%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU023+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 09:16:26 EDT 2022
% Result : Theorem 0.23s 1.41s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 6 unt; 0 def)
% Number of atoms : 234 ( 67 equ)
% Maximal formula atoms : 130 ( 9 avg)
% Number of connectives : 362 ( 153 ~; 159 |; 36 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 2 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t54_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = function_inverse(X1)
<=> ( relation_dom(X2) = relation_rng(X1)
& ! [X3,X4] :
( ( ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) )
=> ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) )
& ( ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) )
=> ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t54_funct_1) ).
fof(t56_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_dom(X2)) )
=> ( X1 = apply(function_inverse(X2),apply(X2,X1))
& X1 = apply(relation_composition(X2,function_inverse(X2)),X1) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t56_funct_1) ).
fof(dt_k2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',dt_k2_funct_1) ).
fof(t23_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t23_funct_1) ).
fof(c_0_4,plain,
! [X5,X6,X7,X8,X7,X8] :
( ( relation_dom(X6) = relation_rng(X5)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(X8,relation_dom(X5))
| ~ in(X7,relation_rng(X5))
| X8 != apply(X6,X7)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( X7 = apply(X5,X8)
| ~ in(X7,relation_rng(X5))
| X8 != apply(X6,X7)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(X7,relation_rng(X5))
| ~ in(X8,relation_dom(X5))
| X7 != apply(X5,X8)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( X8 = apply(X6,X7)
| ~ in(X8,relation_dom(X5))
| X7 != apply(X5,X8)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk6_2(X5,X6),relation_dom(X5))
| in(esk3_2(X5,X6),relation_rng(X5))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk5_2(X5,X6) = apply(X5,esk6_2(X5,X6))
| in(esk3_2(X5,X6),relation_rng(X5))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk5_2(X5,X6),relation_rng(X5))
| esk6_2(X5,X6) != apply(X6,esk5_2(X5,X6))
| in(esk3_2(X5,X6),relation_rng(X5))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk6_2(X5,X6),relation_dom(X5))
| esk4_2(X5,X6) = apply(X6,esk3_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk5_2(X5,X6) = apply(X5,esk6_2(X5,X6))
| esk4_2(X5,X6) = apply(X6,esk3_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk5_2(X5,X6),relation_rng(X5))
| esk6_2(X5,X6) != apply(X6,esk5_2(X5,X6))
| esk4_2(X5,X6) = apply(X6,esk3_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk6_2(X5,X6),relation_dom(X5))
| ~ in(esk4_2(X5,X6),relation_dom(X5))
| esk3_2(X5,X6) != apply(X5,esk4_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk5_2(X5,X6) = apply(X5,esk6_2(X5,X6))
| ~ in(esk4_2(X5,X6),relation_dom(X5))
| esk3_2(X5,X6) != apply(X5,esk4_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk5_2(X5,X6),relation_rng(X5))
| esk6_2(X5,X6) != apply(X6,esk5_2(X5,X6))
| ~ in(esk4_2(X5,X6),relation_dom(X5))
| esk3_2(X5,X6) != apply(X5,esk4_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t54_funct_1])])])])])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_dom(X2)) )
=> ( X1 = apply(function_inverse(X2),apply(X2,X1))
& X1 = apply(relation_composition(X2,function_inverse(X2)),X1) ) ) ),
inference(assume_negation,[status(cth)],[t56_funct_1]) ).
cnf(c_0_6,plain,
( X4 = apply(X2,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_7,plain,
! [X2] :
( ( relation(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) )
& ( function(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
fof(c_0_8,negated_conjecture,
( relation(esk2_0)
& function(esk2_0)
& one_to_one(esk2_0)
& in(esk1_0,relation_dom(esk2_0))
& ( esk1_0 != apply(function_inverse(esk2_0),apply(esk2_0,esk1_0))
| esk1_0 != apply(relation_composition(esk2_0,function_inverse(esk2_0)),esk1_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_9,plain,
! [X4,X5,X6] :
( ~ relation(X5)
| ~ function(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ in(X4,relation_dom(X5))
| apply(relation_composition(X5,X6),X4) = apply(X6,apply(X5,X4)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])])])]) ).
cnf(c_0_10,plain,
( apply(X1,apply(X2,X3)) = X3
| X1 != function_inverse(X2)
| ~ one_to_one(X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X1)
| ~ function(X2)
| ~ in(X3,relation_dom(X2)) ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
( esk1_0 != apply(relation_composition(esk2_0,function_inverse(esk2_0)),esk1_0)
| esk1_0 != apply(function_inverse(esk2_0),apply(esk2_0,esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ in(X3,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
relation(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
function(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
in(esk1_0,relation_dom(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,plain,
( apply(function_inverse(X1),apply(X1,X2)) = X2
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_10]),c_0_11]),c_0_12]) ).
cnf(c_0_19,negated_conjecture,
one_to_one(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
( apply(function_inverse(esk2_0),apply(esk2_0,esk1_0)) != esk1_0
| ~ relation(function_inverse(esk2_0))
| ~ function(function_inverse(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_21,negated_conjecture,
( apply(function_inverse(esk2_0),apply(esk2_0,X1)) = X1
| ~ in(X1,relation_dom(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_15]),c_0_16])]) ).
cnf(c_0_22,negated_conjecture,
( ~ relation(function_inverse(esk2_0))
| ~ function(function_inverse(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_17])]) ).
cnf(c_0_23,negated_conjecture,
~ relation(function_inverse(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_11]),c_0_15]),c_0_16])]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_12]),c_0_15]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU023+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 22:21:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.23/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.41 # Preprocessing time : 0.018 s
% 0.23/1.41
% 0.23/1.41 # Proof found!
% 0.23/1.41 # SZS status Theorem
% 0.23/1.41 # SZS output start CNFRefutation
% See solution above
% 0.23/1.41 # Proof object total steps : 25
% 0.23/1.41 # Proof object clause steps : 16
% 0.23/1.41 # Proof object formula steps : 9
% 0.23/1.41 # Proof object conjectures : 13
% 0.23/1.41 # Proof object clause conjectures : 10
% 0.23/1.41 # Proof object formula conjectures : 3
% 0.23/1.41 # Proof object initial clauses used : 9
% 0.23/1.41 # Proof object initial formulas used : 4
% 0.23/1.41 # Proof object generating inferences : 7
% 0.23/1.41 # Proof object simplifying inferences : 17
% 0.23/1.41 # Training examples: 0 positive, 0 negative
% 0.23/1.41 # Parsed axioms : 40
% 0.23/1.41 # Removed by relevancy pruning/SinE : 7
% 0.23/1.41 # Initial clauses : 67
% 0.23/1.41 # Removed in clause preprocessing : 2
% 0.23/1.41 # Initial clauses in saturation : 65
% 0.23/1.41 # Processed clauses : 1031
% 0.23/1.41 # ...of these trivial : 0
% 0.23/1.41 # ...subsumed : 729
% 0.23/1.41 # ...remaining for further processing : 302
% 0.23/1.41 # Other redundant clauses eliminated : 2
% 0.23/1.41 # Clauses deleted for lack of memory : 0
% 0.23/1.41 # Backward-subsumed : 29
% 0.23/1.41 # Backward-rewritten : 15
% 0.23/1.41 # Generated clauses : 3102
% 0.23/1.41 # ...of the previous two non-trivial : 2910
% 0.23/1.41 # Contextual simplify-reflections : 598
% 0.23/1.41 # Paramodulations : 3086
% 0.23/1.41 # Factorizations : 0
% 0.23/1.41 # Equation resolutions : 16
% 0.23/1.41 # Current number of processed clauses : 258
% 0.23/1.41 # Positive orientable unit clauses : 21
% 0.23/1.41 # Positive unorientable unit clauses: 0
% 0.23/1.41 # Negative unit clauses : 9
% 0.23/1.41 # Non-unit-clauses : 228
% 0.23/1.41 # Current number of unprocessed clauses: 1746
% 0.23/1.41 # ...number of literals in the above : 11148
% 0.23/1.41 # Current number of archived formulas : 0
% 0.23/1.41 # Current number of archived clauses : 44
% 0.23/1.41 # Clause-clause subsumption calls (NU) : 84508
% 0.23/1.41 # Rec. Clause-clause subsumption calls : 29848
% 0.23/1.41 # Non-unit clause-clause subsumptions : 1278
% 0.23/1.41 # Unit Clause-clause subsumption calls : 431
% 0.23/1.41 # Rewrite failures with RHS unbound : 0
% 0.23/1.41 # BW rewrite match attempts : 4
% 0.23/1.41 # BW rewrite match successes : 4
% 0.23/1.41 # Condensation attempts : 0
% 0.23/1.41 # Condensation successes : 0
% 0.23/1.41 # Termbank termtop insertions : 53962
% 0.23/1.41
% 0.23/1.41 # -------------------------------------------------
% 0.23/1.41 # User time : 0.119 s
% 0.23/1.41 # System time : 0.005 s
% 0.23/1.41 # Total time : 0.124 s
% 0.23/1.41 # Maximum resident set size: 5208 pages
%------------------------------------------------------------------------------