%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU220+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.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 : 300s
% DateTime : Tue May 5 05:11:07 PM UTC 2026
% Result : Theorem 1.91s 1.95s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 6 unt; 0 def)
% Number of atoms : 245 ( 69 equ)
% Maximal formula atoms : 130 ( 9 avg)
% Number of connectives : 376 ( 158 ~; 163 |; 39 &)
% ( 1 <=>; 15 =>; 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 : 36 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t57_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_rng(X2)) )
=> ( X1 = apply(X2,apply(function_inverse(X2),X1))
& X1 = apply(relation_composition(function_inverse(X2),X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
fof(t23_funct_1,lemma,
! [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/benchmark/theBenchmark.p',t23_funct_1) ).
fof(t54_funct_1,lemma,
! [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/benchmark/theBenchmark.p',t54_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/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(t55_funct_1,lemma,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_rng(X1) = relation_dom(function_inverse(X1))
& relation_dom(X1) = relation_rng(function_inverse(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_rng(X2)) )
=> ( X1 = apply(X2,apply(function_inverse(X2),X1))
& X1 = apply(relation_composition(function_inverse(X2),X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[t57_funct_1]) ).
fof(c_0_6,negated_conjecture,
( relation(esk78_0)
& function(esk78_0)
& one_to_one(esk78_0)
& in(esk77_0,relation_rng(esk78_0))
& ( esk77_0 != apply(esk78_0,apply(function_inverse(esk78_0),esk77_0))
| esk77_0 != apply(relation_composition(function_inverse(esk78_0),esk78_0),esk77_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_7,lemma,
! [X939,X940,X941] :
( ~ relation(X940)
| ~ function(X940)
| ~ relation(X941)
| ~ function(X941)
| ~ in(X939,relation_dom(X940))
| apply(relation_composition(X940,X941),X939) = apply(X941,apply(X940,X939)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
fof(c_0_8,lemma,
! [X1034,X1035,X1036,X1037,X1038,X1039] :
( ( relation_dom(X1035) = relation_rng(X1034)
| X1035 != function_inverse(X1034)
| ~ relation(X1035)
| ~ function(X1035)
| ~ one_to_one(X1034)
| ~ relation(X1034)
| ~ function(X1034) )
& ( in(X1037,relation_dom(X1034))
| ~ in(X1036,relation_rng(X1034))
| X1037 != apply(X1035,X1036)
| X1035 != function_inverse(X1034)
| ~ relation(X1035)
| ~ function(X1035)
| ~ one_to_one(X1034)
| ~ relation(X1034)
| ~ function(X1034) )
& ( X1036 = apply(X1034,X1037)
| ~ in(X1036,relation_rng(X1034))
| X1037 != apply(X1035,X1036)
| X1035 != function_inverse(X1034)
| ~ relation(X1035)
| ~ function(X1035)
| ~ one_to_one(X1034)
| ~ relation(X1034)
| ~ function(X1034) )
& ( in(X1038,relation_rng(X1034))
| ~ in(X1039,relation_dom(X1034))
| X1038 != apply(X1034,X1039)
| X1035 != function_inverse(X1034)
| ~ relation(X1035)
| ~ function(X1035)
| ~ one_to_one(X1034)
| ~ relation(X1034)
| ~ function(X1034) )
& ( X1039 = apply(X1035,X1038)
| ~ in(X1039,relation_dom(X1034))
| X1038 != apply(X1034,X1039)
| X1035 != function_inverse(X1034)
| ~ relation(X1035)
| ~ function(X1035)
| ~ one_to_one(X1034)
| ~ relation(X1034)
| ~ function(X1034) )
& ( in(esk74_2(X1034,X1035),relation_dom(X1034))
| in(esk71_2(X1034,X1035),relation_rng(X1034))
| relation_dom(X1035) != relation_rng(X1034)
| X1035 = function_inverse(X1034)
| ~ relation(X1035)
| ~ function(X1035)
| ~ one_to_one(X1034)
| ~ relation(X1034)
| ~ function(X1034) )
& ( esk73_2(X1034,X1035) = apply(X1034,esk74_2(X1034,X1035))
| in(esk71_2(X1034,X1035),relation_rng(X1034))
| relation_dom(X1035) != relation_rng(X1034)
| X1035 = function_inverse(X1034)
| ~ relation(X1035)
| ~ function(X1035)
| ~ one_to_one(X1034)
| ~ relation(X1034)
| ~ function(X1034) )
& ( ~ in(esk73_2(X1034,X1035),relation_rng(X1034))
| esk74_2(X1034,X1035) != apply(X1035,esk73_2(X1034,X1035))
| in(esk71_2(X1034,X1035),relation_rng(X1034))
| relation_dom(X1035) != relation_rng(X1034)
| X1035 = function_inverse(X1034)
| ~ relation(X1035)
| ~ function(X1035)
| ~ one_to_one(X1034)
| ~ relation(X1034)
| ~ function(X1034) )
& ( in(esk74_2(X1034,X1035),relation_dom(X1034))
| esk72_2(X1034,X1035) = apply(X1035,esk71_2(X1034,X1035))
| relation_dom(X1035) != relation_rng(X1034)
| X1035 = function_inverse(X1034)
| ~ relation(X1035)
| ~ function(X1035)
| ~ one_to_one(X1034)
| ~ relation(X1034)
| ~ function(X1034) )
& ( esk73_2(X1034,X1035) = apply(X1034,esk74_2(X1034,X1035))
| esk72_2(X1034,X1035) = apply(X1035,esk71_2(X1034,X1035))
| relation_dom(X1035) != relation_rng(X1034)
| X1035 = function_inverse(X1034)
| ~ relation(X1035)
| ~ function(X1035)
| ~ one_to_one(X1034)
| ~ relation(X1034)
| ~ function(X1034) )
& ( ~ in(esk73_2(X1034,X1035),relation_rng(X1034))
| esk74_2(X1034,X1035) != apply(X1035,esk73_2(X1034,X1035))
| esk72_2(X1034,X1035) = apply(X1035,esk71_2(X1034,X1035))
| relation_dom(X1035) != relation_rng(X1034)
| X1035 = function_inverse(X1034)
| ~ relation(X1035)
| ~ function(X1035)
| ~ one_to_one(X1034)
| ~ relation(X1034)
| ~ function(X1034) )
& ( in(esk74_2(X1034,X1035),relation_dom(X1034))
| ~ in(esk72_2(X1034,X1035),relation_dom(X1034))
| esk71_2(X1034,X1035) != apply(X1034,esk72_2(X1034,X1035))
| relation_dom(X1035) != relation_rng(X1034)
| X1035 = function_inverse(X1034)
| ~ relation(X1035)
| ~ function(X1035)
| ~ one_to_one(X1034)
| ~ relation(X1034)
| ~ function(X1034) )
& ( esk73_2(X1034,X1035) = apply(X1034,esk74_2(X1034,X1035))
| ~ in(esk72_2(X1034,X1035),relation_dom(X1034))
| esk71_2(X1034,X1035) != apply(X1034,esk72_2(X1034,X1035))
| relation_dom(X1035) != relation_rng(X1034)
| X1035 = function_inverse(X1034)
| ~ relation(X1035)
| ~ function(X1035)
| ~ one_to_one(X1034)
| ~ relation(X1034)
| ~ function(X1034) )
& ( ~ in(esk73_2(X1034,X1035),relation_rng(X1034))
| esk74_2(X1034,X1035) != apply(X1035,esk73_2(X1034,X1035))
| ~ in(esk72_2(X1034,X1035),relation_dom(X1034))
| esk71_2(X1034,X1035) != apply(X1034,esk72_2(X1034,X1035))
| relation_dom(X1035) != relation_rng(X1034)
| X1035 = function_inverse(X1034)
| ~ relation(X1035)
| ~ function(X1035)
| ~ one_to_one(X1034)
| ~ relation(X1034)
| ~ function(X1034) ) ),
inference(distribute,[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)],[t54_funct_1])])])])])]) ).
fof(c_0_9,plain,
! [X747] :
( ( relation(function_inverse(X747))
| ~ relation(X747)
| ~ function(X747) )
& ( function(function_inverse(X747))
| ~ relation(X747)
| ~ function(X747) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
cnf(c_0_10,negated_conjecture,
( esk77_0 != apply(esk78_0,apply(function_inverse(esk78_0),esk77_0))
| esk77_0 != apply(relation_composition(function_inverse(esk78_0),esk78_0),esk77_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,lemma,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
relation(esk78_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
function(esk78_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,lemma,
( X1 = apply(X2,X3)
| ~ in(X1,relation_rng(X2))
| X3 != apply(X4,X1)
| X4 != function_inverse(X2)
| ~ relation(X4)
| ~ function(X4)
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
( apply(esk78_0,apply(function_inverse(esk78_0),esk77_0)) != esk77_0
| ~ relation(function_inverse(esk78_0))
| ~ function(function_inverse(esk78_0))
| ~ in(esk77_0,relation_dom(function_inverse(esk78_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]) ).
cnf(c_0_18,lemma,
( apply(X1,apply(function_inverse(X1),X2)) = X2
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])]),c_0_15]),c_0_16]) ).
cnf(c_0_19,negated_conjecture,
one_to_one(esk78_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
in(esk77_0,relation_rng(esk78_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_21,lemma,
! [X1047] :
( ( relation_rng(X1047) = relation_dom(function_inverse(X1047))
| ~ one_to_one(X1047)
| ~ relation(X1047)
| ~ function(X1047) )
& ( relation_dom(X1047) = relation_rng(function_inverse(X1047))
| ~ one_to_one(X1047)
| ~ relation(X1047)
| ~ function(X1047) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_funct_1])])]) ).
cnf(c_0_22,lemma,
( ~ relation(function_inverse(esk78_0))
| ~ function(function_inverse(esk78_0))
| ~ in(esk77_0,relation_dom(function_inverse(esk78_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_12]),c_0_13]),c_0_20])]) ).
cnf(c_0_23,lemma,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,lemma,
( ~ relation(function_inverse(esk78_0))
| ~ function(function_inverse(esk78_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_20]),c_0_19]),c_0_12]),c_0_13])]) ).
cnf(c_0_25,lemma,
~ relation(function_inverse(esk78_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_15]),c_0_12]),c_0_13])]) ).
cnf(c_0_26,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_16]),c_0_12]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU220+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n015.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:49:31 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.91/1.95 % Version : CSE_E---1.7
% 1.91/1.95 % Problem : theBenchmark.p
% 1.91/1.95 % SZS status Theorem for theBenchmark.p
% 1.91/1.95 % SZS output start CNFRefutation
% See solution above
% 1.91/1.95 % Total time : 1.425s
%------------------------------------------------------------------------------