%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU215+2 : 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 : n012.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 02:24:17 PM UTC 2026
% Result : Theorem 0.08s 0.67s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 160 ( 23 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 207 ( 79 ~; 75 |; 29 &)
% ( 5 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2,X3] :
( ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) )
& ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(t23_funct_1,conjecture,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(t22_funct_1,lemma,
! [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,lemma,
! [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(c_0_6,plain,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2,X3] :
( ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) )
& ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
inference(fof_simplification,[status(thm)],[d4_funct_1]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
inference(assume_negation,[status(cth)],[t23_funct_1]) ).
fof(c_0_8,plain,
! [X176,X177,X178] :
( ( ~ function(X176)
| ~ relation(X176)
| in(X177,relation_dom(X176))
| X178 = apply(X176,X177)
| X178 != empty_set )
& ( ~ function(X176)
| ~ relation(X176)
| in(X177,relation_dom(X176))
| X178 = empty_set
| X178 != apply(X176,X177) )
& ( ~ function(X176)
| ~ relation(X176)
| ~ in(X177,relation_dom(X176))
| X178 = apply(X176,X177)
| ~ in(ordered_pair(X177,X178),X176) )
& ( ~ function(X176)
| ~ relation(X176)
| ~ in(X177,relation_dom(X176))
| in(ordered_pair(X177,X178),X176)
| X178 != apply(X176,X177) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
fof(c_0_9,negated_conjecture,
( apply(relation_composition(esk66_0,esk67_0),esk65_0) != apply(esk67_0,apply(esk66_0,esk65_0))
& in(esk65_0,relation_dom(esk66_0))
& function(esk67_0)
& relation(esk67_0)
& function(esk66_0)
& relation(esk66_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_10,plain,
( ~ function(X2)
| ~ relation(X2)
| X1 != apply(X2,X3)
| in(X3,relation_dom(X2))
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,lemma,
! [X438,X439,X440] :
( apply(relation_composition(X440,X439),X438) = apply(X439,apply(X440,X438))
| ~ in(X438,relation_dom(relation_composition(X440,X439)))
| ~ function(X440)
| ~ relation(X440)
| ~ function(X439)
| ~ relation(X439) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_funct_1])])])]) ).
cnf(c_0_12,negated_conjecture,
apply(relation_composition(esk66_0,esk67_0),esk65_0) != apply(esk67_0,apply(esk66_0,esk65_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( ~ function(X1)
| ~ relation(X1)
| in(X2,relation_dom(X1))
| apply(X1,X2) = empty_set ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
relation(esk67_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
function(esk67_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,lemma,
( ~ 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_11]) ).
cnf(c_0_17,negated_conjecture,
relation(esk66_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
function(esk66_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_19,lemma,
! [X434,X435,X436] :
( ( ~ function(X435)
| ~ relation(X435)
| ~ function(X436)
| ~ relation(X436)
| in(X434,relation_dom(relation_composition(X436,X435)))
| ~ in(apply(X436,X434),relation_dom(X435))
| ~ in(X434,relation_dom(X436)) )
& ( ~ function(X435)
| ~ relation(X435)
| ~ function(X436)
| ~ relation(X436)
| ~ in(X434,relation_dom(relation_composition(X436,X435)))
| in(apply(X436,X434),relation_dom(X435)) )
& ( ~ function(X435)
| ~ relation(X435)
| ~ function(X436)
| ~ relation(X436)
| ~ in(X434,relation_dom(relation_composition(X436,X435)))
| in(X434,relation_dom(X436)) ) ),
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_20,negated_conjecture,
( apply(relation_composition(esk66_0,esk67_0),esk65_0) != empty_set
| in(apply(esk66_0,esk65_0),relation_dom(esk67_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_21,negated_conjecture,
~ in(esk65_0,relation_dom(relation_composition(esk66_0,esk67_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_12,c_0_16]),c_0_17]),c_0_14]),c_0_18]),c_0_15])]) ).
cnf(c_0_22,lemma,
( ~ 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_19]) ).
cnf(c_0_23,negated_conjecture,
( ~ function(relation_composition(esk66_0,esk67_0))
| ~ relation(relation_composition(esk66_0,esk67_0))
| in(apply(esk66_0,esk65_0),relation_dom(esk67_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_13]),c_0_21]) ).
cnf(c_0_24,negated_conjecture,
in(esk65_0,relation_dom(esk66_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_25,plain,
! [X279,X280] :
( ( ~ function(X280)
| ~ relation(X280)
| ~ function(X279)
| ~ relation(X279)
| function(relation_composition(X279,X280)) )
& ( ~ function(X280)
| ~ relation(X280)
| ~ function(X279)
| ~ relation(X279)
| relation(relation_composition(X279,X280)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])])]) ).
cnf(c_0_26,lemma,
( ~ function(relation_composition(esk66_0,esk67_0))
| ~ relation(relation_composition(esk66_0,esk67_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[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_14]),c_0_17]),c_0_15]),c_0_18]),c_0_24])]),c_0_21]) ).
cnf(c_0_27,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1)
| function(relation_composition(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_28,plain,
! [X259,X260] :
( relation(relation_composition(X259,X260))
| ~ relation(X260)
| ~ relation(X259) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])])]) ).
cnf(c_0_29,lemma,
~ relation(relation_composition(esk66_0,esk67_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_26,c_0_27]),c_0_14]),c_0_17]),c_0_15]),c_0_18])]) ).
cnf(c_0_30,plain,
( ~ relation(X2)
| ~ relation(X1)
| relation(relation_composition(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_14]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU215+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.50 % Computer : n012.cluster.edu
% 0.04/0.50 % Model : x86_64 x86_64
% 0.04/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.50 % Memory : 8046.5625MB
% 0.04/0.50 % OS : Linux 6.8.0-71-generic
% 0.04/0.50 % CPULimit : 300
% 0.04/0.51 % WCLimit : 300
% 0.04/0.51 % DateTime : Mon Sep 21 05:58:37 UTC 2026
% 0.04/0.51 % CPUTime :
% 0.04/0.51 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.53 Running first-order theorem proving
% 0.07/0.53 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
% 0.08/0.67 % Version: 3.5.1
% 0.08/0.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.67 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.67 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.67 % Starting sh5l with 300s (1) cores
% 0.08/0.67 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1699446 completed with status 0
% 0.08/0.67 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.08/0.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.67 % No SInE strategy applied
% 0.08/0.67 % Search class: FGHSM-FSLM32-MFFFFFNN
% 0.08/0.67 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.67 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.08/0.67 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 0.08/0.67 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 123s (1) cores
% 0.08/0.67 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 123s (1) cores
% 0.08/0.67 % G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with pid 1699457 completed with status 0
% 0.08/0.67 % Result found by G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N
% 0.08/0.67 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.08/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.08/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.67 % No SInE strategy applied
% 0.08/0.67 % Search class: FGHSM-FSLM32-MFFFFFNN
% 0.08/0.67 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.67 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.67 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.08/0.67 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 0.08/0.67 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 123s (1) cores
% 0.08/0.67 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 123s (1) cores
% 0.08/0.67 % Preprocessing time : 0.004 s
% 0.08/0.67 % Presaturation interreduction done
% 0.08/0.67
% 0.08/0.67 % Proof found!
% 0.08/0.67 % SZS status Theorem
% 0.08/0.67 % SZS output start CNFRefutation
% See solution above
% 0.08/0.67 % Parsed axioms : 219
% 0.08/0.67 % Removed by relevancy pruning/SinE : 0
% 0.08/0.67 % Initial clauses : 403
% 0.08/0.67 % Removed in clause preprocessing : 24
% 0.08/0.67 % Initial clauses in saturation : 379
% 0.08/0.67 % Processed clauses : 796
% 0.08/0.67 % ...of these trivial : 7
% 0.08/0.67 % ...subsumed : 36
% 0.08/0.67 % ...remaining for further processing : 753
% 0.08/0.67 % Other redundant clauses eliminated : 112
% 0.08/0.67 % Clauses deleted for lack of memory : 0
% 0.08/0.67 % Backward-subsumed : 2
% 0.08/0.67 % Backward-rewritten : 3
% 0.08/0.67 % Generated clauses : 5057
% 0.08/0.67 % ...of the previous two non-redundant : 4791
% 0.08/0.67 % ...aggressively subsumed : 0
% 0.08/0.67 % Contextual simplify-reflections : 16
% 0.08/0.67 % Paramodulations : 4933
% 0.08/0.67 % Factorizations : 14
% 0.08/0.67 % NegExts : 0
% 0.08/0.67 % Equation resolutions : 117
% 0.08/0.67 % Disequality decompositions : 0
% 0.08/0.67 % Total rewrite steps : 589
% 0.08/0.67 % ...of those cached : 487
% 0.08/0.67 % Propositional unsat checks : 0
% 0.08/0.67 % Propositional check models : 0
% 0.08/0.67 % Propositional check unsatisfiable : 0
% 0.08/0.67 % Propositional clauses : 0
% 0.08/0.67 % Propositional clauses after purity: 0
% 0.08/0.67 % Propositional unsat core size : 0
% 0.08/0.67 % Propositional preprocessing time : 0.000
% 0.08/0.67 % Propositional encoding time : 0.000
% 0.08/0.67 % Propositional solver time : 0.000
% 0.08/0.67 % Success case prop preproc time : 0.000
% 0.08/0.67 % Success case prop encoding time : 0.000
% 0.08/0.67 % Success case prop solver time : 0.000
% 0.08/0.67 % Current number of processed clauses : 345
% 0.08/0.67 % Positive orientable unit clauses : 43
% 0.08/0.67 % Positive unorientable unit clauses: 3
% 0.08/0.67 % Negative unit clauses : 15
% 0.08/0.67 % Non-unit-clauses : 284
% 0.08/0.67 % Current number of unprocessed clauses: 4709
% 0.08/0.67 % ...number of literals in the above : 19771
% 0.08/0.67 % Current number of archived formulas : 0
% 0.08/0.67 % Current number of archived clauses : 346
% 0.08/0.67 % Clause-clause subsumption calls (NU) : 49858
% 0.08/0.67 % Rec. Clause-clause subsumption calls : 21054
% 0.08/0.67 % Non-unit clause-clause subsumptions : 43
% 0.08/0.67 % Unit Clause-clause subsumption calls : 686
% 0.08/0.67 % Rewrite failures with RHS unbound : 0
% 0.08/0.67 % BW rewrite match attempts : 72
% 0.08/0.67 % BW rewrite match successes : 50
% 0.08/0.67 % Condensation attempts : 0
% 0.08/0.67 % Condensation successes : 0
% 0.08/0.67 % Termbank termtop insertions : 116093
% 0.08/0.67 % Search garbage collected termcells : 6798
% 0.08/0.67
% 0.08/0.67 % -------------------------------------------------
% 0.08/0.67 % User time : 0.110 s
% 0.08/0.67 % System time : 0.010 s
% 0.08/0.67 % Total time : 0.120 s
% 0.08/0.67 % Maximum resident set size: 4880 pages
% 0.08/0.67
% 0.08/0.67 % -------------------------------------------------
% 0.08/0.67 % User time : 0.511 s
% 0.08/0.67 % System time : 0.046 s
% 0.08/0.67 % Total time : 0.557 s
% 0.08/0.67 % Maximum resident set size: 4864 pages
% 0.08/0.67 % E exiting
%------------------------------------------------------------------------------