%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU243+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 : n001.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 02:28:42 PM UTC 2026
% Result : Theorem 0.24s 0.59s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 4 unt; 0 def)
% Number of atoms : 137 ( 16 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 184 ( 76 ~; 74 |; 22 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 51 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_well_founded_in(X1,X2)
<=> ! [X3] :
~ ( ! [X4] :
~ ( disjoint(fiber(X1,X4),X3)
& in(X4,X3) )
& X3 != empty_set
& subset(X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_wellord1) ).
fof(d2_wellord1,axiom,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> ! [X2] :
~ ( ! [X3] :
~ ( disjoint(fiber(X1,X3),X2)
& in(X3,X2) )
& X2 != empty_set
& subset(X2,relation_field(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_wellord1) ).
fof(t5_wellord1,conjecture,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord1) ).
fof(c_0_3,plain,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_well_founded_in(X1,X2)
<=> ! [X3] :
~ ( ! [X4] :
~ ( disjoint(fiber(X1,X4),X3)
& in(X4,X3) )
& X3 != empty_set
& subset(X3,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d3_wellord1]) ).
fof(c_0_4,plain,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> ! [X2] :
~ ( ! [X3] :
~ ( disjoint(fiber(X1,X3),X2)
& in(X3,X2) )
& X2 != empty_set
& subset(X2,relation_field(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[d2_wellord1]) ).
fof(c_0_5,plain,
! [X16,X17,X18,X20,X22] :
( ( ~ relation(X16)
| is_well_founded_in(X16,X20)
| ~ disjoint(fiber(X16,X22),esk4_2(X16,X20))
| ~ in(X22,esk4_2(X16,X20)) )
& ( ~ relation(X16)
| is_well_founded_in(X16,X20)
| esk4_2(X16,X20) != empty_set )
& ( ~ relation(X16)
| is_well_founded_in(X16,X20)
| subset(esk4_2(X16,X20),X20) )
& ( ~ relation(X16)
| ~ is_well_founded_in(X16,X17)
| X18 = empty_set
| ~ subset(X18,X17)
| disjoint(fiber(X16,esk3_3(X16,X17,X18)),X18) )
& ( ~ relation(X16)
| ~ is_well_founded_in(X16,X17)
| X18 = empty_set
| ~ subset(X18,X17)
| in(esk3_3(X16,X17,X18),X18) ) ),
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)],[c_0_3])])])])])])]) ).
fof(c_0_6,plain,
! [X11,X12,X15] :
( ( ~ relation(X11)
| well_founded_relation(X11)
| ~ disjoint(fiber(X11,X15),esk2_1(X11))
| ~ in(X15,esk2_1(X11)) )
& ( ~ relation(X11)
| well_founded_relation(X11)
| esk2_1(X11) != empty_set )
& ( ~ relation(X11)
| well_founded_relation(X11)
| subset(esk2_1(X11),relation_field(X11)) )
& ( ~ relation(X11)
| ~ well_founded_relation(X11)
| X12 = empty_set
| ~ subset(X12,relation_field(X11))
| disjoint(fiber(X11,esk1_2(X11,X12)),X12) )
& ( ~ relation(X11)
| ~ well_founded_relation(X11)
| X12 = empty_set
| ~ subset(X12,relation_field(X11))
| in(esk1_2(X11,X12),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_4])])])])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
inference(assume_negation,[status(cth)],[t5_wellord1]) ).
cnf(c_0_8,plain,
( ~ relation(X2)
| ~ disjoint(fiber(X2,X1),esk4_2(X2,X3))
| ~ in(X1,esk4_2(X2,X3))
| is_well_founded_in(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1))
| X2 = empty_set
| disjoint(fiber(X1,esk1_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1))
| X2 = empty_set
| in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( ~ relation(X1)
| esk4_2(X1,X2) != empty_set
| is_well_founded_in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_12,negated_conjecture,
( ( is_well_founded_in(esk11_0,relation_field(esk11_0))
| well_founded_relation(esk11_0) )
& ( ~ is_well_founded_in(esk11_0,relation_field(esk11_0))
| ~ well_founded_relation(esk11_0) )
& relation(esk11_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_13,plain,
( ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(esk4_2(X1,X2),relation_field(X1))
| is_well_founded_in(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]),c_0_11]) ).
cnf(c_0_14,plain,
( ~ relation(X1)
| is_well_founded_in(X1,X2)
| subset(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,plain,
( ~ relation(X2)
| ~ disjoint(fiber(X2,X1),esk2_1(X2))
| ~ in(X1,esk2_1(X2))
| well_founded_relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,plain,
( ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2)
| X3 = empty_set
| disjoint(fiber(X1,esk3_3(X1,X2,X3)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,plain,
( ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2)
| X3 = empty_set
| in(esk3_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,plain,
( ~ relation(X1)
| esk2_1(X1) != empty_set
| well_founded_relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( ~ is_well_founded_in(esk11_0,relation_field(esk11_0))
| ~ well_founded_relation(esk11_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( ~ relation(X1)
| ~ well_founded_relation(X1)
| is_well_founded_in(X1,relation_field(X1)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,negated_conjecture,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,plain,
( ~ relation(X1)
| ~ subset(esk2_1(X1),X2)
| ~ is_well_founded_in(X1,X2)
| well_founded_relation(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]) ).
cnf(c_0_23,plain,
( ~ relation(X1)
| well_founded_relation(X1)
| subset(esk2_1(X1),relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
( is_well_founded_in(esk11_0,relation_field(esk11_0))
| well_founded_relation(esk11_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,negated_conjecture,
~ well_founded_relation(esk11_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_26,plain,
( ~ relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1))
| well_founded_relation(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
is_well_founded_in(esk11_0,relation_field(esk11_0)),
inference(sr,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_21])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU243+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n001.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 06:08:29 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.49 Running first-order theorem proving
% 0.24/0.49 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
% 0.24/0.59 % Version: 3.5.1
% 0.24/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.59 % Starting sh5l with 300s (1) cores
% 0.24/0.59 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2354098 completed with status 0
% 0.24/0.59 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.24/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.59 % No SInE strategy applied
% 0.24/0.59 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.24/0.59 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.24/0.59 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.24/0.59 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.24/0.59 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.24/0.59 % SubtermCWHack with pid 2354102 completed with status 0
% 0.24/0.59 % Result found by SubtermCWHack
% 0.24/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.59 % No SInE strategy applied
% 0.24/0.59 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.24/0.59 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.59 % Preprocessing time : 0.001 s
% 0.24/0.59
% 0.24/0.59 % Proof found!
% 0.24/0.59 % SZS status Theorem
% 0.24/0.59 % SZS output start CNFRefutation
% See solution above
% 0.24/0.59 % Parsed axioms : 37
% 0.24/0.59 % Removed by relevancy pruning/SinE : 0
% 0.24/0.59 % Initial clauses : 55
% 0.24/0.59 % Removed in clause preprocessing : 10
% 0.24/0.59 % Initial clauses in saturation : 45
% 0.24/0.59 % Processed clauses : 608
% 0.24/0.59 % ...of these trivial : 1
% 0.24/0.59 % ...subsumed : 392
% 0.24/0.59 % ...remaining for further processing : 215
% 0.24/0.59 % Other redundant clauses eliminated : 0
% 0.24/0.59 % Clauses deleted for lack of memory : 0
% 0.24/0.59 % Backward-subsumed : 27
% 0.24/0.59 % Backward-rewritten : 6
% 0.24/0.59 % Generated clauses : 1712
% 0.24/0.59 % ...of the previous two non-redundant : 1460
% 0.24/0.59 % ...aggressively subsumed : 0
% 0.24/0.59 % Contextual simplify-reflections : 11
% 0.24/0.59 % Paramodulations : 1711
% 0.24/0.59 % Factorizations : 0
% 0.24/0.59 % NegExts : 0
% 0.24/0.59 % Equation resolutions : 0
% 0.24/0.59 % Disequality decompositions : 0
% 0.24/0.59 % Total rewrite steps : 484
% 0.24/0.59 % ...of those cached : 466
% 0.24/0.59 % Propositional unsat checks : 0
% 0.24/0.59 % Propositional check models : 0
% 0.24/0.59 % Propositional check unsatisfiable : 0
% 0.24/0.59 % Propositional clauses : 0
% 0.24/0.59 % Propositional clauses after purity: 0
% 0.24/0.59 % Propositional unsat core size : 0
% 0.24/0.59 % Propositional preprocessing time : 0.000
% 0.24/0.59 % Propositional encoding time : 0.000
% 0.24/0.59 % Propositional solver time : 0.000
% 0.24/0.59 % Success case prop preproc time : 0.000
% 0.24/0.59 % Success case prop encoding time : 0.000
% 0.24/0.59 % Success case prop solver time : 0.000
% 0.24/0.59 % Current number of processed clauses : 181
% 0.24/0.59 % Positive orientable unit clauses : 20
% 0.24/0.59 % Positive unorientable unit clauses: 1
% 0.24/0.59 % Negative unit clauses : 3
% 0.24/0.59 % Non-unit-clauses : 157
% 0.24/0.59 % Current number of unprocessed clauses: 844
% 0.24/0.59 % ...number of literals in the above : 4057
% 0.24/0.59 % Current number of archived formulas : 0
% 0.24/0.59 % Current number of archived clauses : 34
% 0.24/0.59 % Clause-clause subsumption calls (NU) : 11354
% 0.24/0.59 % Rec. Clause-clause subsumption calls : 6336
% 0.24/0.59 % Non-unit clause-clause subsumptions : 359
% 0.24/0.59 % Unit Clause-clause subsumption calls : 35
% 0.24/0.59 % Rewrite failures with RHS unbound : 0
% 0.24/0.59 % BW rewrite match attempts : 15
% 0.24/0.59 % BW rewrite match successes : 12
% 0.24/0.59 % Condensation attempts : 0
% 0.24/0.59 % Condensation successes : 0
% 0.24/0.59 % Termbank termtop insertions : 26923
% 0.24/0.59 % Search garbage collected termcells : 580
% 0.24/0.59
% 0.24/0.59 % -------------------------------------------------
% 0.24/0.59 % User time : 0.036 s
% 0.24/0.59 % System time : 0.006 s
% 0.24/0.59 % Total time : 0.042 s
% 0.24/0.59 % Maximum resident set size: 3656 pages
% 0.24/0.59
% 0.24/0.59 % -------------------------------------------------
% 0.24/0.59 % User time : 0.081 s
% 0.24/0.59 % System time : 0.021 s
% 0.24/0.59 % Total time : 0.101 s
% 0.24/0.59 % Maximum resident set size: 4864 pages
% 0.24/0.59 % E exiting
%------------------------------------------------------------------------------