%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET992+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 02:15:54 PM UTC 2026
% Result : Theorem 0.53s 0.67s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 124 ( 50 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 157 ( 64 ~; 69 |; 15 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 56 ( 0 sgn 23 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(t14_funct_1,conjecture,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_dom(X2) = singleton(X1)
=> relation_rng(X2) = singleton(apply(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_1) ).
fof(d5_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X1,X4)
& in(X4,relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(c_0_3,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( X14 = singleton(X13)
| esk1_2(X13,X14) = X13
| in(esk1_2(X13,X14),X14) )
& ( X14 = singleton(X13)
| esk1_2(X13,X14) != X13
| ~ in(esk1_2(X13,X14),X14) )
& ( X10 != singleton(X9)
| in(X12,X10)
| X12 != X9 )
& ( X10 != singleton(X9)
| X11 = X9
| ~ in(X11,X10) ) ),
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,negated_conjecture,
~ ! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_dom(X2) = singleton(X1)
=> relation_rng(X2) = singleton(apply(X2,X1)) ) ),
inference(assume_negation,[status(cth)],[t14_funct_1]) ).
cnf(c_0_5,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_6,negated_conjecture,
( relation_rng(esk15_0) != singleton(apply(esk15_0,esk14_0))
& relation_dom(esk15_0) = singleton(esk14_0)
& function(esk15_0)
& relation(esk15_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_7,plain,
! [X16,X17,X18,X20,X21,X22,X24] :
( ( ~ function(X16)
| ~ relation(X16)
| X22 = relation_rng(X16)
| in(esk3_2(X16,X22),X22)
| esk3_2(X16,X22) = apply(X16,esk4_2(X16,X22)) )
& ( ~ function(X16)
| ~ relation(X16)
| X22 = relation_rng(X16)
| in(esk3_2(X16,X22),X22)
| in(esk4_2(X16,X22),relation_dom(X16)) )
& ( ~ function(X16)
| ~ relation(X16)
| X22 = relation_rng(X16)
| esk3_2(X16,X22) != apply(X16,X24)
| ~ in(X24,relation_dom(X16))
| ~ in(esk3_2(X16,X22),X22) )
& ( ~ function(X16)
| ~ relation(X16)
| X17 != relation_rng(X16)
| in(X20,X17)
| X20 != apply(X16,X21)
| ~ in(X21,relation_dom(X16)) )
& ( ~ function(X16)
| ~ relation(X16)
| X17 != relation_rng(X16)
| ~ in(X18,X17)
| X18 = apply(X16,esk2_3(X16,X17,X18)) )
& ( ~ function(X16)
| ~ relation(X16)
| X17 != relation_rng(X16)
| ~ in(X18,X17)
| in(esk2_3(X16,X17,X18),relation_dom(X16)) ) ),
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_funct_1])])])])])])]) ).
cnf(c_0_8,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
relation_dom(esk15_0) = singleton(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2)
| in(esk2_3(X1,X2,X3),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ function(X2)
| ~ relation(X2)
| X3 != relation_rng(X2)
| ~ in(X1,X3)
| X1 = apply(X2,esk2_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( ~ in(X1,relation_dom(esk15_0))
| X1 = esk14_0 ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( ~ in(X2,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| in(esk2_3(X1,relation_rng(X1),X2),relation_dom(X1)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,plain,
( ~ in(X2,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| apply(X1,esk2_3(X1,relation_rng(X1),X2)) = X2 ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( ~ in(X1,relation_rng(esk15_0))
| esk2_3(esk15_0,relation_rng(esk15_0),X1) = esk14_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_18,negated_conjecture,
relation_rng(esk15_0) != singleton(apply(esk15_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,plain,
( X2 = singleton(X1)
| esk1_2(X1,X2) = X1
| in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_20,negated_conjecture,
( ~ in(X1,relation_rng(esk15_0))
| apply(esk15_0,esk14_0) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14]),c_0_15])]) ).
cnf(c_0_21,negated_conjecture,
( in(esk1_2(apply(esk15_0,esk14_0),relation_rng(esk15_0)),relation_rng(esk15_0))
| esk1_2(apply(esk15_0,esk14_0),relation_rng(esk15_0)) = apply(esk15_0,esk14_0) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19])]) ).
cnf(c_0_22,plain,
( X3 != singleton(X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_23,plain,
( esk1_2(X1,X2) != X1
| ~ in(esk1_2(X1,X2),X2)
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_24,negated_conjecture,
esk1_2(apply(esk15_0,esk14_0),relation_rng(esk15_0)) = apply(esk15_0,esk14_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( ~ function(X2)
| ~ relation(X2)
| X4 != relation_rng(X2)
| X3 != apply(X2,X1)
| ~ in(X1,relation_dom(X2))
| in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_22])]) ).
cnf(c_0_27,negated_conjecture,
~ in(apply(esk15_0,esk14_0),relation_rng(esk15_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_18]) ).
cnf(c_0_28,plain,
( ~ in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| in(apply(X1,X2),relation_rng(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_25])]) ).
cnf(c_0_29,negated_conjecture,
in(esk14_0,relation_dom(esk15_0)),
inference(spm,[status(thm)],[c_0_26,c_0_9]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_14]),c_0_15]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET992+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 % Computer : n005.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Mon Sep 21 05:46:19 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.54 Running first-order theorem proving
% 0.25/0.54 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
% 0.53/0.67 % Version: 3.5.1
% 0.53/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.53/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.53/0.67 % Starting new_bool_3 with 300s (1) cores
% 0.53/0.67 % Starting new_bool_1 with 300s (1) cores
% 0.53/0.67 % Starting sh5l with 300s (1) cores
% 0.53/0.67 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2682237 completed with status 0
% 0.53/0.67 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.53/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.53/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.53/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.53/0.67 % No SInE strategy applied
% 0.53/0.67 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.53/0.67 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.53/0.67 % Starting SubtermCWHack with 136s (1) cores
% 0.53/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.53/0.67 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.53/0.67 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.53/0.67 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.53/0.67 % G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2682245 completed with status 0
% 0.53/0.67 % Result found by G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.53/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.53/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.53/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.53/0.67 % No SInE strategy applied
% 0.53/0.67 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.53/0.67 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.53/0.67 % Starting SubtermCWHack with 136s (1) cores
% 0.53/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.53/0.67 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.53/0.67 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.53/0.67 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.53/0.67 % Preprocessing time : 0.003 s
% 0.53/0.67 % Presaturation interreduction done
% 0.53/0.67
% 0.53/0.67 % Proof found!
% 0.53/0.67 % SZS status Theorem
% 0.53/0.67 % SZS output start CNFRefutation
% See solution above
% 0.53/0.67 % Parsed axioms : 34
% 0.53/0.67 % Removed by relevancy pruning/SinE : 0
% 0.53/0.67 % Initial clauses : 58
% 0.53/0.67 % Removed in clause preprocessing : 0
% 0.53/0.67 % Initial clauses in saturation : 58
% 0.53/0.67 % Processed clauses : 214
% 0.53/0.67 % ...of these trivial : 3
% 0.53/0.67 % ...subsumed : 53
% 0.53/0.67 % ...remaining for further processing : 158
% 0.53/0.67 % Other redundant clauses eliminated : 9
% 0.53/0.67 % Clauses deleted for lack of memory : 0
% 0.53/0.67 % Backward-subsumed : 3
% 0.53/0.67 % Backward-rewritten : 8
% 0.53/0.67 % Generated clauses : 295
% 0.53/0.67 % ...of the previous two non-redundant : 261
% 0.53/0.67 % ...aggressively subsumed : 0
% 0.53/0.67 % Contextual simplify-reflections : 4
% 0.53/0.67 % Paramodulations : 286
% 0.53/0.67 % Factorizations : 2
% 0.53/0.67 % NegExts : 0
% 0.53/0.67 % Equation resolutions : 9
% 0.53/0.67 % Disequality decompositions : 0
% 0.53/0.67 % Total rewrite steps : 74
% 0.53/0.67 % ...of those cached : 60
% 0.53/0.67 % Propositional unsat checks : 0
% 0.53/0.67 % Propositional check models : 0
% 0.53/0.67 % Propositional check unsatisfiable : 0
% 0.53/0.67 % Propositional clauses : 0
% 0.53/0.67 % Propositional clauses after purity: 0
% 0.53/0.67 % Propositional unsat core size : 0
% 0.53/0.67 % Propositional preprocessing time : 0.000
% 0.53/0.67 % Propositional encoding time : 0.000
% 0.53/0.67 % Propositional solver time : 0.000
% 0.53/0.67 % Success case prop preproc time : 0.000
% 0.53/0.67 % Success case prop encoding time : 0.000
% 0.53/0.67 % Success case prop solver time : 0.000
% 0.53/0.67 % Current number of processed clauses : 87
% 0.53/0.67 % Positive orientable unit clauses : 24
% 0.53/0.67 % Positive unorientable unit clauses: 0
% 0.53/0.67 % Negative unit clauses : 13
% 0.53/0.67 % Non-unit-clauses : 50
% 0.53/0.67 % Current number of unprocessed clauses: 150
% 0.53/0.67 % ...number of literals in the above : 582
% 0.53/0.67 % Current number of archived formulas : 0
% 0.53/0.67 % Current number of archived clauses : 66
% 0.53/0.67 % Clause-clause subsumption calls (NU) : 689
% 0.53/0.67 % Rec. Clause-clause subsumption calls : 501
% 0.53/0.67 % Non-unit clause-clause subsumptions : 24
% 0.53/0.67 % Unit Clause-clause subsumption calls : 83
% 0.53/0.67 % Rewrite failures with RHS unbound : 0
% 0.53/0.67 % BW rewrite match attempts : 13
% 0.53/0.67 % BW rewrite match successes : 5
% 0.53/0.67 % Condensation attempts : 0
% 0.53/0.67 % Condensation successes : 0
% 0.53/0.67 % Termbank termtop insertions : 6438
% 0.53/0.67 % Search garbage collected termcells : 685
% 0.53/0.67
% 0.53/0.67 % -------------------------------------------------
% 0.53/0.67 % User time : 0.022 s
% 0.53/0.67 % System time : 0.007 s
% 0.53/0.67 % Total time : 0.028 s
% 0.53/0.67 % Maximum resident set size: 3656 pages
% 0.53/0.67
% 0.53/0.67 % -------------------------------------------------
% 0.53/0.67 % User time : 0.144 s
% 0.53/0.67 % System time : 0.027 s
% 0.53/0.67 % Total time : 0.171 s
% 0.53/0.67 % Maximum resident set size: 4608 pages
% 0.53/0.67 % E exiting
%------------------------------------------------------------------------------