/5.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/5.62 % Starting new_bool_3 with 300s (1) cores
% 0.19/5.62 % Starting new_bool_1 with 300s (1) cores
% 0.19/5.62 % Starting sh5l with 300s (1) cores
% 0.19/5.62 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2716114 completed with status 0
% 0.19/5.62 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.19/5.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/5.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/5.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/5.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/5.62 % No SInE strategy applied
% 0.19/5.62 % Search class: FHUNM-FFSF21-SFFFFFNN
% 0.19/5.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/5.62 % Starting SubtermCWHack with 136s (1) cores
% 0.19/5.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.19/5.62 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.19/5.62 % Starting new_bool_3 with 136s (1) cores
% 0.19/5.62 % Starting new_bool_1 with 136s (1) cores
% 0.19/5.62 % new_bool_1 with pid 2716124 completed with status 0
% 0.19/5.62 % Result found by new_bool_1
% 0.19/5.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/5.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/5.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/5.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/5.62 % No SInE strategy applied
% 0.19/5.62 % Search class: FHUNM-FFSF21-SFFFFFNN
% 0.19/5.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/5.62 % Starting SubtermCWHack with 136s (1) cores
% 0.19/5.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.19/5.62 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.19/5.62 % Starting new_bool_3 with 136s (1) cores
% 0.19/5.62 % Starting new_bool_1 with 136s (1) cores
% 0.19/5.62 % Preprocessing time : 0.002 s
% 0.19/5.62 % Presaturation interreduction done
% 0.19/5.62
% 0.19/5.62 % Proof found!
% 0.19/5.62 % SZS status Theorem
% 0.19/5.62 % SZS output start CNFRefutation
% See solution above
% 0.19/5.62 % Parsed axioms : 20
% 0.19/5.62 % Removed by relevancy pruning/SinE : 0
% 0.19/5.62 % Initial clauses : 26
% 0.19/5.62 % Removed in clause preprocessing : 6
% 0.19/5.62 % Initial clauses in saturation : 20
% 0.19/5.62 % Processed clauses : 252
% 0.19/5.62 % ...of these trivial : 1
% 0.19/5.62 % ...subsumed : 3
% 0.19/5.62 % ...remaining for further processing : 248
% 0.19/5.62 % Other redundant clauses eliminated : 0
% 0.19/5.62 % Clauses deleted for lack of memory : 0
% 0.19/5.62 % Backward-subsumed : 0
% 0.19/5.62 % Backward-rewritten : 0
% 0.19/5.62 % Generated clauses : 1669
% 0.19/5.62 % ...of the previous two non-redundant : 1512
% 0.19/5.62 % ...aggressively subsumed : 0
% 0.19/5.62 % Contextual simplify-reflections : 0
% 0.19/5.62 % Paramodulations : 1669
% 0.19/5.62 % Factorizations : 0
% 0.19/5.62 % NegExts : 0
% 0.19/5.62 % Equation resolutions : 0
% 0.19/5.62 % Disequality decompositions : 0
% 0.19/5.62 % Total rewrite steps : 178
% 0.19/5.62 % ...of those cached : 61
% 0.19/5.62 % Propositional unsat checks : 0
% 0.19/5.62 % Propositional check models : 0
% 0.19/5.62 % Propositional check unsatisfiable : 0
% 0.19/5.62 % Propositional clauses : 0
% 0.19/5.62 % Propositional clauses after purity: 0
% 0.19/5.62 % Propositional unsat core size : 0
% 0.19/5.62 % Propositional preprocessing time : 0.000
% 0.19/5.62 % Propositional encoding time : 0.000
% 0.19/5.62 % Propositional solver time : 0.000
% 0.19/5.62 % Success case prop preproc time : 0.000
% 0.19/5.62 % Success case prop encoding time : 0.000
% 0.19/5.62 % Success case prop solver time : 0.000
% 0.19/5.62 % Current number of processed clauses : 228
% 0.19/5.62 % Positive orientable unit clauses : 136
% 0.19/5.62 % Positive unorientable unit clauses: 0
% 0.19/5.62 % Negative unit clauses : 1
% 0.19/5.62 % Non-unit-clauses : 91
% 0.19/5.62 % Current number of unprocessed clauses: 1300
% 0.19/5.62 % ...number of literals in the above : 1473
% 0.19/5.62 % Current number of archived formulas : 0
% 0.19/5.62 % Current number of archived clauses : 20
% 0.19/5.62 % Clause-clause subsumption calls (NU) : 1923
% 0.19/5.62 % Rec. Clause-clause subsumption calls : 1591
% 0.19/5.62 % Non-unit clause-clause subsumptions : 3
% 0.19/5.62 % Unit Clause-clause subsumption calls : 138
% 0.19/5.62 % Rewrite failures with RHS unbound : 0
% 0.19/5.62 % BW rewrite match attempts : 35
% 0.19/5.62 % BW rewrite match successes : 0
% 0.19/5.62 % Condensation attempts : 0
% 0.19/5.62 % Condensation successes : 0
% 0.19/5.62 % Termbank termtop insertions : 23893
% 0.19/5.62 % Search garbage collected termcells : 222
% 0.19/5.62
% 0.19/5.62 % -------------------------------------------------
% 0.19/5.62 % User time : 0.050 s
% 0.19/5.62 % System time : 0.005 s
% 0.19/5.62 % Total time : 0.055 s
% 0.19/5.62 % Maximum resident set size: 3624 pages
% 0.19/5.62
% 0.19/5.62 % -------------------------------------------------
% 0.19/5.62 % User time : 0.232 s
% 0.19/5.62 % System time : 0.030 s
% 0.19/5.62 % Total time : 0.262 s
% 0.19/5.62 % Maximum resident set size: 4608 pages
% 0.19/5.62 % E exiting
%------------------------------------------------------------------------------