%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU187+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 : n017.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 02:24:10 PM UTC 2026
% Result : Theorem 0.29s 0.87s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 17 unt; 0 def)
% Number of atoms : 101 ( 40 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 115 ( 51 ~; 46 |; 10 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-3 aty)
% Number of variables : 68 ( 4 sgn 37 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
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(d5_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(t60_relat_1,conjecture,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(c_0_8,plain,
! [X154,X155] : ordered_pair(X154,X155) = unordered_pair(unordered_pair(X154,X155),singleton(X154)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_9,lemma,
! [X414] : unordered_pair(X414,X414) = singleton(X414),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_10,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_11,plain,
! [X111,X112,X113,X115,X116,X117,X119] :
( ( ~ relation(X111)
| X117 = relation_dom(X111)
| in(ordered_pair(esk20_2(X111,X117),esk21_2(X111,X117)),X111)
| in(esk20_2(X111,X117),X117) )
& ( ~ relation(X111)
| X117 = relation_dom(X111)
| ~ in(ordered_pair(esk20_2(X111,X117),X119),X111)
| ~ in(esk20_2(X111,X117),X117) )
& ( ~ relation(X111)
| X112 != relation_dom(X111)
| in(X115,X112)
| ~ in(ordered_pair(X115,X116),X111) )
& ( ~ relation(X111)
| X112 != relation_dom(X111)
| in(ordered_pair(X113,esk19_3(X111,X112,X113)),X111)
| ~ in(X113,X112) ) ),
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_12,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X48,X49,X50] :
( ( X50 = empty_set
| in(esk8_1(X50),X50) )
& ( ~ in(X49,X48)
| X48 != empty_set ) ),
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)],[c_0_10])])])])])]) ).
cnf(c_0_15,plain,
( ~ relation(X3)
| X2 != relation_dom(X3)
| ~ in(X1,X2)
| in(ordered_pair(X1,esk19_3(X3,X2,X1)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_17,plain,
! [X12,X13] : unordered_pair(X12,X13) = unordered_pair(X13,X12),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_18,plain,
! [X142,X143,X144,X146,X147,X148,X150] :
( ( ~ relation(X142)
| X148 = relation_rng(X142)
| in(ordered_pair(esk28_2(X142,X148),esk27_2(X142,X148)),X142)
| in(esk27_2(X142,X148),X148) )
& ( ~ relation(X142)
| X148 = relation_rng(X142)
| ~ in(ordered_pair(X150,esk27_2(X142,X148)),X142)
| ~ in(esk27_2(X142,X148),X148) )
& ( ~ relation(X142)
| X143 != relation_rng(X142)
| in(X146,X143)
| ~ in(ordered_pair(X147,X146),X142) )
& ( ~ relation(X142)
| X143 != relation_rng(X142)
| in(ordered_pair(esk26_3(X142,X143,X144),X144),X142)
| ~ in(X144,X143) ) ),
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)],[d5_relat_1])])])])])])]) ).
cnf(c_0_19,plain,
( ~ in(X2,X1)
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ in(X1,X2)
| ~ relation(X3)
| X2 != relation_dom(X3)
| in(unordered_pair(unordered_pair(X1,esk19_3(X3,X2,X1)),unordered_pair(X1,X1)),X3) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( ~ relation(X3)
| X2 != relation_rng(X3)
| ~ in(X1,X2)
| in(ordered_pair(esk26_3(X3,X2,X1),X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,negated_conjecture,
~ ( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(assume_negation,[status(cth)],[t60_relat_1]) ).
cnf(c_0_24,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( ~ in(X1,relation_dom(X2))
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,esk19_3(X2,relation_dom(X2),X1))),X2) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
cnf(c_0_26,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]) ).
cnf(c_0_27,plain,
( ~ in(X1,X2)
| ~ relation(X3)
| X2 != relation_rng(X3)
| in(unordered_pair(unordered_pair(esk26_3(X3,X2,X1),X1),unordered_pair(esk26_3(X3,X2,X1),esk26_3(X3,X2,X1))),X3) ),
inference(rw,[status(thm)],[c_0_22,c_0_16]) ).
fof(c_0_28,negated_conjecture,
( relation_rng(empty_set) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
cnf(c_0_29,plain,
~ in(X1,relation_dom(empty_set)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_30,plain,
( X1 = empty_set
| in(esk8_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_31,plain,
( ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X1,esk26_3(X2,relation_rng(X2),X1)),unordered_pair(esk26_3(X2,relation_rng(X2),X1),esk26_3(X2,relation_rng(X2),X1))),X2) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_21])]) ).
cnf(c_0_32,negated_conjecture,
( relation_rng(empty_set) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
relation_dom(empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
~ in(X1,relation_rng(empty_set)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_31]),c_0_26])]) ).
cnf(c_0_35,negated_conjecture,
relation_rng(empty_set) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
cnf(c_0_36,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_30]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU187+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.50 % Computer : n017.cluster.edu
% 0.19/0.50 % Model : x86_64 x86_64
% 0.19/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.50 % Memory : 8046.5625MB
% 0.19/0.50 % OS : Linux 6.8.0-71-generic
% 0.19/0.50 % CPULimit : 300
% 0.19/0.50 % WCLimit : 300
% 0.19/0.50 % DateTime : Mon Sep 21 05:51:27 UTC 2026
% 0.24/0.51 % CPUTime :
% 0.24/0.51 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.58 Running first-order theorem proving
% 0.24/0.58 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
% 0.29/0.87 % Version: 3.5.1
% 0.29/0.87 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.29/0.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.29/0.87 % Starting new_bool_3 with 300s (1) cores
% 0.29/0.87 % Starting new_bool_1 with 300s (1) cores
% 0.29/0.87 % Starting sh5l with 300s (1) cores
% 0.29/0.87 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1576869 completed with status 0
% 0.29/0.87 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.29/0.87 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.29/0.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.29/0.87 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.87 % No SInE strategy applied
% 0.29/0.87 % Search class: FGHSM-FSLM32-MFFFFFNN
% 0.29/0.87 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/0.87 % Starting SubtermCWHack with 136s (1) cores
% 0.29/0.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.29/0.87 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 0.29/0.87 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 123s (1) cores
% 0.29/0.87 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 123s (1) cores
% 0.29/0.87 % G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with pid 1576879 completed with status 0
% 0.29/0.87 % Result found by G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N
% 0.29/0.87 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.29/0.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.29/0.87 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.87 % No SInE strategy applied
% 0.29/0.87 % Search class: FGHSM-FSLM32-MFFFFFNN
% 0.29/0.87 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/0.87 % Starting SubtermCWHack with 136s (1) cores
% 0.29/0.87 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.29/0.87 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 0.29/0.87 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 123s (1) cores
% 0.29/0.87 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 123s (1) cores
% 0.29/0.87 % Preprocessing time : 0.004 s
% 0.29/0.87 % Presaturation interreduction done
% 0.29/0.87
% 0.29/0.87 % Proof found!
% 0.29/0.87 % SZS status Theorem
% 0.29/0.87 % SZS output start CNFRefutation
% See solution above
% 0.29/0.87 % Parsed axioms : 167
% 0.29/0.87 % Removed by relevancy pruning/SinE : 0
% 0.29/0.87 % Initial clauses : 284
% 0.29/0.87 % Removed in clause preprocessing : 19
% 0.29/0.87 % Initial clauses in saturation : 265
% 0.29/0.87 % Processed clauses : 563
% 0.29/0.87 % ...of these trivial : 6
% 0.29/0.87 % ...subsumed : 29
% 0.29/0.87 % ...remaining for further processing : 528
% 0.29/0.87 % Other redundant clauses eliminated : 90
% 0.29/0.87 % Clauses deleted for lack of memory : 0
% 0.29/0.87 % Backward-subsumed : 0
% 0.29/0.87 % Backward-rewritten : 7
% 0.29/0.87 % Generated clauses : 3044
% 0.29/0.87 % ...of the previous two non-redundant : 2813
% 0.29/0.87 % ...aggressively subsumed : 0
% 0.29/0.87 % Contextual simplify-reflections : 8
% 0.29/0.87 % Paramodulations : 2941
% 0.29/0.87 % Factorizations : 14
% 0.29/0.87 % NegExts : 0
% 0.29/0.87 % Equation resolutions : 95
% 0.29/0.87 % Disequality decompositions : 0
% 0.29/0.87 % Total rewrite steps : 325
% 0.29/0.87 % ...of those cached : 256
% 0.29/0.87 % Propositional unsat checks : 0
% 0.29/0.87 % Propositional check models : 0
% 0.29/0.87 % Propositional check unsatisfiable : 0
% 0.29/0.87 % Propositional clauses : 0
% 0.29/0.87 % Propositional clauses after purity: 0
% 0.29/0.87 % Propositional unsat core size : 0
% 0.29/0.87 % Propositional preprocessing time : 0.000
% 0.29/0.87 % Propositional encoding time : 0.000
% 0.29/0.87 % Propositional solver time : 0.000
% 0.29/0.87 % Success case prop preproc time : 0.000
% 0.29/0.87 % Success case prop encoding time : 0.000
% 0.29/0.87 % Success case prop solver time : 0.000
% 0.29/0.87 % Current number of processed clauses : 241
% 0.29/0.87 % Positive orientable unit clauses : 31
% 0.29/0.87 % Positive unorientable unit clauses: 3
% 0.29/0.87 % Negative unit clauses : 13
% 0.29/0.87 % Non-unit-clauses : 194
% 0.29/0.87 % Current number of unprocessed clauses: 2718
% 0.29/0.87 % ...number of literals in the above : 10382
% 0.29/0.87 % Current number of archived formulas : 0
% 0.29/0.87 % Current number of archived clauses : 244
% 0.29/0.87 % Clause-clause subsumption calls (NU) : 20345
% 0.29/0.87 % Rec. Clause-clause subsumption calls : 10945
% 0.29/0.87 % Non-unit clause-clause subsumptions : 26
% 0.29/0.87 % Unit Clause-clause subsumption calls : 802
% 0.29/0.87 % Rewrite failures with RHS unbound : 0
% 0.29/0.87 % BW rewrite match attempts : 71
% 0.29/0.87 % BW rewrite match successes : 54
% 0.29/0.87 % Condensation attempts : 0
% 0.29/0.87 % Condensation successes : 0
% 0.29/0.87 % Termbank termtop insertions : 63666
% 0.29/0.87 % Search garbage collected termcells : 4584
% 0.29/0.87
% 0.29/0.87 % -------------------------------------------------
% 0.29/0.87 % User time : 0.142 s
% 0.29/0.87 % System time : 0.011 s
% 0.29/0.87 % Total time : 0.153 s
% 0.29/0.87 % Maximum resident set size: 4304 pages
% 0.29/0.87
% 0.29/0.87 % -------------------------------------------------
% 0.29/0.87 % User time : 0.620 s
% 0.29/0.87 % System time : 0.057 s
% 0.29/0.87 % Total time : 0.677 s
% 0.29/0.87 % Maximum resident set size: 4864 pages
% 0.29/0.87 % E exiting
%------------------------------------------------------------------------------