%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU049+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 02:23:44 PM UTC 2026
% Result : Theorem 14.26s 2.53s
% Output : CNFRefutation 14.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 138 ( 48 equ)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 183 ( 74 ~; 82 |; 18 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-4 aty)
% Number of variables : 65 ( 0 sgn 26 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(d12_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( X4 = apply(X1,X5)
& in(X5,X2)
& in(X5,relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
fof(t117_funct_1,conjecture,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(X2))
=> relation_image(X2,singleton(X1)) = singleton(apply(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).
fof(c_0_3,plain,
! [X23,X24,X25,X26,X27,X28] :
( ( X28 = singleton(X27)
| esk4_2(X27,X28) = X27
| in(esk4_2(X27,X28),X28) )
& ( X28 = singleton(X27)
| esk4_2(X27,X28) != X27
| ~ in(esk4_2(X27,X28),X28) )
& ( X24 != singleton(X23)
| in(X26,X24)
| X26 != X23 )
& ( X24 != singleton(X23)
| X25 = X23
| ~ in(X25,X24) ) ),
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)],[d1_tarski])])])])])])]) ).
fof(c_0_4,plain,
! [X11,X12,X13,X14,X16,X17,X18,X19,X21] :
( ( ~ function(X11)
| ~ relation(X11)
| X19 = relation_image(X11,X18)
| in(esk2_3(X11,X18,X19),X19)
| esk2_3(X11,X18,X19) = apply(X11,esk3_3(X11,X18,X19)) )
& ( ~ function(X11)
| ~ relation(X11)
| X19 = relation_image(X11,X18)
| in(esk2_3(X11,X18,X19),X19)
| in(esk3_3(X11,X18,X19),X18) )
& ( ~ function(X11)
| ~ relation(X11)
| X19 = relation_image(X11,X18)
| in(esk2_3(X11,X18,X19),X19)
| in(esk3_3(X11,X18,X19),relation_dom(X11)) )
& ( ~ function(X11)
| ~ relation(X11)
| X19 = relation_image(X11,X18)
| esk2_3(X11,X18,X19) != apply(X11,X21)
| ~ in(X21,X18)
| ~ in(X21,relation_dom(X11))
| ~ in(esk2_3(X11,X18,X19),X19) )
& ( ~ function(X11)
| ~ relation(X11)
| X13 != relation_image(X11,X12)
| in(X16,X13)
| X16 != apply(X11,X17)
| ~ in(X17,X12)
| ~ in(X17,relation_dom(X11)) )
& ( ~ function(X11)
| ~ relation(X11)
| X13 != relation_image(X11,X12)
| ~ in(X14,X13)
| X14 = apply(X11,esk1_4(X11,X12,X13,X14)) )
& ( ~ function(X11)
| ~ relation(X11)
| X13 != relation_image(X11,X12)
| ~ in(X14,X13)
| in(esk1_4(X11,X12,X13,X14),X12) )
& ( ~ function(X11)
| ~ relation(X11)
| X13 != relation_image(X11,X12)
| ~ in(X14,X13)
| in(esk1_4(X11,X12,X13,X14),relation_dom(X11)) ) ),
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)],[d12_funct_1])])])])])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(X2))
=> relation_image(X2,singleton(X1)) = singleton(apply(X2,X1)) ) ),
inference(assume_negation,[status(cth)],[t117_funct_1]) ).
cnf(c_0_6,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_7,plain,
( ~ function(X1)
| ~ relation(X1)
| X3 != relation_image(X1,X2)
| ~ in(X4,X3)
| in(esk1_4(X1,X2,X3,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,negated_conjecture,
( relation_image(esk17_0,singleton(esk16_0)) != singleton(apply(esk17_0,esk16_0))
& in(esk16_0,relation_dom(esk17_0))
& function(esk17_0)
& relation(esk17_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_9,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ in(X3,relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| in(esk1_4(X1,X2,relation_image(X1,X2),X3),X2) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
relation_image(esk17_0,singleton(esk16_0)) != singleton(apply(esk17_0,esk16_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( X2 = singleton(X1)
| esk4_2(X1,X2) = X1
| in(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_13,plain,
( ~ function(X2)
| ~ relation(X2)
| X4 != relation_image(X2,X3)
| ~ in(X1,X4)
| X1 = apply(X2,esk1_4(X2,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,plain,
( ~ in(X3,relation_image(X1,singleton(X2)))
| ~ function(X1)
| ~ relation(X1)
| esk1_4(X1,singleton(X2),relation_image(X1,singleton(X2)),X3) = X2 ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( in(esk4_2(apply(esk17_0,esk16_0),relation_image(esk17_0,singleton(esk16_0))),relation_image(esk17_0,singleton(esk16_0)))
| esk4_2(apply(esk17_0,esk16_0),relation_image(esk17_0,singleton(esk16_0))) = apply(esk17_0,esk16_0) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12])]) ).
cnf(c_0_16,negated_conjecture,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
function(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,plain,
( ~ in(X3,relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| apply(X1,esk1_4(X1,X2,relation_image(X1,X2),X3)) = X3 ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( esk4_2(apply(esk17_0,esk16_0),relation_image(esk17_0,singleton(esk16_0))) = apply(esk17_0,esk16_0)
| esk1_4(esk17_0,singleton(esk16_0),relation_image(esk17_0,singleton(esk16_0)),esk4_2(apply(esk17_0,esk16_0),relation_image(esk17_0,singleton(esk16_0)))) = esk16_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_20,plain,
( esk4_2(X1,X2) != X1
| ~ in(esk4_2(X1,X2),X2)
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_21,negated_conjecture,
esk4_2(apply(esk17_0,esk16_0),relation_image(esk17_0,singleton(esk16_0))) = apply(esk17_0,esk16_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_16]),c_0_17])]),c_0_15]) ).
cnf(c_0_22,plain,
( ~ function(X2)
| ~ relation(X2)
| X5 != relation_image(X2,X3)
| X4 != apply(X2,X1)
| ~ in(X1,X3)
| ~ in(X1,relation_dom(X2))
| in(X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_23,plain,
( X3 != singleton(X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_24,negated_conjecture,
~ in(apply(esk17_0,esk16_0),relation_image(esk17_0,singleton(esk16_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_11]) ).
cnf(c_0_25,plain,
( ~ in(X2,X3)
| ~ in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,X2),relation_image(X1,X3)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_22])]) ).
cnf(c_0_26,negated_conjecture,
in(esk16_0,relation_dom(esk17_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_23])]) ).
cnf(c_0_28,negated_conjecture,
$false,
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_24,c_0_25]),c_0_16]),c_0_17]),c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU049+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:46:06 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 14.26/2.53 % Version: 3.5.1
% 14.26/2.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 14.26/2.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.26/2.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.26/2.53 % Starting new_bool_3 with 300s (1) cores
% 14.26/2.53 % Starting new_bool_1 with 300s (1) cores
% 14.26/2.53 % Starting sh5l with 300s (1) cores
% 14.26/2.53 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 305712 completed with status 0
% 14.26/2.53 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 14.26/2.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 14.26/2.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.26/2.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.26/2.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.26/2.53 % No SInE strategy applied
% 14.26/2.53 % Search class: FGHSM-FFMM31-SFFFFFNN
% 14.26/2.53 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 14.26/2.53 % Starting SubtermCWHack with 136s (1) cores
% 14.26/2.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.26/2.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 14.26/2.53 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 14.26/2.53 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 14.26/2.53 % G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 305726 completed with status 0
% 14.26/2.53 % Result found by G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 14.26/2.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 14.26/2.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.26/2.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.26/2.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.26/2.53 % No SInE strategy applied
% 14.26/2.53 % Search class: FGHSM-FFMM31-SFFFFFNN
% 14.26/2.53 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 14.26/2.53 % Starting SubtermCWHack with 136s (1) cores
% 14.26/2.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.26/2.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 14.26/2.53 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 14.26/2.53 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 14.26/2.53 % Preprocessing time : 0.002 s
% 14.26/2.53 % Presaturation interreduction done
% 14.26/2.53
% 14.26/2.53 % Proof found!
% 14.26/2.53 % SZS status Theorem
% 14.26/2.53 % SZS output start CNFRefutation
% See solution above
% 14.26/2.53 % Parsed axioms : 35
% 14.26/2.53 % Removed by relevancy pruning/SinE : 0
% 14.26/2.53 % Initial clauses : 66
% 14.26/2.53 % Removed in clause preprocessing : 2
% 14.26/2.53 % Initial clauses in saturation : 64
% 14.26/2.53 % Processed clauses : 3337
% 14.26/2.53 % ...of these trivial : 28
% 14.26/2.53 % ...subsumed : 2546
% 14.26/2.53 % ...remaining for further processing : 763
% 14.26/2.53 % Other redundant clauses eliminated : 190
% 14.26/2.53 % Clauses deleted for lack of memory : 0
% 14.26/2.53 % Backward-subsumed : 77
% 14.26/2.53 % Backward-rewritten : 47
% 14.26/2.53 % Generated clauses : 49197
% 14.26/2.53 % ...of the previous two non-redundant : 46507
% 14.26/2.53 % ...aggressively subsumed : 0
% 14.26/2.53 % Contextual simplify-reflections : 24
% 14.26/2.53 % Paramodulations : 48891
% 14.26/2.53 % Factorizations : 110
% 14.26/2.53 % NegExts : 0
% 14.26/2.53 % Equation resolutions : 190
% 14.26/2.53 % Disequality decompositions : 0
% 14.26/2.53 % Total rewrite steps : 10730
% 14.26/2.53 % ...of those cached : 10613
% 14.26/2.53 % Propositional unsat checks : 0
% 14.26/2.53 % Propositional check models : 0
% 14.26/2.53 % Propositional check unsatisfiable : 0
% 14.26/2.53 % Propositional clauses : 0
% 14.26/2.53 % Propositional clauses after purity: 0
% 14.26/2.53 % Propositional unsat core size : 0
% 14.26/2.53 % Propositional preprocessing time : 0.000
% 14.26/2.53 % Propositional encoding time : 0.000
% 14.26/2.53 % Propositional solver time : 0.000
% 14.26/2.53 % Success case prop preproc time : 0.000
% 14.26/2.53 % Success case prop encoding time : 0.000
% 14.26/2.53 % Success case prop solver time : 0.000
% 14.26/2.53 % Current number of processed clauses : 564
% 14.26/2.53 % Positive orientable unit clauses : 72
% 14.26/2.53 % Positive unorientable unit clauses: 0
% 14.26/2.53 % Negative unit clauses : 31
% 14.26/2.53 % Non-unit-clauses : 461
% 14.26/2.53 % Current number of unprocessed clauses: 42668
% 14.26/2.53 % ...number of literals in the above : 248805
% 14.26/2.53 % Current number of archived formulas : 0
% 14.26/2.53 % Current number of archived clauses : 193
% 14.26/2.53 % Clause-clause subsumption calls (NU) : 51855
% 14.26/2.53 % Rec. Clause-clause subsumption calls : 23351
% 14.26/2.53 % Non-unit clause-clause subsumptions : 1257
% 14.26/2.53 % Unit Clause-clause subsumption calls : 2239
% 14.26/2.53 % Rewrite failures with RHS unbound : 0
% 14.26/2.53 % BW rewrite match attempts : 43
% 14.26/2.53 % BW rewrite match successes : 26
% 14.26/2.53 % Condensation attempts : 0
% 14.26/2.53 % Condensation successes : 0
% 14.26/2.53 % Termbank termtop insertions : 959915
% 14.26/2.53 % Search garbage collected termcells : 761
% 14.26/2.53
% 14.26/2.53 % -------------------------------------------------
% 14.26/2.53 % User time : 1.926 s
% 14.26/2.53 % System time : 0.066 s
% 14.26/2.53 % Total time : 1.992 s
% 14.26/2.53 % Maximum resident set size: 3660 pages
% 14.26/2.53
% 14.26/2.53 % -------------------------------------------------
% 14.26/2.53 % User time : 9.612 s
% 14.26/2.53 % System time : 0.367 s
% 14.26/2.53 % Total time : 9.979 s
% 14.26/2.53 % Maximum resident set size: 4864 pages
% 14.26/2.53 % E exiting
%------------------------------------------------------------------------------