%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU225+3 : 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 : n016.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 0.69s 0.59s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 8 unt; 0 def)
% Number of atoms : 162 ( 39 equ)
% Maximal formula atoms : 27 ( 5 avg)
% Number of connectives : 216 ( 85 ~; 84 |; 25 &)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 62 ( 3 sgn 37 !; 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(t68_funct_1,axiom,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( X2 = relation_dom_restriction(X3,X1)
<=> ( ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) )
& relation_dom(X2) = set_intersection2(relation_dom(X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_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/sandbox/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/sandbox/benchmark/theBenchmark.p',dt_k7_relat_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/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
fof(l82_funct_1,axiom,
! [X1,X2,X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
<=> ( in(X2,X1)
& in(X2,relation_dom(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_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,plain,
! [X67,X68,X69,X70] :
( ( ~ function(X68)
| ~ relation(X68)
| ~ function(X69)
| ~ relation(X69)
| X68 = relation_dom_restriction(X69,X67)
| relation_dom(X68) != set_intersection2(relation_dom(X69),X67)
| apply(X68,esk12_3(X67,X68,X69)) != apply(X69,esk12_3(X67,X68,X69)) )
& ( ~ function(X68)
| ~ relation(X68)
| ~ function(X69)
| ~ relation(X69)
| X68 = relation_dom_restriction(X69,X67)
| relation_dom(X68) != set_intersection2(relation_dom(X69),X67)
| in(esk12_3(X67,X68,X69),relation_dom(X68)) )
& ( ~ function(X68)
| ~ relation(X68)
| ~ function(X69)
| ~ relation(X69)
| X68 != relation_dom_restriction(X69,X67)
| apply(X68,X70) = apply(X69,X70)
| ~ in(X70,relation_dom(X68)) )
& ( ~ function(X68)
| ~ relation(X68)
| ~ function(X69)
| ~ relation(X69)
| X68 != relation_dom_restriction(X69,X67)
| relation_dom(X68) = set_intersection2(relation_dom(X69),X67) ) ),
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)],[t68_funct_1])])])])])]) ).
fof(c_0_8,plain,
! [X33,X34] :
( ( ~ function(X33)
| ~ relation(X33)
| function(relation_dom_restriction(X33,X34)) )
& ( ~ function(X33)
| ~ relation(X33)
| relation(relation_dom_restriction(X33,X34)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])])]) ).
fof(c_0_9,plain,
! [X19,X20] :
( relation(relation_dom_restriction(X19,X20))
| ~ relation(X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])])]) ).
fof(c_0_10,plain,
! [X14,X15,X16] :
( ( ~ function(X14)
| ~ relation(X14)
| in(X15,relation_dom(X14))
| X16 = apply(X14,X15)
| X16 != empty_set )
& ( ~ function(X14)
| ~ relation(X14)
| in(X15,relation_dom(X14))
| X16 = empty_set
| X16 != apply(X14,X15) )
& ( ~ function(X14)
| ~ relation(X14)
| ~ in(X15,relation_dom(X14))
| X16 = apply(X14,X15)
| ~ in(ordered_pair(X15,X16),X14) )
& ( ~ function(X14)
| ~ relation(X14)
| ~ in(X15,relation_dom(X14))
| in(ordered_pair(X15,X16),X14)
| X16 != apply(X14,X15) ) ),
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_11,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]) ).
cnf(c_0_12,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ function(X3)
| ~ relation(X3)
| X2 != relation_dom_restriction(X3,X4)
| ~ in(X1,relation_dom(X2))
| apply(X2,X1) = apply(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( ~ function(X1)
| ~ relation(X1)
| function(relation_dom_restriction(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ relation(X1)
| relation(relation_dom_restriction(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ function(X2)
| ~ relation(X2)
| X1 != empty_set
| in(X3,relation_dom(X2))
| X1 = apply(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,negated_conjecture,
( apply(relation_dom_restriction(esk15_0,esk13_0),esk14_0) != apply(esk15_0,esk14_0)
& in(esk14_0,esk13_0)
& function(esk15_0)
& relation(esk15_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_17,plain,
( ~ in(X3,relation_dom(relation_dom_restriction(X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_12]),c_0_13]),c_0_14]) ).
cnf(c_0_18,plain,
( ~ function(X1)
| ~ relation(X1)
| in(X2,relation_dom(X1))
| apply(X1,X2) = empty_set ),
inference(er,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X38,X39,X40] :
( ( ~ function(X40)
| ~ relation(X40)
| in(X39,relation_dom(relation_dom_restriction(X40,X38)))
| ~ in(X39,X38)
| ~ in(X39,relation_dom(X40)) )
& ( ~ function(X40)
| ~ relation(X40)
| ~ in(X39,relation_dom(relation_dom_restriction(X40,X38)))
| in(X39,X38) )
& ( ~ function(X40)
| ~ relation(X40)
| ~ in(X39,relation_dom(relation_dom_restriction(X40,X38)))
| in(X39,relation_dom(X40)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l82_funct_1])])])]) ).
cnf(c_0_20,negated_conjecture,
apply(relation_dom_restriction(esk15_0,esk13_0),esk14_0) != apply(esk15_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( ~ function(X1)
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X2),X3) = empty_set
| apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_13]),c_0_14]) ).
cnf(c_0_22,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(X1,relation_dom(X2))
| in(X1,relation_dom(relation_dom_restriction(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
apply(relation_dom_restriction(esk15_0,esk13_0),esk14_0) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_26,plain,
( ~ in(X3,X2)
| ~ in(X3,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
in(esk14_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_28,negated_conjecture,
apply(esk15_0,esk14_0) != empty_set,
inference(rw,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
~ in(esk14_0,relation_dom(esk15_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_22]),c_0_23]),c_0_27])]),c_0_28]) ).
cnf(c_0_30,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_29,c_0_18]),c_0_22]),c_0_23])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU225+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n016.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 06:05:22 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 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
% 0.69/0.59 % Version: 3.5.1
% 0.69/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.69/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.69/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.69/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.69/0.59 % Starting sh5l with 300s (1) cores
% 0.69/0.59 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1717280 completed with status 0
% 0.69/0.59 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.69/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.69/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.69/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.69/0.59 % No SInE strategy applied
% 0.69/0.59 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.69/0.59 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.69/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.69/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.69/0.59 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.69/0.59 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.69/0.59 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.69/0.59 % SubtermCWHack with pid 1717285 completed with status 0
% 0.69/0.59 % Result found by SubtermCWHack
% 0.69/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.69/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.69/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.69/0.59 % No SInE strategy applied
% 0.69/0.59 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.69/0.59 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.69/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.69/0.59 % Preprocessing time : 0.002 s
% 0.69/0.59
% 0.69/0.59 % Proof found!
% 0.69/0.59 % SZS status Theorem
% 0.69/0.59 % SZS output start CNFRefutation
% See solution above
% 0.69/0.59 % Parsed axioms : 46
% 0.69/0.59 % Removed by relevancy pruning/SinE : 0
% 0.69/0.59 % Initial clauses : 76
% 0.69/0.59 % Removed in clause preprocessing : 3
% 0.69/0.59 % Initial clauses in saturation : 73
% 0.69/0.59 % Processed clauses : 1211
% 0.69/0.59 % ...of these trivial : 7
% 0.69/0.59 % ...subsumed : 844
% 0.69/0.59 % ...remaining for further processing : 360
% 0.69/0.59 % Other redundant clauses eliminated : 5
% 0.69/0.59 % Clauses deleted for lack of memory : 0
% 0.69/0.59 % Backward-subsumed : 34
% 0.69/0.59 % Backward-rewritten : 21
% 0.69/0.59 % Generated clauses : 4862
% 0.69/0.59 % ...of the previous two non-redundant : 3982
% 0.69/0.59 % ...aggressively subsumed : 0
% 0.69/0.59 % Contextual simplify-reflections : 43
% 0.69/0.59 % Paramodulations : 4855
% 0.69/0.59 % Factorizations : 1
% 0.69/0.59 % NegExts : 0
% 0.69/0.59 % Equation resolutions : 6
% 0.69/0.59 % Disequality decompositions : 0
% 0.69/0.59 % Total rewrite steps : 1783
% 0.69/0.59 % ...of those cached : 1687
% 0.69/0.59 % Propositional unsat checks : 0
% 0.69/0.59 % Propositional check models : 0
% 0.69/0.59 % Propositional check unsatisfiable : 0
% 0.69/0.59 % Propositional clauses : 0
% 0.69/0.59 % Propositional clauses after purity: 0
% 0.69/0.59 % Propositional unsat core size : 0
% 0.69/0.59 % Propositional preprocessing time : 0.000
% 0.69/0.59 % Propositional encoding time : 0.000
% 0.69/0.59 % Propositional solver time : 0.000
% 0.69/0.59 % Success case prop preproc time : 0.000
% 0.69/0.59 % Success case prop encoding time : 0.000
% 0.69/0.59 % Success case prop solver time : 0.000
% 0.69/0.59 % Current number of processed clauses : 300
% 0.69/0.59 % Positive orientable unit clauses : 36
% 0.69/0.59 % Positive unorientable unit clauses: 2
% 0.69/0.59 % Negative unit clauses : 13
% 0.69/0.59 % Non-unit-clauses : 249
% 0.69/0.59 % Current number of unprocessed clauses: 2606
% 0.69/0.59 % ...number of literals in the above : 12108
% 0.69/0.59 % Current number of archived formulas : 0
% 0.69/0.59 % Current number of archived clauses : 56
% 0.69/0.59 % Clause-clause subsumption calls (NU) : 40337
% 0.69/0.59 % Rec. Clause-clause subsumption calls : 22306
% 0.69/0.59 % Non-unit clause-clause subsumptions : 779
% 0.69/0.59 % Unit Clause-clause subsumption calls : 517
% 0.69/0.59 % Rewrite failures with RHS unbound : 0
% 0.69/0.59 % BW rewrite match attempts : 28
% 0.69/0.59 % BW rewrite match successes : 16
% 0.69/0.59 % Condensation attempts : 0
% 0.69/0.59 % Condensation successes : 0
% 0.69/0.59 % Termbank termtop insertions : 65512
% 0.69/0.59 % Search garbage collected termcells : 693
% 0.69/0.59
% 0.69/0.59 % -------------------------------------------------
% 0.69/0.59 % User time : 0.082 s
% 0.69/0.59 % System time : 0.013 s
% 0.69/0.59 % Total time : 0.096 s
% 0.69/0.59 % Maximum resident set size: 3672 pages
% 0.69/0.59
% 0.69/0.59 % -------------------------------------------------
% 0.69/0.59 % User time : 0.321 s
% 0.69/0.59 % System time : 0.037 s
% 0.69/0.59 % Total time : 0.358 s
% 0.69/0.59 % Maximum resident set size: 4864 pages
% 0.69/0.59 % E exiting
%------------------------------------------------------------------------------