%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU178+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 02:24:08 PM UTC 2026
% Result : Theorem 263.54s 34.30s
% Output : CNFRefutation 263.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 3 unt; 0 def)
% Number of atoms : 152 ( 23 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 193 ( 77 ~; 87 |; 16 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 1 con; 0-3 aty)
% Number of variables : 106 ( 2 sgn 51 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_relat_1,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( ! [X3,X4] : X2 != ordered_pair(X3,X4)
& in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
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/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
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/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(t21_relat_1,conjecture,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
fof(t106_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X2,X4)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(c_0_6,plain,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( ! [X3,X4] : X2 != ordered_pair(X3,X4)
& in(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[d1_relat_1]) ).
fof(c_0_7,plain,
! [X21,X22,X23,X25,X26,X27,X29] :
( ( ~ relation(X21)
| X27 = relation_rng(X21)
| in(ordered_pair(esk5_2(X21,X27),esk4_2(X21,X27)),X21)
| in(esk4_2(X21,X27),X27) )
& ( ~ relation(X21)
| X27 = relation_rng(X21)
| ~ in(ordered_pair(X29,esk4_2(X21,X27)),X21)
| ~ in(esk4_2(X21,X27),X27) )
& ( ~ relation(X21)
| X22 != relation_rng(X21)
| in(X25,X22)
| ~ in(ordered_pair(X26,X25),X21) )
& ( ~ relation(X21)
| X22 != relation_rng(X21)
| in(ordered_pair(esk3_3(X21,X22,X23),X23),X21)
| ~ in(X23,X22) ) ),
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])])])])])])]) ).
fof(c_0_8,plain,
! [X41,X42,X45,X47,X48] :
( ( relation(X45)
| esk11_1(X45) != ordered_pair(X47,X48) )
& ( relation(X45)
| in(esk11_1(X45),X45) )
& ( X42 = ordered_pair(esk9_2(X41,X42),esk10_2(X41,X42))
| ~ in(X42,X41)
| ~ relation(X41) ) ),
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)],[c_0_6])])])])])])]) ).
cnf(c_0_9,plain,
( ~ relation(X3)
| X4 != relation_rng(X3)
| ~ in(ordered_pair(X1,X2),X3)
| in(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( ~ in(X2,X1)
| ~ relation(X1)
| X2 = ordered_pair(esk9_2(X1,X2),esk10_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X6,X7,X8,X9,X10] :
( ( subset(X9,X10)
| ~ in(esk2_2(X9,X10),X10) )
& ( subset(X9,X10)
| in(esk2_2(X9,X10),X9) )
& ( in(X8,X7)
| ~ in(X8,X6)
| ~ subset(X6,X7) ) ),
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])])])])])])]) ).
fof(c_0_12,plain,
! [X31,X32,X33,X35,X36,X37,X39] :
( ( ~ relation(X31)
| X37 = relation_dom(X31)
| in(ordered_pair(esk7_2(X31,X37),esk8_2(X31,X37)),X31)
| in(esk7_2(X31,X37),X37) )
& ( ~ relation(X31)
| X37 = relation_dom(X31)
| ~ in(ordered_pair(esk7_2(X31,X37),X39),X31)
| ~ in(esk7_2(X31,X37),X37) )
& ( ~ relation(X31)
| X32 != relation_dom(X31)
| in(X35,X32)
| ~ in(ordered_pair(X35,X36),X31) )
& ( ~ relation(X31)
| X32 != relation_dom(X31)
| in(ordered_pair(X33,esk6_3(X31,X32,X33)),X31)
| ~ in(X33,X32) ) ),
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_13,plain,
( ~ in(X2,X1)
| ~ in(X2,X4)
| ~ relation(X1)
| ~ relation(X4)
| X3 != relation_rng(X4)
| in(esk10_2(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| in(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
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_12]) ).
cnf(c_0_16,plain,
( ~ in(esk2_2(X1,X2),X3)
| ~ relation(X3)
| ~ relation(X1)
| X4 != relation_rng(X1)
| in(esk10_2(X3,esk2_2(X1,X2)),X4)
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
inference(assume_negation,[status(cth)],[t21_relat_1]) ).
cnf(c_0_18,plain,
( ~ in(X2,X1)
| ~ in(X2,X4)
| ~ relation(X1)
| ~ relation(X4)
| X3 != relation_dom(X4)
| in(esk9_2(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_10]) ).
fof(c_0_19,plain,
! [X17,X18,X19,X20] :
( ( in(ordered_pair(X17,X18),cartesian_product2(X19,X20))
| ~ in(X18,X20)
| ~ in(X17,X19) )
& ( ~ in(ordered_pair(X17,X18),cartesian_product2(X19,X20))
| in(X18,X20) )
& ( ~ in(ordered_pair(X17,X18),cartesian_product2(X19,X20))
| in(X17,X19) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])])]) ).
cnf(c_0_20,plain,
( ~ relation(X1)
| X3 != relation_rng(X1)
| in(esk10_2(X1,esk2_2(X1,X2)),X3)
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
fof(c_0_21,negated_conjecture,
( ~ subset(esk1_0,cartesian_product2(relation_dom(esk1_0),relation_rng(esk1_0)))
& relation(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
cnf(c_0_22,plain,
( ~ in(esk2_2(X1,X2),X3)
| ~ relation(X3)
| ~ relation(X1)
| X4 != relation_dom(X1)
| in(esk9_2(X3,esk2_2(X1,X2)),X4)
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_23,plain,
( ~ in(X3,X4)
| ~ in(X1,X2)
| in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( ~ relation(X1)
| in(esk10_2(X1,esk2_2(X1,X2)),relation_rng(X1))
| subset(X1,X2) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
relation(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
( ~ relation(X1)
| X3 != relation_dom(X1)
| in(esk9_2(X1,esk2_2(X1,X2)),X3)
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_14]) ).
cnf(c_0_27,plain,
( ~ in(X1,X4)
| ~ in(esk9_2(X4,X1),X2)
| ~ in(esk10_2(X4,X1),X3)
| ~ relation(X4)
| in(X1,cartesian_product2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_23,c_0_10]) ).
cnf(c_0_28,negated_conjecture,
( in(esk10_2(esk1_0,esk2_2(esk1_0,X1)),relation_rng(esk1_0))
| subset(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
( ~ relation(X1)
| in(esk9_2(X1,esk2_2(X1,X2)),relation_dom(X1))
| subset(X1,X2) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( ~ in(esk9_2(esk1_0,esk2_2(esk1_0,X1)),X2)
| in(esk2_2(esk1_0,X1),cartesian_product2(X2,relation_rng(esk1_0)))
| subset(esk1_0,X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25])]),c_0_14]) ).
cnf(c_0_31,negated_conjecture,
( in(esk9_2(esk1_0,esk2_2(esk1_0,X1)),relation_dom(esk1_0))
| subset(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_32,plain,
( ~ in(esk2_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_33,negated_conjecture,
( in(esk2_2(esk1_0,X1),cartesian_product2(relation_dom(esk1_0),relation_rng(esk1_0)))
| subset(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
~ subset(esk1_0,cartesian_product2(relation_dom(esk1_0),relation_rng(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU178+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.52 % Computer : n001.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Mon Sep 21 06:00:58 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.53 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.57 Running first-order theorem proving
% 0.14/0.57 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
% 263.54/34.30 % Version: 3.5.1
% 263.54/34.30 % Preprocessing class: FSMSSMSSSSSNFFN.
% 263.54/34.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 263.54/34.30 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 263.54/34.30 % Starting new_bool_3 with 300s (1) cores
% 263.54/34.30 % Starting new_bool_1 with 300s (1) cores
% 263.54/34.30 % Starting sh5l with 300s (1) cores
% 263.54/34.30 % new_bool_3 with pid 2340683 completed with status 0
% 263.54/34.30 % Result found by new_bool_3
% 263.54/34.30 % Preprocessing class: FSMSSMSSSSSNFFN.
% 263.54/34.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 263.54/34.30 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 263.54/34.30 % Starting new_bool_3 with 300s (1) cores
% 263.54/34.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 263.54/34.30 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 263.54/34.30 % Search class: FGHSM-FFMS31-SFFFFFNN
% 263.54/34.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 263.54/34.30 % Starting SubtermCWHack with 31s (1) cores
% 263.54/34.30 % SubtermCWHack with pid 2340689 completed with status 8
% 263.54/34.30 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 181s (1) cores
% 263.54/34.30 % G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with pid 2340787 completed with status 0
% 263.54/34.30 % Result found by G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN
% 263.54/34.30 % Preprocessing class: FSMSSMSSSSSNFFN.
% 263.54/34.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 263.54/34.30 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 263.54/34.30 % Starting new_bool_3 with 300s (1) cores
% 263.54/34.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 263.54/34.30 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 263.54/34.30 % Search class: FGHSM-FFMS31-SFFFFFNN
% 263.54/34.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 263.54/34.30 % Starting SubtermCWHack with 31s (1) cores
% 263.54/34.30 % SubtermCWHack with pid 2340689 completed with status 8
% 263.54/34.30 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 181s (1) cores
% 263.54/34.30 % Preprocessing time : 0.004 s
% 263.54/34.30
% 263.54/34.30 % Proof found!
% 263.54/34.30 % SZS status Theorem
% 263.54/34.30 % SZS output start CNFRefutation
% See solution above
% 263.54/34.30 % Parsed axioms : 39
% 263.54/34.30 % Removed by relevancy pruning/SinE : 15
% 263.54/34.30 % Initial clauses : 41
% 263.54/34.30 % Removed in clause preprocessing : 0
% 263.54/34.30 % Initial clauses in saturation : 41
% 263.54/34.30 % Processed clauses : 2438
% 263.54/34.30 % ...of these trivial : 7
% 263.54/34.30 % ...subsumed : 1318
% 263.54/34.30 % ...remaining for further processing : 1113
% 263.54/34.30 % Other redundant clauses eliminated : 0
% 263.54/34.30 % Clauses deleted for lack of memory : 0
% 263.54/34.30 % Backward-subsumed : 71
% 263.54/34.30 % Backward-rewritten : 16
% 263.54/34.30 % Generated clauses : 26897
% 263.54/34.30 % ...of the previous two non-redundant : 25910
% 263.54/34.30 % ...aggressively subsumed : 0
% 263.54/34.30 % Contextual simplify-reflections : 82
% 263.54/34.30 % Paramodulations : 26665
% 263.54/34.30 % Factorizations : 18
% 263.54/34.30 % NegExts : 0
% 263.54/34.30 % Equation resolutions : 164
% 263.54/34.30 % Disequality decompositions : 0
% 263.54/34.30 % Total rewrite steps : 1579
% 263.54/34.30 % ...of those cached : 1547
% 263.54/34.30 % Propositional unsat checks : 0
% 263.54/34.30 % Propositional check models : 0
% 263.54/34.30 % Propositional check unsatisfiable : 0
% 263.54/34.30 % Propositional clauses : 0
% 263.54/34.30 % Propositional clauses after purity: 0
% 263.54/34.30 % Propositional unsat core size : 0
% 263.54/34.30 % Propositional preprocessing time : 0.000
% 263.54/34.30 % Propositional encoding time : 0.000
% 263.54/34.30 % Propositional solver time : 0.000
% 263.54/34.30 % Success case prop preproc time : 0.000
% 263.54/34.30 % Success case prop encoding time : 0.000
% 263.54/34.30 % Success case prop solver time : 0.000
% 263.54/34.30 % Current number of processed clauses : 976
% 263.54/34.30 % Positive orientable unit clauses : 26
% 263.54/34.30 % Positive unorientable unit clauses: 0
% 263.54/34.30 % Negative unit clauses : 29
% 263.54/34.30 % Non-unit-clauses : 921
% 263.54/34.30 % Current number of unprocessed clauses: 23071
% 263.54/34.30 % ...number of literals in the above : 150067
% 263.54/34.30 % Current number of archived formulas : 0
% 263.54/34.30 % Current number of archived clauses : 137
% 263.54/34.30 % Clause-clause subsumption calls (NU) : 207745
% 263.54/34.30 % Rec. Clause-clause subsumption calls : 45642
% 263.54/34.30 % Non-unit clause-clause subsumptions : 1062
% 263.54/34.30 % Unit Clause-clause subsumption calls : 2117
% 263.54/34.30 % Rewrite failures with RHS unbound : 0
% 263.54/34.30 % BW rewrite match attempts : 72
% 263.54/34.30 % BW rewrite match successes : 17
% 263.54/34.30 % Condensation attempts : 0
% 263.54/34.30 % Condensation successes : 0
% 263.54/34.30 % Termbank termtop insertions : 539104
% 263.54/34.30 % Search garbage collected termcells : 761
% 263.54/34.30
% 263.54/34.30 % -------------------------------------------------
% 263.54/34.30 % User time : 31.688 s
% 263.54/34.30 % System time : 1.197 s
% 263.54/34.30 % Total time : 32.885 s
% 263.54/34.30 % Maximum resident set size: 3660 pages
% 263.54/34.30
% 263.54/34.30 % -------------------------------------------------
% 263.54/34.30 % User time : 31.691 s
% 263.54/34.30 % System time : 1.204 s
% 263.54/34.30 % Total time : 32.895 s
% 263.54/34.30 % Maximum resident set size: 4864 pages
% 263.54/34.30 % E exiting
%------------------------------------------------------------------------------