%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU209+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 : n011.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 02:24:15 PM UTC 2026
% Result : Theorem 2.99s 1.17s
% Output : CNFRefutation 2.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 105 ( 22 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 126 ( 50 ~; 54 |; 12 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 2 con; 0-4 aty)
% Number of variables : 75 ( 3 sgn 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d14_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,X2)
& in(ordered_pair(X4,X5),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(t167_relat_1,conjecture,
! [X1,X2] :
( relation(X2)
=> subset(relation_inverse_image(X2,X1),relation_dom(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(c_0_6,plain,
! [X11,X12,X13,X14,X16,X17,X18,X19,X21] :
( ( ~ relation(X11)
| X19 = relation_inverse_image(X11,X18)
| in(esk2_3(X11,X18,X19),X19)
| in(esk3_3(X11,X18,X19),X18) )
& ( ~ relation(X11)
| X19 = relation_inverse_image(X11,X18)
| in(esk2_3(X11,X18,X19),X19)
| in(ordered_pair(esk2_3(X11,X18,X19),esk3_3(X11,X18,X19)),X11) )
& ( ~ relation(X11)
| X19 = relation_inverse_image(X11,X18)
| ~ in(X21,X18)
| ~ in(ordered_pair(esk2_3(X11,X18,X19),X21),X11)
| ~ in(esk2_3(X11,X18,X19),X19) )
& ( ~ relation(X11)
| X13 != relation_inverse_image(X11,X12)
| in(X16,X13)
| ~ in(X17,X12)
| ~ in(ordered_pair(X16,X17),X11) )
& ( ~ relation(X11)
| X13 != relation_inverse_image(X11,X12)
| ~ in(X14,X13)
| in(esk1_4(X11,X12,X13,X14),X12) )
& ( ~ relation(X11)
| X13 != relation_inverse_image(X11,X12)
| ~ in(X14,X13)
| in(ordered_pair(X14,esk1_4(X11,X12,X13,X14)),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)],[d14_relat_1])])])])])])]) ).
fof(c_0_7,plain,
! [X39,X40] : ordered_pair(X39,X40) = unordered_pair(unordered_pair(X39,X40),singleton(X39)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> subset(relation_inverse_image(X2,X1),relation_dom(X2)) ),
inference(assume_negation,[status(cth)],[t167_relat_1]) ).
fof(c_0_9,plain,
! [X29,X30,X31,X33,X34,X35,X37] :
( ( ~ relation(X29)
| X35 = relation_dom(X29)
| in(ordered_pair(esk6_2(X29,X35),esk7_2(X29,X35)),X29)
| in(esk6_2(X29,X35),X35) )
& ( ~ relation(X29)
| X35 = relation_dom(X29)
| ~ in(ordered_pair(esk6_2(X29,X35),X37),X29)
| ~ in(esk6_2(X29,X35),X35) )
& ( ~ relation(X29)
| X30 != relation_dom(X29)
| in(X33,X30)
| ~ in(ordered_pair(X33,X34),X29) )
& ( ~ relation(X29)
| X30 != relation_dom(X29)
| in(ordered_pair(X31,esk5_3(X29,X30,X31)),X29)
| ~ in(X31,X30) ) ),
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)],[d4_relat_1])])])])])])]) ).
cnf(c_0_10,plain,
( ~ relation(X2)
| X4 != relation_inverse_image(X2,X3)
| ~ in(X1,X4)
| in(ordered_pair(X1,esk1_4(X2,X3,X4,X1)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_13,negated_conjecture,
( ~ subset(relation_inverse_image(esk16_0,esk15_0),relation_dom(esk16_0))
& relation(esk16_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_14,plain,
! [X23,X24,X25,X26,X27] :
( ( subset(X26,X27)
| ~ in(esk4_2(X26,X27),X27) )
& ( subset(X26,X27)
| in(esk4_2(X26,X27),X26) )
& ( in(X25,X24)
| ~ in(X25,X23)
| ~ subset(X23,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)],[d3_tarski])])])])])])]) ).
cnf(c_0_15,plain,
( ~ relation(X3)
| X4 != relation_dom(X3)
| ~ in(ordered_pair(X1,X2),X3)
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( ~ in(X1,X4)
| ~ relation(X2)
| X4 != relation_inverse_image(X2,X3)
| in(unordered_pair(unordered_pair(X1,esk1_4(X2,X3,X4,X1)),singleton(X1)),X2) ),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
~ subset(relation_inverse_image(esk16_0,esk15_0),relation_dom(esk16_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( subset(X1,X2)
| in(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ relation(X3)
| X4 != relation_dom(X3)
| in(X1,X4) ),
inference(rw,[status(thm)],[c_0_15,c_0_11]) ).
cnf(c_0_21,plain,
( ~ in(X1,relation_inverse_image(X2,X3))
| ~ relation(X2)
| in(unordered_pair(singleton(X1),unordered_pair(X1,esk1_4(X2,X3,relation_inverse_image(X2,X3),X1))),X2) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_22,negated_conjecture,
in(esk4_2(relation_inverse_image(esk16_0,esk15_0),relation_dom(esk16_0)),relation_inverse_image(esk16_0,esk15_0)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,plain,
( ~ in(esk4_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,plain,
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2)
| ~ relation(X2)
| in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_17])]) ).
cnf(c_0_26,negated_conjecture,
in(unordered_pair(singleton(esk4_2(relation_inverse_image(esk16_0,esk15_0),relation_dom(esk16_0))),unordered_pair(esk4_2(relation_inverse_image(esk16_0,esk15_0),relation_dom(esk16_0)),esk1_4(esk16_0,esk15_0,relation_inverse_image(esk16_0,esk15_0),esk4_2(relation_inverse_image(esk16_0,esk15_0),relation_dom(esk16_0))))),esk16_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_27,negated_conjecture,
~ in(esk4_2(relation_inverse_image(esk16_0,esk15_0),relation_dom(esk16_0)),relation_dom(esk16_0)),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU209+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n011.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 05:58:25 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.53 Running first-order theorem proving
% 0.23/0.53 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
% 2.99/1.17 % Version: 3.5.1
% 2.99/1.17 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.99/1.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.99/1.17 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.99/1.17 % Starting new_bool_3 with 300s (1) cores
% 2.99/1.17 % Starting new_bool_1 with 300s (1) cores
% 2.99/1.17 % Starting sh5l with 300s (1) cores
% 2.99/1.17 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1124394 completed with status 0
% 2.99/1.17 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.99/1.17 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.99/1.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.99/1.17 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.99/1.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.99/1.17 % No SInE strategy applied
% 2.99/1.17 % Search class: FGHSM-FFMM31-MFFFFFNN
% 2.99/1.17 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 2.99/1.17 % Starting SubtermCWHack with 136s (1) cores
% 2.99/1.17 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.99/1.17 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 113s (1) cores
% 2.99/1.17 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SE_S0Y with 113s (1) cores
% 2.99/1.17 % Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 113s (1) cores
% 2.99/1.17 % G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with pid 1124400 completed with status 0
% 2.99/1.17 % Result found by G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I
% 2.99/1.17 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.99/1.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.99/1.17 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.99/1.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.99/1.17 % No SInE strategy applied
% 2.99/1.17 % Search class: FGHSM-FFMM31-MFFFFFNN
% 2.99/1.17 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 2.99/1.17 % Starting SubtermCWHack with 136s (1) cores
% 2.99/1.17 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.99/1.17 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 113s (1) cores
% 2.99/1.17 % Preprocessing time : 0.003 s
% 2.99/1.17 % Presaturation interreduction done
% 2.99/1.17
% 2.99/1.17 % Proof found!
% 2.99/1.17 % SZS status Theorem
% 2.99/1.17 % SZS output start CNFRefutation
% See solution above
% 2.99/1.17 % Parsed axioms : 40
% 2.99/1.17 % Removed by relevancy pruning/SinE : 0
% 2.99/1.17 % Initial clauses : 58
% 2.99/1.17 % Removed in clause preprocessing : 9
% 2.99/1.17 % Initial clauses in saturation : 49
% 2.99/1.17 % Processed clauses : 1700
% 2.99/1.17 % ...of these trivial : 16
% 2.99/1.17 % ...subsumed : 705
% 2.99/1.17 % ...remaining for further processing : 979
% 2.99/1.17 % Other redundant clauses eliminated : 5
% 2.99/1.17 % Clauses deleted for lack of memory : 0
% 2.99/1.17 % Backward-subsumed : 44
% 2.99/1.17 % Backward-rewritten : 8
% 2.99/1.17 % Generated clauses : 11845
% 2.99/1.17 % ...of the previous two non-redundant : 10667
% 2.99/1.17 % ...aggressively subsumed : 0
% 2.99/1.17 % Contextual simplify-reflections : 0
% 2.99/1.17 % Paramodulations : 11840
% 2.99/1.17 % Factorizations : 0
% 2.99/1.17 % NegExts : 0
% 2.99/1.17 % Equation resolutions : 5
% 2.99/1.17 % Disequality decompositions : 0
% 2.99/1.17 % Total rewrite steps : 4457
% 2.99/1.17 % ...of those cached : 4380
% 2.99/1.17 % Propositional unsat checks : 0
% 2.99/1.17 % Propositional check models : 0
% 2.99/1.17 % Propositional check unsatisfiable : 0
% 2.99/1.17 % Propositional clauses : 0
% 2.99/1.17 % Propositional clauses after purity: 0
% 2.99/1.17 % Propositional unsat core size : 0
% 2.99/1.17 % Propositional preprocessing time : 0.000
% 2.99/1.17 % Propositional encoding time : 0.000
% 2.99/1.17 % Propositional solver time : 0.000
% 2.99/1.17 % Success case prop preproc time : 0.000
% 2.99/1.17 % Success case prop encoding time : 0.000
% 2.99/1.17 % Success case prop solver time : 0.000
% 2.99/1.17 % Current number of processed clauses : 875
% 2.99/1.17 % Positive orientable unit clauses : 85
% 2.99/1.17 % Positive unorientable unit clauses: 1
% 2.99/1.17 % Negative unit clauses : 76
% 2.99/1.17 % Non-unit-clauses : 713
% 2.99/1.17 % Current number of unprocessed clauses: 9021
% 2.99/1.17 % ...number of literals in the above : 27189
% 2.99/1.17 % Current number of archived formulas : 0
% 2.99/1.17 % Current number of archived clauses : 100
% 2.99/1.17 % Clause-clause subsumption calls (NU) : 65966
% 2.99/1.17 % Rec. Clause-clause subsumption calls : 57982
% 2.99/1.17 % Non-unit clause-clause subsumptions : 585
% 2.99/1.17 % Unit Clause-clause subsumption calls : 8484
% 2.99/1.17 % Rewrite failures with RHS unbound : 0
% 2.99/1.17 % BW rewrite match attempts : 56
% 2.99/1.17 % BW rewrite match successes : 10
% 2.99/1.17 % Condensation attempts : 0
% 2.99/1.17 % Condensation successes : 0
% 2.99/1.17 % Termbank termtop insertions : 229589
% 2.99/1.17 % Search garbage collected termcells : 703
% 2.99/1.17
% 2.99/1.17 % -------------------------------------------------
% 2.99/1.17 % User time : 0.434 s
% 2.99/1.17 % System time : 0.022 s
% 2.99/1.17 % Total time : 0.455 s
% 2.99/1.17 % Maximum resident set size: 3864 pages
% 2.99/1.17
% 2.99/1.17 % -------------------------------------------------
% 2.99/1.17 % User time : 1.956 s
% 2.99/1.17 % System time : 0.100 s
% 2.99/1.17 % Total time : 2.056 s
% 2.99/1.17 % Maximum resident set size: 4864 pages
% 2.99/1.17 % E exiting
%------------------------------------------------------------------------------