%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU002+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 02:23:39 PM UTC 2026
% Result : Theorem 2.27s 0.77s
% Output : CNFRefutation 2.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 7 unt; 0 def)
% Number of atoms : 184 ( 26 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 259 ( 106 ~; 107 |; 29 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 72 ( 0 sgn 36 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X1,X4)
& in(X4,relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(t22_funct_1,axiom,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
=> apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_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(fc1_funct_1,axiom,
! [X1,X2] :
( ( function(X2)
& relation(X2)
& function(X1)
& relation(X1) )
=> ( function(relation_composition(X1,X2))
& relation(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X2)
& relation(X1) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(t25_funct_1,conjecture,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X1,relation_rng(relation_composition(X3,X2)))
=> in(X1,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_funct_1) ).
fof(c_0_6,plain,
! [X9,X10,X11,X13,X14,X15,X17] :
( ( ~ function(X9)
| ~ relation(X9)
| X15 = relation_rng(X9)
| in(esk2_2(X9,X15),X15)
| esk2_2(X9,X15) = apply(X9,esk3_2(X9,X15)) )
& ( ~ function(X9)
| ~ relation(X9)
| X15 = relation_rng(X9)
| in(esk2_2(X9,X15),X15)
| in(esk3_2(X9,X15),relation_dom(X9)) )
& ( ~ function(X9)
| ~ relation(X9)
| X15 = relation_rng(X9)
| esk2_2(X9,X15) != apply(X9,X17)
| ~ in(X17,relation_dom(X9))
| ~ in(esk2_2(X9,X15),X15) )
& ( ~ function(X9)
| ~ relation(X9)
| X10 != relation_rng(X9)
| in(X13,X10)
| X13 != apply(X9,X14)
| ~ in(X14,relation_dom(X9)) )
& ( ~ function(X9)
| ~ relation(X9)
| X10 != relation_rng(X9)
| ~ in(X11,X10)
| X11 = apply(X9,esk1_3(X9,X10,X11)) )
& ( ~ function(X9)
| ~ relation(X9)
| X10 != relation_rng(X9)
| ~ in(X11,X10)
| in(esk1_3(X9,X10,X11),relation_dom(X9)) ) ),
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)],[d5_funct_1])])])])])])]) ).
fof(c_0_7,plain,
! [X50,X51,X52] :
( apply(relation_composition(X52,X51),X50) = apply(X51,apply(X52,X50))
| ~ in(X50,relation_dom(relation_composition(X52,X51)))
| ~ function(X52)
| ~ relation(X52)
| ~ function(X51)
| ~ relation(X51) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_funct_1])])])]) ).
fof(c_0_8,plain,
! [X47,X48,X49] :
( ( ~ function(X48)
| ~ relation(X48)
| ~ function(X49)
| ~ relation(X49)
| in(X47,relation_dom(relation_composition(X49,X48)))
| ~ in(apply(X49,X47),relation_dom(X48))
| ~ in(X47,relation_dom(X49)) )
& ( ~ function(X48)
| ~ relation(X48)
| ~ function(X49)
| ~ relation(X49)
| ~ in(X47,relation_dom(relation_composition(X49,X48)))
| in(apply(X49,X47),relation_dom(X48)) )
& ( ~ function(X48)
| ~ relation(X48)
| ~ function(X49)
| ~ relation(X49)
| ~ in(X47,relation_dom(relation_composition(X49,X48)))
| in(X47,relation_dom(X49)) ) ),
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])])])])]) ).
cnf(c_0_9,plain,
( ~ function(X2)
| ~ relation(X2)
| X4 != relation_rng(X2)
| X3 != apply(X2,X1)
| ~ in(X1,relation_dom(X2))
| in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ in(X3,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1)
| apply(relation_composition(X2,X1),X3) = apply(X1,apply(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,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_8]) ).
fof(c_0_12,plain,
! [X25,X26] :
( ( ~ function(X26)
| ~ relation(X26)
| ~ function(X25)
| ~ relation(X25)
| function(relation_composition(X25,X26)) )
& ( ~ function(X26)
| ~ relation(X26)
| ~ function(X25)
| ~ relation(X25)
| relation(relation_composition(X25,X26)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])])]) ).
fof(c_0_13,plain,
! [X19,X20] :
( relation(relation_composition(X19,X20))
| ~ relation(X20)
| ~ relation(X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])])]) ).
cnf(c_0_14,plain,
( ~ in(X5,relation_dom(relation_composition(X3,X4)))
| ~ function(X3)
| ~ function(X4)
| ~ relation(X3)
| ~ relation(X4)
| X2 != relation_rng(X4)
| X1 != apply(relation_composition(X3,X4),X5)
| in(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_15,plain,
( ~ function(X2)
| ~ relation(X2)
| X3 != relation_rng(X2)
| ~ in(X1,X3)
| X1 = apply(X2,esk1_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,plain,
( ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2)
| in(esk1_3(X1,X2,X3),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1)
| function(relation_composition(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ relation(X2)
| ~ relation(X1)
| relation(relation_composition(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X1,relation_rng(relation_composition(X3,X2)))
=> in(X1,relation_rng(X2)) ) ) ),
inference(assume_negation,[status(cth)],[t25_funct_1]) ).
cnf(c_0_20,plain,
( ~ in(X1,X3)
| ~ function(X4)
| ~ function(X5)
| ~ relation(X4)
| ~ relation(X5)
| X2 != relation_rng(X5)
| X3 != relation_rng(relation_composition(X4,X5))
| in(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15])]),c_0_16]),c_0_17]),c_0_18]) ).
fof(c_0_21,negated_conjecture,
( ~ in(esk13_0,relation_rng(esk14_0))
& in(esk13_0,relation_rng(relation_composition(esk15_0,esk14_0)))
& function(esk15_0)
& relation(esk15_0)
& function(esk14_0)
& relation(esk14_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
cnf(c_0_22,plain,
( ~ in(X1,relation_rng(relation_composition(X4,X3)))
| ~ function(X4)
| ~ function(X3)
| ~ relation(X4)
| ~ relation(X3)
| X2 != relation_rng(X3)
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_23,negated_conjecture,
in(esk13_0,relation_rng(relation_composition(esk15_0,esk14_0))),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
function(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( X1 != relation_rng(esk14_0)
| in(esk13_0,X1) ),
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_22,c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_27])]) ).
cnf(c_0_29,negated_conjecture,
~ in(esk13_0,relation_rng(esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU002+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n015.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:49:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.27/0.77 % Version: 3.5.1
% 2.27/0.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.27/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.27/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.27/0.77 % Starting new_bool_3 with 300s (1) cores
% 2.27/0.77 % Starting new_bool_1 with 300s (1) cores
% 2.27/0.77 % Starting sh5l with 300s (1) cores
% 2.27/0.77 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 689996 completed with status 0
% 2.27/0.77 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.27/0.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.27/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.27/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.27/0.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.27/0.77 % No SInE strategy applied
% 2.27/0.77 % Search class: FGHSM-FFMM31-SFFFFFNN
% 2.27/0.77 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 2.27/0.77 % Starting SubtermCWHack with 136s (1) cores
% 2.27/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.27/0.77 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 2.27/0.77 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 2.27/0.77 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.27/0.77 % G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with pid 690007 completed with status 0
% 2.27/0.77 % Result found by G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y
% 2.27/0.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.27/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.27/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.27/0.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.27/0.77 % No SInE strategy applied
% 2.27/0.77 % Search class: FGHSM-FFMM31-SFFFFFNN
% 2.27/0.77 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 2.27/0.77 % Starting SubtermCWHack with 136s (1) cores
% 2.27/0.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.27/0.77 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 2.27/0.77 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 2.27/0.77 % Preprocessing time : 0.003 s
% 2.27/0.77
% 2.27/0.77 % Proof found!
% 2.27/0.77 % SZS status Theorem
% 2.27/0.77 % SZS output start CNFRefutation
% See solution above
% 2.27/0.77 % Parsed axioms : 37
% 2.27/0.77 % Removed by relevancy pruning/SinE : 0
% 2.27/0.77 % Initial clauses : 64
% 2.27/0.77 % Removed in clause preprocessing : 0
% 2.27/0.77 % Initial clauses in saturation : 64
% 2.27/0.77 % Processed clauses : 1357
% 2.27/0.77 % ...of these trivial : 12
% 2.27/0.77 % ...subsumed : 868
% 2.27/0.77 % ...remaining for further processing : 477
% 2.27/0.77 % Other redundant clauses eliminated : 3
% 2.27/0.77 % Clauses deleted for lack of memory : 0
% 2.27/0.77 % Backward-subsumed : 59
% 2.27/0.77 % Backward-rewritten : 21
% 2.27/0.77 % Generated clauses : 7815
% 2.27/0.77 % ...of the previous two non-redundant : 7506
% 2.27/0.77 % ...aggressively subsumed : 0
% 2.27/0.77 % Contextual simplify-reflections : 102
% 2.27/0.77 % Paramodulations : 7775
% 2.27/0.77 % Factorizations : 0
% 2.27/0.77 % NegExts : 0
% 2.27/0.77 % Equation resolutions : 40
% 2.27/0.77 % Disequality decompositions : 0
% 2.27/0.77 % Total rewrite steps : 2014
% 2.27/0.77 % ...of those cached : 1994
% 2.27/0.77 % Propositional unsat checks : 0
% 2.27/0.77 % Propositional check models : 0
% 2.27/0.77 % Propositional check unsatisfiable : 0
% 2.27/0.77 % Propositional clauses : 0
% 2.27/0.77 % Propositional clauses after purity: 0
% 2.27/0.77 % Propositional unsat core size : 0
% 2.27/0.77 % Propositional preprocessing time : 0.000
% 2.27/0.77 % Propositional encoding time : 0.000
% 2.27/0.77 % Propositional solver time : 0.000
% 2.27/0.77 % Success case prop preproc time : 0.000
% 2.27/0.77 % Success case prop encoding time : 0.000
% 2.27/0.77 % Success case prop solver time : 0.000
% 2.27/0.77 % Current number of processed clauses : 397
% 2.27/0.77 % Positive orientable unit clauses : 27
% 2.27/0.77 % Positive unorientable unit clauses: 0
% 2.27/0.77 % Negative unit clauses : 23
% 2.27/0.77 % Non-unit-clauses : 347
% 2.27/0.77 % Current number of unprocessed clauses: 5954
% 2.27/0.77 % ...number of literals in the above : 48455
% 2.27/0.77 % Current number of archived formulas : 0
% 2.27/0.77 % Current number of archived clauses : 80
% 2.27/0.77 % Clause-clause subsumption calls (NU) : 50008
% 2.27/0.77 % Rec. Clause-clause subsumption calls : 11025
% 2.27/0.77 % Non-unit clause-clause subsumptions : 697
% 2.27/0.77 % Unit Clause-clause subsumption calls : 1526
% 2.27/0.77 % Rewrite failures with RHS unbound : 0
% 2.27/0.77 % BW rewrite match attempts : 10
% 2.27/0.77 % BW rewrite match successes : 8
% 2.27/0.77 % Condensation attempts : 0
% 2.27/0.77 % Condensation successes : 0
% 2.27/0.77 % Termbank termtop insertions : 148703
% 2.27/0.77 % Search garbage collected termcells : 739
% 2.27/0.77
% 2.27/0.77 % -------------------------------------------------
% 2.27/0.77 % User time : 0.319 s
% 2.27/0.77 % System time : 0.015 s
% 2.27/0.77 % Total time : 0.333 s
% 2.27/0.77 % Maximum resident set size: 3612 pages
% 2.27/0.77
% 2.27/0.77 % -------------------------------------------------
% 2.27/0.77 % User time : 1.572 s
% 2.27/0.77 % System time : 0.104 s
% 2.27/0.77 % Total time : 1.676 s
% 2.27/0.77 % Maximum resident set size: 4864 pages
% 2.27/0.77 % E exiting
%------------------------------------------------------------------------------