%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU225+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 02:24:20 PM UTC 2026
% Result : Theorem 2.10s 0.76s
% Output : CNFRefutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 119 ( 25 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 145 ( 56 ~; 50 |; 19 &)
% ( 5 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 ( 2 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/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(t72_funct_1,conjecture,
! [X1,X2,X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
fof(t70_funct_1,lemma,
! [X1,X2,X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).
fof(fc4_funct_1,axiom,
! [X1,X2] :
( ( function(X1)
& relation(X1) )
=> ( function(relation_dom_restriction(X1,X2))
& relation(relation_dom_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(dt_k7_relat_1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(t86_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_dom(relation_dom_restriction(X3,X2)))
<=> ( in(X1,relation_dom(X3))
& in(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_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,X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
inference(assume_negation,[status(cth)],[t72_funct_1]) ).
fof(c_0_8,plain,
! [X177,X178,X179] :
( ( ~ function(X177)
| ~ relation(X177)
| in(X178,relation_dom(X177))
| X179 = apply(X177,X178)
| X179 != empty_set )
& ( ~ function(X177)
| ~ relation(X177)
| in(X178,relation_dom(X177))
| X179 = empty_set
| X179 != apply(X177,X178) )
& ( ~ function(X177)
| ~ relation(X177)
| ~ in(X178,relation_dom(X177))
| X179 = apply(X177,X178)
| ~ in(ordered_pair(X178,X179),X177) )
& ( ~ function(X177)
| ~ relation(X177)
| ~ in(X178,relation_dom(X177))
| in(ordered_pair(X178,X179),X177)
| X179 != apply(X177,X178) ) ),
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_dom_restriction(esk82_0,esk80_0),esk81_0) != apply(esk82_0,esk81_0)
& in(esk81_0,esk80_0)
& function(esk82_0)
& relation(esk82_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_10,lemma,
! [X597,X598,X599] :
( apply(relation_dom_restriction(X599,X597),X598) = apply(X599,X598)
| ~ in(X598,relation_dom(relation_dom_restriction(X599,X597)))
| ~ function(X599)
| ~ relation(X599) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t70_funct_1])])]) ).
cnf(c_0_11,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]) ).
cnf(c_0_12,negated_conjecture,
apply(relation_dom_restriction(esk82_0,esk80_0),esk81_0) != apply(esk82_0,esk81_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,lemma,
( ~ in(X2,relation_dom(relation_dom_restriction(X1,X3)))
| ~ function(X1)
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X3),X2) = apply(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
relation(esk82_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
function(esk82_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( ~ function(X1)
| ~ relation(X1)
| in(X2,relation_dom(X1))
| apply(X1,X2) = empty_set ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
~ in(esk81_0,relation_dom(relation_dom_restriction(esk82_0,esk80_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])]) ).
fof(c_0_18,plain,
! [X308,X309] :
( ( ~ function(X308)
| ~ relation(X308)
| function(relation_dom_restriction(X308,X309)) )
& ( ~ function(X308)
| ~ relation(X308)
| relation(relation_dom_restriction(X308,X309)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])])]) ).
cnf(c_0_19,negated_conjecture,
( ~ function(relation_dom_restriction(esk82_0,esk80_0))
| ~ relation(relation_dom_restriction(esk82_0,esk80_0))
| apply(esk82_0,esk81_0) != empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_16]),c_0_17]) ).
cnf(c_0_20,plain,
( ~ function(X1)
| ~ relation(X1)
| function(relation_dom_restriction(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X277,X278] :
( relation(relation_dom_restriction(X277,X278))
| ~ relation(X277) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])])]) ).
fof(c_0_22,lemma,
! [X614,X615,X616] :
( ( ~ relation(X616)
| in(X614,relation_dom(relation_dom_restriction(X616,X615)))
| ~ in(X614,relation_dom(X616))
| ~ in(X614,X615) )
& ( ~ relation(X616)
| ~ in(X614,relation_dom(relation_dom_restriction(X616,X615)))
| in(X614,relation_dom(X616)) )
& ( ~ relation(X616)
| ~ in(X614,relation_dom(relation_dom_restriction(X616,X615)))
| in(X614,X615) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t86_relat_1])])])]) ).
cnf(c_0_23,negated_conjecture,
( ~ relation(relation_dom_restriction(esk82_0,esk80_0))
| apply(esk82_0,esk81_0) != empty_set ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_14]),c_0_15])]) ).
cnf(c_0_24,plain,
( ~ relation(X1)
| relation(relation_dom_restriction(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,lemma,
( ~ relation(X3)
| ~ in(X1,relation_dom(X3))
| ~ in(X1,X2)
| in(X1,relation_dom(relation_dom_restriction(X3,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
in(esk81_0,esk80_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
apply(esk82_0,esk81_0) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_14])]) ).
cnf(c_0_28,lemma,
~ in(esk81_0,relation_dom(esk82_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_25]),c_0_14]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_16]),c_0_14]),c_0_15])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU225+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.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 06:00:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 2.10/0.76 % Version: 3.5.1
% 2.10/0.76 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.10/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.10/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.10/0.76 % Starting new_bool_3 with 300s (1) cores
% 2.10/0.76 % Starting new_bool_1 with 300s (1) cores
% 2.10/0.76 % Starting sh5l with 300s (1) cores
% 2.10/0.76 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 83406 completed with status 0
% 2.10/0.76 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 2.10/0.76 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.10/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.10/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.10/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.10/0.76 % No SInE strategy applied
% 2.10/0.76 % Search class: FGHSM-FSLM32-MFFFFFNN
% 2.10/0.76 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 2.10/0.76 % Starting SubtermCWHack with 136s (1) cores
% 2.10/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 2.10/0.76 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 2.10/0.76 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 123s (1) cores
% 2.10/0.76 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 123s (1) cores
% 2.10/0.76 % G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with pid 83417 completed with status 0
% 2.10/0.76 % Result found by G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N
% 2.10/0.76 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.10/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.10/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.10/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.10/0.76 % No SInE strategy applied
% 2.10/0.76 % Search class: FGHSM-FSLM32-MFFFFFNN
% 2.10/0.76 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 2.10/0.76 % Starting SubtermCWHack with 136s (1) cores
% 2.10/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 2.10/0.76 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 2.10/0.76 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 123s (1) cores
% 2.10/0.76 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 123s (1) cores
% 2.10/0.76 % Preprocessing time : 0.008 s
% 2.10/0.76 % Presaturation interreduction done
% 2.10/0.76
% 2.10/0.76 % Proof found!
% 2.10/0.76 % SZS status Theorem
% 2.10/0.76 % SZS output start CNFRefutation
% See solution above
% 2.10/0.76 % Parsed axioms : 240
% 2.10/0.76 % Removed by relevancy pruning/SinE : 0
% 2.10/0.76 % Initial clauses : 461
% 2.10/0.76 % Removed in clause preprocessing : 26
% 2.10/0.76 % Initial clauses in saturation : 435
% 2.10/0.76 % Processed clauses : 925
% 2.10/0.76 % ...of these trivial : 8
% 2.10/0.76 % ...subsumed : 58
% 2.10/0.76 % ...remaining for further processing : 859
% 2.10/0.76 % Other redundant clauses eliminated : 137
% 2.10/0.76 % Clauses deleted for lack of memory : 0
% 2.10/0.76 % Backward-subsumed : 2
% 2.10/0.76 % Backward-rewritten : 11
% 2.10/0.76 % Generated clauses : 5734
% 2.10/0.76 % ...of the previous two non-redundant : 5436
% 2.10/0.76 % ...aggressively subsumed : 0
% 2.10/0.76 % Contextual simplify-reflections : 24
% 2.10/0.76 % Paramodulations : 5588
% 2.10/0.76 % Factorizations : 14
% 2.10/0.76 % NegExts : 0
% 2.10/0.76 % Equation resolutions : 143
% 2.10/0.76 % Disequality decompositions : 0
% 2.10/0.76 % Total rewrite steps : 713
% 2.10/0.76 % ...of those cached : 592
% 2.10/0.76 % Propositional unsat checks : 0
% 2.10/0.76 % Propositional check models : 0
% 2.10/0.76 % Propositional check unsatisfiable : 0
% 2.10/0.76 % Propositional clauses : 0
% 2.10/0.76 % Propositional clauses after purity: 0
% 2.10/0.76 % Propositional unsat core size : 0
% 2.10/0.76 % Propositional preprocessing time : 0.000
% 2.10/0.76 % Propositional encoding time : 0.000
% 2.10/0.76 % Propositional solver time : 0.000
% 2.10/0.76 % Success case prop preproc time : 0.000
% 2.10/0.76 % Success case prop encoding time : 0.000
% 2.10/0.76 % Success case prop solver time : 0.000
% 2.10/0.76 % Current number of processed clauses : 389
% 2.10/0.76 % Positive orientable unit clauses : 48
% 2.10/0.76 % Positive unorientable unit clauses: 3
% 2.10/0.76 % Negative unit clauses : 17
% 2.10/0.76 % Non-unit-clauses : 321
% 2.10/0.76 % Current number of unprocessed clauses: 5325
% 2.10/0.76 % ...number of literals in the above : 24251
% 2.10/0.76 % Current number of archived formulas : 0
% 2.10/0.76 % Current number of archived clauses : 397
% 2.10/0.76 % Clause-clause subsumption calls (NU) : 72131
% 2.10/0.76 % Rec. Clause-clause subsumption calls : 23974
% 2.10/0.76 % Non-unit clause-clause subsumptions : 62
% 2.10/0.76 % Unit Clause-clause subsumption calls : 1715
% 2.10/0.76 % Rewrite failures with RHS unbound : 0
% 2.10/0.76 % BW rewrite match attempts : 73
% 2.10/0.76 % BW rewrite match successes : 54
% 2.10/0.76 % Condensation attempts : 0
% 2.10/0.76 % Condensation successes : 0
% 2.10/0.76 % Termbank termtop insertions : 137615
% 2.10/0.76 % Search garbage collected termcells : 7861
% 2.10/0.76
% 2.10/0.76 % -------------------------------------------------
% 2.10/0.76 % User time : 0.250 s
% 2.10/0.76 % System time : 0.014 s
% 2.10/0.76 % Total time : 0.264 s
% 2.10/0.76 % Maximum resident set size: 5108 pages
% 2.10/0.76
% 2.10/0.76 % -------------------------------------------------
% 2.10/0.76 % User time : 1.357 s
% 2.10/0.76 % System time : 0.073 s
% 2.10/0.76 % Total time : 1.430 s
% 2.10/0.76 % Maximum resident set size: 5120 pages
% 2.10/0.76 % E exiting
%------------------------------------------------------------------------------