%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU009+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 02:23:40 PM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 126 ( 15 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 162 ( 66 ~; 66 |; 20 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 2 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t40_funct_1,conjecture,
! [X1,X2,X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X2,relation_dom(relation_composition(X3,identity_relation(X1))))
<=> ( in(apply(X3,X2),X1)
& in(X2,relation_dom(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_1) ).
fof(t34_funct_1,axiom,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( X2 = identity_relation(X1)
<=> ( ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 )
& relation_dom(X2) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( function(identity_relation(X1))
& relation(identity_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(t21_funct_1,axiom,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(apply(X3,X1),relation_dom(X2))
& in(X1,relation_dom(X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X2,relation_dom(relation_composition(X3,identity_relation(X1))))
<=> ( in(apply(X3,X2),X1)
& in(X2,relation_dom(X3)) ) ) ),
inference(assume_negation,[status(cth)],[t40_funct_1]) ).
fof(c_0_6,plain,
! [X41,X42,X43] :
( ( ~ function(X42)
| ~ relation(X42)
| X42 = identity_relation(X41)
| relation_dom(X42) != X41
| apply(X42,esk10_2(X41,X42)) != esk10_2(X41,X42) )
& ( ~ function(X42)
| ~ relation(X42)
| X42 = identity_relation(X41)
| relation_dom(X42) != X41
| in(esk10_2(X41,X42),X41) )
& ( ~ function(X42)
| ~ relation(X42)
| X42 != identity_relation(X41)
| apply(X42,X43) = X43
| ~ in(X43,X41) )
& ( ~ function(X42)
| ~ relation(X42)
| X42 != identity_relation(X41)
| relation_dom(X42) = X41 ) ),
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)],[t34_funct_1])])])])])]) ).
fof(c_0_7,plain,
! [X10] : relation(identity_relation(X10)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_8,plain,
! [X18] :
( function(identity_relation(X18))
& relation(identity_relation(X18)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(c_0_9,plain,
! [X36,X37,X38] :
( ( ~ function(X37)
| ~ relation(X37)
| ~ function(X38)
| ~ relation(X38)
| in(X36,relation_dom(relation_composition(X38,X37)))
| ~ in(apply(X38,X36),relation_dom(X37))
| ~ in(X36,relation_dom(X38)) )
& ( ~ function(X37)
| ~ relation(X37)
| ~ function(X38)
| ~ relation(X38)
| ~ in(X36,relation_dom(relation_composition(X38,X37)))
| in(apply(X38,X36),relation_dom(X37)) )
& ( ~ function(X37)
| ~ relation(X37)
| ~ function(X38)
| ~ relation(X38)
| ~ in(X36,relation_dom(relation_composition(X38,X37)))
| in(X36,relation_dom(X38)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_funct_1])])])])]) ).
fof(c_0_10,negated_conjecture,
( ( in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0))))
| in(apply(esk13_0,esk12_0),esk11_0) )
& ( in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0))))
| in(esk12_0,relation_dom(esk13_0)) )
& ( ~ in(apply(esk13_0,esk12_0),esk11_0)
| ~ in(esk12_0,relation_dom(esk13_0))
| ~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))) )
& function(esk13_0)
& relation(esk13_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
cnf(c_0_11,plain,
( ~ function(X1)
| ~ relation(X1)
| X1 != identity_relation(X2)
| relation_dom(X1) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ function(X3)
| ~ relation(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(relation_composition(X2,X3)))
| in(X1,relation_dom(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0))))
| in(esk12_0,relation_dom(esk13_0)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
function(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( ~ function(X3)
| ~ relation(X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_dom(relation_composition(X1,X3)))
| in(apply(X1,X2),relation_dom(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
relation_dom(identity_relation(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_11]),c_0_12]),c_0_13])]) ).
cnf(c_0_20,negated_conjecture,
( ~ in(apply(esk13_0,esk12_0),esk11_0)
| ~ in(esk12_0,relation_dom(esk13_0))
| ~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
in(esk12_0,relation_dom(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_12]),c_0_16]),c_0_13]),c_0_17])]) ).
cnf(c_0_22,plain,
( ~ in(X2,relation_dom(relation_composition(X1,identity_relation(X3))))
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_12]),c_0_13])]) ).
cnf(c_0_23,negated_conjecture,
( in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0))))
| in(apply(esk13_0,esk12_0),esk11_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(apply(esk13_0,esk12_0),esk11_0)
| ~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
cnf(c_0_25,negated_conjecture,
in(apply(esk13_0,esk12_0),esk11_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_16]),c_0_17])]) ).
cnf(c_0_26,plain,
( ~ function(X3)
| ~ relation(X3)
| ~ function(X2)
| ~ relation(X2)
| ~ in(apply(X2,X1),relation_dom(X3))
| ~ in(X1,relation_dom(X2))
| in(X1,relation_dom(relation_composition(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_28,plain,
( ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),X3)
| ~ function(X2)
| ~ relation(X2)
| in(X1,relation_dom(relation_composition(X2,identity_relation(X3)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_19]),c_0_12]),c_0_13])]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_16]),c_0_17]),c_0_25]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU009+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 05:50:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.46 % Version: 3.5.1
% 0.10/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.46 % Starting sh5l with 300s (1) cores
% 0.10/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 692478 completed with status 0
% 0.10/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.46 % No SInE strategy applied
% 0.10/0.46 % Search class: FGHSM-FFMM21-MFFFFFNN
% 0.10/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.46 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.10/0.46 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.10/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.46 % SAT001_MinMin_p005000_rr_RG with pid 692487 completed with status 0
% 0.10/0.46 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.10/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.46 % No SInE strategy applied
% 0.10/0.46 % Search class: FGHSM-FFMM21-MFFFFFNN
% 0.10/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.46 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.10/0.46 % Preprocessing time : 0.001 s
% 0.10/0.46 % Presaturation interreduction done
% 0.10/0.46
% 0.10/0.46 % Proof found!
% 0.10/0.46 % SZS status Theorem
% 0.10/0.46 % SZS output start CNFRefutation
% See solution above
% 0.10/0.46 % Parsed axioms : 36
% 0.10/0.46 % Removed by relevancy pruning/SinE : 0
% 0.10/0.46 % Initial clauses : 60
% 0.10/0.46 % Removed in clause preprocessing : 0
% 0.10/0.46 % Initial clauses in saturation : 60
% 0.10/0.46 % Processed clauses : 622
% 0.10/0.46 % ...of these trivial : 6
% 0.10/0.46 % ...subsumed : 357
% 0.10/0.46 % ...remaining for further processing : 259
% 0.10/0.46 % Other redundant clauses eliminated : 4
% 0.10/0.46 % Clauses deleted for lack of memory : 0
% 0.10/0.46 % Backward-subsumed : 22
% 0.10/0.46 % Backward-rewritten : 18
% 0.10/0.46 % Generated clauses : 1391
% 0.10/0.46 % ...of the previous two non-redundant : 1233
% 0.10/0.46 % ...aggressively subsumed : 0
% 0.10/0.46 % Contextual simplify-reflections : 13
% 0.10/0.46 % Paramodulations : 1387
% 0.10/0.46 % Factorizations : 0
% 0.10/0.46 % NegExts : 0
% 0.10/0.46 % Equation resolutions : 4
% 0.10/0.46 % Disequality decompositions : 0
% 0.10/0.46 % Total rewrite steps : 470
% 0.10/0.46 % ...of those cached : 438
% 0.10/0.46 % Propositional unsat checks : 0
% 0.10/0.46 % Propositional check models : 0
% 0.10/0.46 % Propositional check unsatisfiable : 0
% 0.10/0.46 % Propositional clauses : 0
% 0.10/0.46 % Propositional clauses after purity: 0
% 0.10/0.46 % Propositional unsat core size : 0
% 0.10/0.46 % Propositional preprocessing time : 0.000
% 0.10/0.46 % Propositional encoding time : 0.000
% 0.10/0.46 % Propositional solver time : 0.000
% 0.10/0.46 % Success case prop preproc time : 0.000
% 0.10/0.46 % Success case prop encoding time : 0.000
% 0.10/0.46 % Success case prop solver time : 0.000
% 0.10/0.46 % Current number of processed clauses : 160
% 0.10/0.46 % Positive orientable unit clauses : 29
% 0.10/0.46 % Positive unorientable unit clauses: 0
% 0.10/0.46 % Negative unit clauses : 12
% 0.10/0.46 % Non-unit-clauses : 119
% 0.10/0.46 % Current number of unprocessed clauses: 693
% 0.10/0.46 % ...number of literals in the above : 3957
% 0.10/0.46 % Current number of archived formulas : 0
% 0.10/0.46 % Current number of archived clauses : 95
% 0.10/0.46 % Clause-clause subsumption calls (NU) : 7504
% 0.10/0.46 % Rec. Clause-clause subsumption calls : 4268
% 0.10/0.46 % Non-unit clause-clause subsumptions : 288
% 0.10/0.46 % Unit Clause-clause subsumption calls : 310
% 0.10/0.46 % Rewrite failures with RHS unbound : 0
% 0.10/0.46 % BW rewrite match attempts : 10
% 0.10/0.46 % BW rewrite match successes : 7
% 0.10/0.46 % Condensation attempts : 0
% 0.10/0.46 % Condensation successes : 0
% 0.10/0.46 % Termbank termtop insertions : 21286
% 0.10/0.46 % Search garbage collected termcells : 617
% 0.10/0.46
% 0.10/0.46 % -------------------------------------------------
% 0.10/0.46 % User time : 0.025 s
% 0.10/0.46 % System time : 0.004 s
% 0.10/0.46 % Total time : 0.029 s
% 0.10/0.46 % Maximum resident set size: 3612 pages
% 0.10/0.46
% 0.10/0.46 % -------------------------------------------------
% 0.10/0.46 % User time : 0.114 s
% 0.10/0.46 % System time : 0.018 s
% 0.10/0.46 % Total time : 0.132 s
% 0.10/0.46 % Maximum resident set size: 4864 pages
% 0.10/0.46 % E exiting
%------------------------------------------------------------------------------