%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET994+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 02:15:55 PM UTC 2026
% Result : Theorem 0.15s 0.65s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 23 unt; 0 def)
% Number of atoms : 135 ( 41 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 129 ( 49 ~; 40 |; 25 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 59 ( 5 sgn 29 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t16_funct_1,conjecture,
! [X1] :
( ! [X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( ( relation_dom(X3) = X1
& relation_dom(X2) = X1 )
=> X2 = X3 ) ) )
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(s3_funct_1__e7_14__funct_1,axiom,
! [X1] :
? [X2] :
( ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = n1 )
& relation_dom(X2) = X1
& function(X2)
& relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_1__e7_14__funct_1) ).
fof(fc7_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( relation(relation_dom(X1))
& empty(relation_dom(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(s3_funct_1__e4_14__funct_1,axiom,
! [X1] :
? [X2] :
( ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = n0 )
& relation_dom(X2) = X1
& function(X2)
& relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_1__e4_14__funct_1) ).
fof(spc0_boole,axiom,
empty(n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',spc0_boole) ).
fof(fc5_relat_1,axiom,
! [X1] :
( ( relation(X1)
& ~ empty(X1) )
=> ~ empty(relation_dom(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( in(X1,X2)
| empty(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(spc1_boole,axiom,
~ empty(n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',spc1_boole) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ! [X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( ( relation_dom(X3) = X1
& relation_dom(X2) = X1 )
=> X2 = X3 ) ) )
=> X1 = empty_set ),
inference(assume_negation,[status(cth)],[t16_funct_1]) ).
fof(c_0_12,plain,
! [X45] :
( X45 = empty_set
| ~ empty(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])]) ).
fof(c_0_13,negated_conjecture,
! [X31,X32] :
( esk12_0 != empty_set
& ( X31 = X32
| relation_dom(X32) != esk12_0
| relation_dom(X31) != esk12_0
| ~ function(X32)
| ~ relation(X32)
| ~ function(X31)
| ~ relation(X31) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])]) ).
fof(c_0_14,plain,
! [X27,X29] :
( ( apply(esk11_1(X27),X29) = n1
| ~ in(X29,X27) )
& relation_dom(esk11_1(X27)) = X27
& function(esk11_1(X27))
& relation(esk11_1(X27)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s3_funct_1__e7_14__funct_1])])])])]) ).
fof(c_0_15,plain,
! [X12] :
( ( ~ empty(X12)
| relation(relation_dom(X12)) )
& ( ~ empty(X12)
| empty(relation_dom(X12)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])])]) ).
fof(c_0_16,plain,
! [X24,X26] :
( ( apply(esk10_1(X24),X26) = n0
| ~ in(X26,X24) )
& relation_dom(esk10_1(X24)) = X24
& function(esk10_1(X24))
& relation(esk10_1(X24)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s3_funct_1__e4_14__funct_1])])])])]) ).
cnf(c_0_17,plain,
( ~ empty(X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
empty(n0),
inference(split_conjunct,[status(thm)],[spc0_boole]) ).
cnf(c_0_19,negated_conjecture,
( relation_dom(X2) != esk12_0
| relation_dom(X1) != esk12_0
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
relation_dom(esk11_1(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
relation(esk11_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
function(esk11_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_23,plain,
! [X1] :
( ( relation(X1)
& ~ empty(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[fc5_relat_1]) ).
cnf(c_0_24,plain,
( ~ empty(X1)
| empty(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
( ~ in(X1,X2)
| apply(esk10_1(X2),X1) = n0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
n0 = empty_set,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_27,negated_conjecture,
( ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != esk12_0
| X1 = esk11_1(esk12_0) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])])]) ).
cnf(c_0_28,plain,
relation_dom(esk10_1(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_29,plain,
relation(esk10_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_30,plain,
function(esk10_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_31,plain,
! [X11] :
( ~ empty(relation_dom(X11))
| ~ relation(X11)
| empty(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
cnf(c_0_32,plain,
( ~ empty(X1)
| relation_dom(X1) = empty_set ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_33,plain,
( ~ in(X2,X1)
| apply(esk10_1(X1),X2) = empty_set ),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,negated_conjecture,
esk10_1(esk12_0) = esk11_1(esk12_0),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])])]) ).
fof(c_0_35,plain,
! [X35,X36] :
( in(X35,X36)
| empty(X36)
| ~ element(X35,X36) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
fof(c_0_36,plain,
! [X8] : element(esk1_1(X8),X8),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_37,plain,
( ~ empty(relation_dom(X1))
| ~ relation(X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
( ~ empty(esk10_1(X1))
| empty_set = X1 ),
inference(spm,[status(thm)],[c_0_28,c_0_32]) ).
cnf(c_0_39,negated_conjecture,
esk12_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_40,plain,
~ empty(n1),
inference(fof_simplification,[status(thm)],[spc1_boole]) ).
cnf(c_0_41,plain,
( ~ in(X1,X2)
| apply(esk11_1(X2),X1) = n1 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_42,negated_conjecture,
( ~ in(X1,esk12_0)
| apply(esk11_1(esk12_0),X1) = empty_set ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_43,plain,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
( ~ empty(X1)
| empty(esk10_1(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_28]),c_0_29])]) ).
cnf(c_0_46,negated_conjecture,
~ empty(esk11_1(esk12_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_34]),c_0_39]) ).
fof(c_0_47,plain,
~ empty(n1),
inference(fof_nnf,[status(thm)],[c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( ~ in(X1,esk12_0)
| n1 = empty_set ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,plain,
( in(esk1_1(X1),X1)
| empty(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
~ empty(esk12_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_34]),c_0_46]) ).
cnf(c_0_51,plain,
~ empty(n1),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,negated_conjecture,
n1 = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_53,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_54,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_53])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET994+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.57 % Computer : n009.cluster.edu
% 0.12/0.57 % Model : x86_64 x86_64
% 0.12/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.57 % Memory : 8046.5625MB
% 0.12/0.57 % OS : Linux 6.8.0-71-generic
% 0.12/0.58 % CPULimit : 300
% 0.12/0.58 % WCLimit : 300
% 0.12/0.58 % DateTime : Mon Sep 21 05:46:29 UTC 2026
% 0.12/0.58 % CPUTime :
% 0.12/0.58 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.62 Running first-order theorem proving
% 0.12/0.62 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
% 0.15/0.65 % Version: 3.5.1
% 0.15/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.65 % Starting sh5l with 300s (1) cores
% 0.15/0.65 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 975615 completed with status 0
% 0.15/0.65 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.65 % No SInE strategy applied
% 0.15/0.65 % Search class: FGHSM-FFMM21-SFFFFFNN
% 0.15/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.65 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/0.65 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.15/0.65 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 136s (1) cores
% 0.15/0.65 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 975622 completed with status 0
% 0.15/0.65 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.65 % No SInE strategy applied
% 0.15/0.65 % Search class: FGHSM-FFMM21-SFFFFFNN
% 0.15/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.65 % Preprocessing time : 0.001 s
% 0.15/0.65 % Presaturation interreduction done
% 0.15/0.65
% 0.15/0.65 % Proof found!
% 0.15/0.65 % SZS status Theorem
% 0.15/0.65 % SZS output start CNFRefutation
% See solution above
% 0.15/0.65 % Parsed axioms : 32
% 0.15/0.65 % Removed by relevancy pruning/SinE : 0
% 0.15/0.65 % Initial clauses : 50
% 0.15/0.65 % Removed in clause preprocessing : 0
% 0.15/0.65 % Initial clauses in saturation : 50
% 0.15/0.65 % Processed clauses : 173
% 0.15/0.65 % ...of these trivial : 3
% 0.15/0.65 % ...subsumed : 35
% 0.15/0.65 % ...remaining for further processing : 135
% 0.15/0.65 % Other redundant clauses eliminated : 4
% 0.15/0.65 % Clauses deleted for lack of memory : 0
% 0.15/0.65 % Backward-subsumed : 0
% 0.15/0.65 % Backward-rewritten : 10
% 0.15/0.65 % Generated clauses : 142
% 0.15/0.65 % ...of the previous two non-redundant : 110
% 0.15/0.65 % ...aggressively subsumed : 0
% 0.15/0.65 % Contextual simplify-reflections : 0
% 0.15/0.65 % Paramodulations : 138
% 0.15/0.65 % Factorizations : 0
% 0.15/0.65 % NegExts : 0
% 0.15/0.65 % Equation resolutions : 4
% 0.15/0.65 % Disequality decompositions : 0
% 0.15/0.65 % Total rewrite steps : 69
% 0.15/0.65 % ...of those cached : 45
% 0.15/0.65 % Propositional unsat checks : 0
% 0.15/0.65 % Propositional check models : 0
% 0.15/0.65 % Propositional check unsatisfiable : 0
% 0.15/0.65 % Propositional clauses : 0
% 0.15/0.65 % Propositional clauses after purity: 0
% 0.15/0.65 % Propositional unsat core size : 0
% 0.15/0.65 % Propositional preprocessing time : 0.000
% 0.15/0.65 % Propositional encoding time : 0.000
% 0.15/0.65 % Propositional solver time : 0.000
% 0.15/0.65 % Success case prop preproc time : 0.000
% 0.15/0.65 % Success case prop encoding time : 0.000
% 0.15/0.65 % Success case prop solver time : 0.000
% 0.15/0.65 % Current number of processed clauses : 78
% 0.15/0.65 % Positive orientable unit clauses : 28
% 0.15/0.65 % Positive unorientable unit clauses: 0
% 0.15/0.65 % Negative unit clauses : 8
% 0.15/0.65 % Non-unit-clauses : 42
% 0.15/0.65 % Current number of unprocessed clauses: 28
% 0.15/0.65 % ...number of literals in the above : 108
% 0.15/0.65 % Current number of archived formulas : 0
% 0.15/0.65 % Current number of archived clauses : 57
% 0.15/0.65 % Clause-clause subsumption calls (NU) : 271
% 0.15/0.65 % Rec. Clause-clause subsumption calls : 226
% 0.15/0.65 % Non-unit clause-clause subsumptions : 25
% 0.15/0.65 % Unit Clause-clause subsumption calls : 46
% 0.15/0.65 % Rewrite failures with RHS unbound : 0
% 0.15/0.65 % BW rewrite match attempts : 12
% 0.15/0.65 % BW rewrite match successes : 7
% 0.15/0.65 % Condensation attempts : 0
% 0.15/0.65 % Condensation successes : 0
% 0.15/0.65 % Termbank termtop insertions : 3757
% 0.15/0.65 % Search garbage collected termcells : 425
% 0.15/0.65
% 0.15/0.65 % -------------------------------------------------
% 0.15/0.65 % User time : 0.009 s
% 0.15/0.65 % System time : 0.002 s
% 0.15/0.65 % Total time : 0.011 s
% 0.15/0.65 % Maximum resident set size: 3656 pages
% 0.15/0.65
% 0.15/0.65 % -------------------------------------------------
% 0.15/0.65 % User time : 0.027 s
% 0.15/0.65 % System time : 0.014 s
% 0.15/0.65 % Total time : 0.041 s
% 0.15/0.65 % Maximum resident set size: 4864 pages
% 0.15/0.65 % E exiting
%------------------------------------------------------------------------------