%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET995+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 0.64s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 154 ( 62 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 191 ( 71 ~; 76 |; 29 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 50 ( 0 sgn 30 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t17_funct_1,conjecture,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( ( relation_rng(X3) = singleton(X1)
& relation_rng(X2) = singleton(X1)
& relation_dom(X2) = relation_dom(X3) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_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/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(t9_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = relation_dom(X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( ( relation_rng(X3) = singleton(X1)
& relation_rng(X2) = singleton(X1)
& relation_dom(X2) = relation_dom(X3) )
=> X2 = X3 ) ) ),
inference(assume_negation,[status(cth)],[t17_funct_1]) ).
fof(c_0_5,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])])])])])])]) ).
fof(c_0_6,negated_conjecture,
( esk15_0 != esk16_0
& relation_rng(esk16_0) = singleton(esk14_0)
& relation_rng(esk15_0) = singleton(esk14_0)
& relation_dom(esk15_0) = relation_dom(esk16_0)
& function(esk16_0)
& relation(esk16_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,
! [X65,X66] :
( ( ~ function(X65)
| ~ relation(X65)
| ~ function(X66)
| ~ relation(X66)
| X65 = X66
| relation_dom(X65) != relation_dom(X66)
| apply(X65,esk17_2(X65,X66)) != apply(X66,esk17_2(X65,X66)) )
& ( ~ function(X65)
| ~ relation(X65)
| ~ function(X66)
| ~ relation(X66)
| X65 = X66
| relation_dom(X65) != relation_dom(X66)
| in(esk17_2(X65,X66),relation_dom(X65)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_funct_1])])])])])]) ).
fof(c_0_8,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])])])])])])]) ).
cnf(c_0_9,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_5]) ).
cnf(c_0_10,negated_conjecture,
relation_rng(esk16_0) = singleton(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
relation_rng(esk15_0) = singleton(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X1) != relation_dom(X2)
| X1 = X2
| in(esk17_2(X1,X2),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
relation_dom(esk15_0) = relation_dom(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
function(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,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_9])]) ).
cnf(c_0_18,negated_conjecture,
relation_rng(esk16_0) = relation_rng(esk15_0),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( ~ function(X1)
| ~ relation(X1)
| relation_dom(esk15_0) != relation_dom(X1)
| in(esk17_2(esk16_0,X1),relation_dom(esk15_0))
| esk16_0 = X1 ),
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_20,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
esk15_0 != esk16_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(X1,relation_dom(esk15_0))
| in(apply(esk16_0,X1),relation_rng(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_18]),c_0_14]),c_0_13])]) ).
cnf(c_0_25,negated_conjecture,
in(esk17_2(esk16_0,esk15_0),relation_dom(esk15_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( ~ in(X1,relation_rng(esk15_0))
| X1 = esk14_0 ),
inference(spm,[status(thm)],[c_0_23,c_0_11]) ).
cnf(c_0_27,negated_conjecture,
in(apply(esk16_0,esk17_2(esk16_0,esk15_0)),relation_rng(esk15_0)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( ~ in(X1,relation_dom(esk15_0))
| in(apply(esk15_0,X1),relation_rng(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_21]),c_0_20])]) ).
cnf(c_0_29,plain,
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom(X1) != relation_dom(X2)
| apply(X1,esk17_2(X1,X2)) != apply(X2,esk17_2(X1,X2))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_30,negated_conjecture,
apply(esk16_0,esk17_2(esk16_0,esk15_0)) = esk14_0,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
in(apply(esk15_0,esk17_2(esk16_0,esk15_0)),relation_rng(esk15_0)),
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
apply(esk15_0,esk17_2(esk16_0,esk15_0)) != esk14_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_13]),c_0_20]),c_0_14]),c_0_21]),c_0_15])]),c_0_22]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_31]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET995+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.56 % Computer : n002.cluster.edu
% 0.11/0.56 % Model : x86_64 x86_64
% 0.11/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.56 % Memory : 8046.5625MB
% 0.11/0.56 % OS : Linux 6.8.0-71-generic
% 0.11/0.56 % CPULimit : 300
% 0.11/0.56 % WCLimit : 300
% 0.11/0.56 % DateTime : Mon Sep 21 05:49:03 UTC 2026
% 0.11/0.56 % CPUTime :
% 0.11/0.56 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.60 Running first-order theorem proving
% 0.11/0.60 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
% 0.15/0.64 % Version: 3.5.1
% 0.15/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.64 % Starting sh5l with 300s (1) cores
% 0.15/0.64 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2560261 completed with status 0
% 0.15/0.64 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.64 % No SInE strategy applied
% 0.15/0.64 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.15/0.64 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.15/0.64 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.15/0.64 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/0.64 % G-E--_208_C18_F1_SE_CS_SP_PS_S4b with pid 2560269 completed with status 0
% 0.15/0.64 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S4b
% 0.15/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.64 % No SInE strategy applied
% 0.15/0.64 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.15/0.64 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.15/0.64 % Preprocessing time : 0.002 s
% 0.15/0.64 % Presaturation interreduction done
% 0.15/0.64
% 0.15/0.64 % Proof found!
% 0.15/0.64 % SZS status Theorem
% 0.15/0.64 % SZS output start CNFRefutation
% See solution above
% 0.15/0.65 % Parsed axioms : 34
% 0.15/0.65 % Removed by relevancy pruning/SinE : 0
% 0.15/0.65 % Initial clauses : 62
% 0.15/0.65 % Removed in clause preprocessing : 0
% 0.15/0.65 % Initial clauses in saturation : 62
% 0.15/0.65 % Processed clauses : 278
% 0.15/0.65 % ...of these trivial : 9
% 0.15/0.65 % ...subsumed : 38
% 0.15/0.65 % ...remaining for further processing : 231
% 0.15/0.65 % Other redundant clauses eliminated : 13
% 0.15/0.65 % Clauses deleted for lack of memory : 0
% 0.15/0.65 % Backward-subsumed : 8
% 0.15/0.65 % Backward-rewritten : 28
% 0.15/0.65 % Generated clauses : 308
% 0.15/0.65 % ...of the previous two non-redundant : 251
% 0.15/0.65 % ...aggressively subsumed : 0
% 0.15/0.65 % Contextual simplify-reflections : 0
% 0.15/0.65 % Paramodulations : 290
% 0.15/0.65 % Factorizations : 4
% 0.15/0.65 % NegExts : 0
% 0.15/0.65 % Equation resolutions : 16
% 0.15/0.65 % Disequality decompositions : 0
% 0.15/0.65 % Total rewrite steps : 227
% 0.15/0.65 % ...of those cached : 182
% 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 : 131
% 0.15/0.65 % Positive orientable unit clauses : 52
% 0.15/0.65 % Positive unorientable unit clauses: 0
% 0.15/0.65 % Negative unit clauses : 17
% 0.15/0.65 % Non-unit-clauses : 62
% 0.15/0.65 % Current number of unprocessed clauses: 48
% 0.15/0.65 % ...number of literals in the above : 121
% 0.15/0.65 % Current number of archived formulas : 0
% 0.15/0.65 % Current number of archived clauses : 95
% 0.15/0.65 % Clause-clause subsumption calls (NU) : 990
% 0.15/0.65 % Rec. Clause-clause subsumption calls : 633
% 0.15/0.65 % Non-unit clause-clause subsumptions : 14
% 0.15/0.65 % Unit Clause-clause subsumption calls : 645
% 0.15/0.65 % Rewrite failures with RHS unbound : 0
% 0.15/0.65 % BW rewrite match attempts : 23
% 0.15/0.65 % BW rewrite match successes : 13
% 0.15/0.65 % Condensation attempts : 0
% 0.15/0.65 % Condensation successes : 0
% 0.15/0.65 % Termbank termtop insertions : 7587
% 0.15/0.65 % Search garbage collected termcells : 772
% 0.15/0.65
% 0.15/0.65 % -------------------------------------------------
% 0.15/0.65 % User time : 0.017 s
% 0.15/0.65 % System time : 0.008 s
% 0.15/0.65 % Total time : 0.025 s
% 0.15/0.65 % Maximum resident set size: 3404 pages
% 0.15/0.65
% 0.15/0.65 % -------------------------------------------------
% 0.15/0.65 % User time : 0.065 s
% 0.15/0.65 % System time : 0.022 s
% 0.15/0.65 % Total time : 0.086 s
% 0.15/0.65 % Maximum resident set size: 4864 pages
% 0.15/0.65 % E exiting
%------------------------------------------------------------------------------