%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU215+1 : 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 : n004.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 02:28:33 PM UTC 2026
% Result : Theorem 0.19s 5.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 8 unt; 0 def)
% Number of atoms : 169 ( 23 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 217 ( 81 ~; 83 |; 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 : 51 ( 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t23_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/sandbox2/benchmark/theBenchmark.p',fc1_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/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X2)
& relation(X1) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_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/sandbox2/benchmark/theBenchmark.p',t22_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,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,
! [X10,X11,X12] :
( ( ~ function(X10)
| ~ relation(X10)
| in(X11,relation_dom(X10))
| X12 = apply(X10,X11)
| X12 != empty_set )
& ( ~ function(X10)
| ~ relation(X10)
| in(X11,relation_dom(X10))
| X12 = empty_set
| X12 != apply(X10,X11) )
& ( ~ function(X10)
| ~ relation(X10)
| ~ in(X11,relation_dom(X10))
| X12 = apply(X10,X11)
| ~ in(ordered_pair(X11,X12),X10) )
& ( ~ function(X10)
| ~ relation(X10)
| ~ in(X11,relation_dom(X10))
| in(ordered_pair(X11,X12),X10)
| X12 != apply(X10,X11) ) ),
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(esk9_0,esk10_0),esk8_0) != apply(esk10_0,apply(esk9_0,esk8_0))
& in(esk8_0,relation_dom(esk9_0))
& function(esk10_0)
& relation(esk10_0)
& function(esk9_0)
& relation(esk9_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]) ).
cnf(c_0_11,negated_conjecture,
apply(relation_composition(esk9_0,esk10_0),esk8_0) != apply(esk10_0,apply(esk9_0,esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,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_13,negated_conjecture,
( ~ function(relation_composition(esk9_0,esk10_0))
| ~ relation(relation_composition(esk9_0,esk10_0))
| apply(esk10_0,apply(esk9_0,esk8_0)) != empty_set
| in(esk8_0,relation_dom(relation_composition(esk9_0,esk10_0))) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,negated_conjecture,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
function(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_16,plain,
! [X21,X22] :
( ( ~ function(X22)
| ~ relation(X22)
| ~ function(X21)
| ~ relation(X21)
| function(relation_composition(X21,X22)) )
& ( ~ function(X22)
| ~ relation(X22)
| ~ function(X21)
| ~ relation(X21)
| relation(relation_composition(X21,X22)) ) ),
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_17,plain,
! [X40,X41,X42] :
( ( ~ function(X41)
| ~ relation(X41)
| ~ function(X42)
| ~ relation(X42)
| in(X40,relation_dom(relation_composition(X42,X41)))
| ~ in(apply(X42,X40),relation_dom(X41))
| ~ in(X40,relation_dom(X42)) )
& ( ~ function(X41)
| ~ relation(X41)
| ~ function(X42)
| ~ relation(X42)
| ~ in(X40,relation_dom(relation_composition(X42,X41)))
| in(apply(X42,X40),relation_dom(X41)) )
& ( ~ function(X41)
| ~ relation(X41)
| ~ function(X42)
| ~ relation(X42)
| ~ in(X40,relation_dom(relation_composition(X42,X41)))
| in(X40,relation_dom(X42)) ) ),
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_18,negated_conjecture,
( ~ function(relation_composition(esk9_0,esk10_0))
| ~ relation(relation_composition(esk9_0,esk10_0))
| in(esk8_0,relation_dom(relation_composition(esk9_0,esk10_0)))
| in(apply(esk9_0,esk8_0),relation_dom(esk10_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_12]),c_0_14]),c_0_15])]) ).
cnf(c_0_19,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1)
| function(relation_composition(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
relation(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,negated_conjecture,
function(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_22,plain,
! [X15,X16] :
( relation(relation_composition(X15,X16))
| ~ relation(X16)
| ~ relation(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])])]) ).
cnf(c_0_23,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_17]) ).
cnf(c_0_24,negated_conjecture,
in(esk8_0,relation_dom(esk9_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,negated_conjecture,
( ~ relation(relation_composition(esk9_0,esk10_0))
| in(apply(esk9_0,esk8_0),relation_dom(esk10_0))
| in(esk8_0,relation_dom(relation_composition(esk9_0,esk10_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_18,c_0_19]),c_0_14]),c_0_20]),c_0_15]),c_0_21])]) ).
cnf(c_0_26,plain,
( ~ relation(X2)
| ~ relation(X1)
| relation(relation_composition(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_27,plain,
! [X43,X44,X45] :
( apply(relation_composition(X45,X44),X43) = apply(X44,apply(X45,X43))
| ~ in(X43,relation_dom(relation_composition(X45,X44)))
| ~ function(X45)
| ~ relation(X45)
| ~ function(X44)
| ~ relation(X44) ),
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_28,negated_conjecture,
( ~ in(apply(esk9_0,esk8_0),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| in(esk8_0,relation_dom(relation_composition(esk9_0,X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20]),c_0_21])]) ).
cnf(c_0_29,negated_conjecture,
( in(esk8_0,relation_dom(relation_composition(esk9_0,esk10_0)))
| in(apply(esk9_0,esk8_0),relation_dom(esk10_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_14]),c_0_20])]) ).
cnf(c_0_30,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_27]) ).
cnf(c_0_31,negated_conjecture,
in(esk8_0,relation_dom(relation_composition(esk9_0,esk10_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_14]),c_0_15])]) ).
cnf(c_0_32,negated_conjecture,
$false,
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(spm,[status(thm)],[c_0_30,c_0_31]),c_0_20]),c_0_14]),c_0_21]),c_0_15])]),c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU215+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/5.41 % Computer : n004.cluster.edu
% 0.16/5.41 % Model : x86_64 x86_64
% 0.16/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.41 % Memory : 8046.5625MB
% 0.16/5.41 % OS : Linux 6.8.0-71-generic
% 0.16/5.41 % CPULimit : 300
% 0.16/5.41 % WCLimit : 300
% 0.16/5.41 % DateTime : Mon Sep 21 05:58:56 UTC 2026
% 0.16/5.42 % CPUTime :
% 0.16/5.42 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/5.46 Running first-order theorem proving
% 0.16/5.46 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
% 0.19/5.50 % Version: 3.5.1
% 0.19/5.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/5.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/5.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/5.50 % Starting new_bool_3 with 300s (1) cores
% 0.19/5.50 % Starting new_bool_1 with 300s (1) cores
% 0.19/5.50 % Starting sh5l with 300s (1) cores
% 0.19/5.50 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2398426 completed with status 0
% 0.19/5.50 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.19/5.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/5.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/5.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/5.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/5.50 % No SInE strategy applied
% 0.19/5.50 % Search class: FGHSS-FFMM21-SFFFFFNN
% 0.19/5.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/5.50 % Starting SubtermCWHack with 136s (1) cores
% 0.19/5.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.19/5.50 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.19/5.50 % Starting new_bool_3 with 136s (1) cores
% 0.19/5.50 % Starting new_bool_1 with 136s (1) cores
% 0.19/5.50 % G-E--_208_B07_F1_SE_CS_SP_PS_S4d with pid 2398434 completed with status 0
% 0.19/5.50 % Result found by G-E--_208_B07_F1_SE_CS_SP_PS_S4d
% 0.19/5.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/5.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/5.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/5.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/5.50 % No SInE strategy applied
% 0.19/5.50 % Search class: FGHSS-FFMM21-SFFFFFNN
% 0.19/5.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/5.50 % Starting SubtermCWHack with 136s (1) cores
% 0.19/5.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.19/5.50 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.19/5.50 % Preprocessing time : 0.002 s
% 0.19/5.50 % Presaturation interreduction done
% 0.19/5.50
% 0.19/5.50 % Proof found!
% 0.19/5.50 % SZS status Theorem
% 0.19/5.50 % SZS output start CNFRefutation
% See solution above
% 0.19/5.50 % Parsed axioms : 40
% 0.19/5.50 % Removed by relevancy pruning/SinE : 0
% 0.19/5.50 % Initial clauses : 61
% 0.19/5.50 % Removed in clause preprocessing : 8
% 0.19/5.50 % Initial clauses in saturation : 53
% 0.19/5.50 % Processed clauses : 257
% 0.19/5.50 % ...of these trivial : 3
% 0.19/5.50 % ...subsumed : 123
% 0.19/5.50 % ...remaining for further processing : 131
% 0.19/5.50 % Other redundant clauses eliminated : 19
% 0.19/5.50 % Clauses deleted for lack of memory : 0
% 0.19/5.50 % Backward-subsumed : 3
% 0.19/5.50 % Backward-rewritten : 11
% 0.19/5.50 % Generated clauses : 420
% 0.19/5.50 % ...of the previous two non-redundant : 358
% 0.19/5.50 % ...aggressively subsumed : 0
% 0.19/5.50 % Contextual simplify-reflections : 0
% 0.19/5.50 % Paramodulations : 401
% 0.19/5.50 % Factorizations : 0
% 0.19/5.50 % NegExts : 0
% 0.19/5.50 % Equation resolutions : 19
% 0.19/5.50 % Disequality decompositions : 0
% 0.19/5.50 % Total rewrite steps : 116
% 0.19/5.50 % ...of those cached : 104
% 0.19/5.50 % Propositional unsat checks : 0
% 0.19/5.50 % Propositional check models : 0
% 0.19/5.50 % Propositional check unsatisfiable : 0
% 0.19/5.50 % Propositional clauses : 0
% 0.19/5.50 % Propositional clauses after purity: 0
% 0.19/5.50 % Propositional unsat core size : 0
% 0.19/5.50 % Propositional preprocessing time : 0.000
% 0.19/5.50 % Propositional encoding time : 0.000
% 0.19/5.50 % Propositional solver time : 0.000
% 0.19/5.50 % Success case prop preproc time : 0.000
% 0.19/5.50 % Success case prop encoding time : 0.000
% 0.19/5.50 % Success case prop solver time : 0.000
% 0.19/5.50 % Current number of processed clauses : 67
% 0.19/5.50 % Positive orientable unit clauses : 18
% 0.19/5.50 % Positive unorientable unit clauses: 1
% 0.19/5.50 % Negative unit clauses : 8
% 0.19/5.50 % Non-unit-clauses : 40
% 0.19/5.50 % Current number of unprocessed clauses: 191
% 0.19/5.50 % ...number of literals in the above : 986
% 0.19/5.50 % Current number of archived formulas : 0
% 0.19/5.50 % Current number of archived clauses : 62
% 0.19/5.50 % Clause-clause subsumption calls (NU) : 979
% 0.19/5.50 % Rec. Clause-clause subsumption calls : 507
% 0.19/5.50 % Non-unit clause-clause subsumptions : 83
% 0.19/5.50 % Unit Clause-clause subsumption calls : 28
% 0.19/5.50 % Rewrite failures with RHS unbound : 0
% 0.19/5.50 % BW rewrite match attempts : 8
% 0.19/5.50 % BW rewrite match successes : 7
% 0.19/5.50 % Condensation attempts : 0
% 0.19/5.50 % Condensation successes : 0
% 0.19/5.50 % Termbank termtop insertions : 8791
% 0.19/5.50 % Search garbage collected termcells : 541
% 0.19/5.50
% 0.19/5.50 % -------------------------------------------------
% 0.19/5.50 % User time : 0.020 s
% 0.19/5.50 % System time : 0.004 s
% 0.19/5.50 % Total time : 0.024 s
% 0.19/5.50 % Maximum resident set size: 3660 pages
% 0.19/5.50
% 0.19/5.50 % -------------------------------------------------
% 0.19/5.50 % User time : 0.086 s
% 0.19/5.50 % System time : 0.015 s
% 0.19/5.50 % Total time : 0.102 s
% 0.19/5.50 % Maximum resident set size: 4864 pages
% 0.19/5.50 % E exiting
%------------------------------------------------------------------------------