%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU219+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 : n018.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 1.57s 2.07s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 5 unt; 0 def)
% Number of atoms : 219 ( 69 equ)
% Maximal formula atoms : 130 ( 9 avg)
% Number of connectives : 334 ( 139 ~; 147 |; 34 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t55_funct_1,conjecture,
! [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(t37_relat_1,lemma,
! [X1] :
( relation(X1)
=> ( relation_rng(X1) = relation_dom(relation_inverse(X1))
& relation_dom(X1) = relation_rng(relation_inverse(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
fof(d9_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(X1) = relation_inverse(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_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(c_0_5,negated_conjecture,
~ ! [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)) ) ) ),
inference(assume_negation,[status(cth)],[t55_funct_1]) ).
fof(c_0_6,lemma,
! [X972] :
( ( relation_rng(X972) = relation_dom(relation_inverse(X972))
| ~ relation(X972) )
& ( relation_dom(X972) = relation_rng(relation_inverse(X972))
| ~ relation(X972) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_relat_1])])]) ).
fof(c_0_7,plain,
! [X744] :
( ~ relation(X744)
| ~ function(X744)
| ~ one_to_one(X744)
| function_inverse(X744) = relation_inverse(X744) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_funct_1])]) ).
fof(c_0_8,negated_conjecture,
( relation(esk75_0)
& function(esk75_0)
& one_to_one(esk75_0)
& ( relation_rng(esk75_0) != relation_dom(function_inverse(esk75_0))
| relation_dom(esk75_0) != relation_rng(function_inverse(esk75_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,lemma,
( relation_dom(X1) = relation_rng(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( function_inverse(X1) = relation_inverse(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,lemma,
! [X1032,X1033,X1034,X1035,X1036,X1037] :
( ( relation_dom(X1033) = relation_rng(X1032)
| X1033 != function_inverse(X1032)
| ~ relation(X1033)
| ~ function(X1033)
| ~ one_to_one(X1032)
| ~ relation(X1032)
| ~ function(X1032) )
& ( in(X1035,relation_dom(X1032))
| ~ in(X1034,relation_rng(X1032))
| X1035 != apply(X1033,X1034)
| X1033 != function_inverse(X1032)
| ~ relation(X1033)
| ~ function(X1033)
| ~ one_to_one(X1032)
| ~ relation(X1032)
| ~ function(X1032) )
& ( X1034 = apply(X1032,X1035)
| ~ in(X1034,relation_rng(X1032))
| X1035 != apply(X1033,X1034)
| X1033 != function_inverse(X1032)
| ~ relation(X1033)
| ~ function(X1033)
| ~ one_to_one(X1032)
| ~ relation(X1032)
| ~ function(X1032) )
& ( in(X1036,relation_rng(X1032))
| ~ in(X1037,relation_dom(X1032))
| X1036 != apply(X1032,X1037)
| X1033 != function_inverse(X1032)
| ~ relation(X1033)
| ~ function(X1033)
| ~ one_to_one(X1032)
| ~ relation(X1032)
| ~ function(X1032) )
& ( X1037 = apply(X1033,X1036)
| ~ in(X1037,relation_dom(X1032))
| X1036 != apply(X1032,X1037)
| X1033 != function_inverse(X1032)
| ~ relation(X1033)
| ~ function(X1033)
| ~ one_to_one(X1032)
| ~ relation(X1032)
| ~ function(X1032) )
& ( in(esk74_2(X1032,X1033),relation_dom(X1032))
| in(esk71_2(X1032,X1033),relation_rng(X1032))
| relation_dom(X1033) != relation_rng(X1032)
| X1033 = function_inverse(X1032)
| ~ relation(X1033)
| ~ function(X1033)
| ~ one_to_one(X1032)
| ~ relation(X1032)
| ~ function(X1032) )
& ( esk73_2(X1032,X1033) = apply(X1032,esk74_2(X1032,X1033))
| in(esk71_2(X1032,X1033),relation_rng(X1032))
| relation_dom(X1033) != relation_rng(X1032)
| X1033 = function_inverse(X1032)
| ~ relation(X1033)
| ~ function(X1033)
| ~ one_to_one(X1032)
| ~ relation(X1032)
| ~ function(X1032) )
& ( ~ in(esk73_2(X1032,X1033),relation_rng(X1032))
| esk74_2(X1032,X1033) != apply(X1033,esk73_2(X1032,X1033))
| in(esk71_2(X1032,X1033),relation_rng(X1032))
| relation_dom(X1033) != relation_rng(X1032)
| X1033 = function_inverse(X1032)
| ~ relation(X1033)
| ~ function(X1033)
| ~ one_to_one(X1032)
| ~ relation(X1032)
| ~ function(X1032) )
& ( in(esk74_2(X1032,X1033),relation_dom(X1032))
| esk72_2(X1032,X1033) = apply(X1033,esk71_2(X1032,X1033))
| relation_dom(X1033) != relation_rng(X1032)
| X1033 = function_inverse(X1032)
| ~ relation(X1033)
| ~ function(X1033)
| ~ one_to_one(X1032)
| ~ relation(X1032)
| ~ function(X1032) )
& ( esk73_2(X1032,X1033) = apply(X1032,esk74_2(X1032,X1033))
| esk72_2(X1032,X1033) = apply(X1033,esk71_2(X1032,X1033))
| relation_dom(X1033) != relation_rng(X1032)
| X1033 = function_inverse(X1032)
| ~ relation(X1033)
| ~ function(X1033)
| ~ one_to_one(X1032)
| ~ relation(X1032)
| ~ function(X1032) )
& ( ~ in(esk73_2(X1032,X1033),relation_rng(X1032))
| esk74_2(X1032,X1033) != apply(X1033,esk73_2(X1032,X1033))
| esk72_2(X1032,X1033) = apply(X1033,esk71_2(X1032,X1033))
| relation_dom(X1033) != relation_rng(X1032)
| X1033 = function_inverse(X1032)
| ~ relation(X1033)
| ~ function(X1033)
| ~ one_to_one(X1032)
| ~ relation(X1032)
| ~ function(X1032) )
& ( in(esk74_2(X1032,X1033),relation_dom(X1032))
| ~ in(esk72_2(X1032,X1033),relation_dom(X1032))
| esk71_2(X1032,X1033) != apply(X1032,esk72_2(X1032,X1033))
| relation_dom(X1033) != relation_rng(X1032)
| X1033 = function_inverse(X1032)
| ~ relation(X1033)
| ~ function(X1033)
| ~ one_to_one(X1032)
| ~ relation(X1032)
| ~ function(X1032) )
& ( esk73_2(X1032,X1033) = apply(X1032,esk74_2(X1032,X1033))
| ~ in(esk72_2(X1032,X1033),relation_dom(X1032))
| esk71_2(X1032,X1033) != apply(X1032,esk72_2(X1032,X1033))
| relation_dom(X1033) != relation_rng(X1032)
| X1033 = function_inverse(X1032)
| ~ relation(X1033)
| ~ function(X1033)
| ~ one_to_one(X1032)
| ~ relation(X1032)
| ~ function(X1032) )
& ( ~ in(esk73_2(X1032,X1033),relation_rng(X1032))
| esk74_2(X1032,X1033) != apply(X1033,esk73_2(X1032,X1033))
| ~ in(esk72_2(X1032,X1033),relation_dom(X1032))
| esk71_2(X1032,X1033) != apply(X1032,esk72_2(X1032,X1033))
| relation_dom(X1033) != relation_rng(X1032)
| X1033 = function_inverse(X1032)
| ~ relation(X1033)
| ~ function(X1033)
| ~ one_to_one(X1032)
| ~ relation(X1032)
| ~ function(X1032) ) ),
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_12,plain,
! [X745] :
( ( relation(function_inverse(X745))
| ~ relation(X745)
| ~ function(X745) )
& ( function(function_inverse(X745))
| ~ relation(X745)
| ~ function(X745) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
cnf(c_0_13,negated_conjecture,
( relation_rng(esk75_0) != relation_dom(function_inverse(esk75_0))
| relation_dom(esk75_0) != relation_rng(function_inverse(esk75_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,lemma,
( relation_rng(function_inverse(X1)) = relation_dom(X1)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
one_to_one(esk75_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
relation(esk75_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
function(esk75_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,lemma,
( relation_dom(X1) = relation_rng(X2)
| X1 != function_inverse(X2)
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,negated_conjecture,
relation_dom(function_inverse(esk75_0)) != relation_rng(esk75_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_22,lemma,
( relation_dom(function_inverse(X1)) = relation_rng(X1)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_19]),c_0_20]) ).
cnf(c_0_23,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_15]),c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.20 % Problem : SEU219+2 : TPTP v9.2.1. Released v3.3.0.
% 0.03/0.20 % 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
% 0.12/0.45 % Computer : n018.cluster.edu
% 0.12/0.45 % Model : x86_64 x86_64
% 0.12/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.45 % Memory : 8042.1875MB
% 0.12/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.45 % CPULimit : 300
% 0.12/0.45 % WCLimit : 300
% 0.12/0.45 % DateTime : Tue May 5 02:49:32 EDT 2026
% 0.12/0.45 % CPUTime :
% 0.12/0.47 % start to proof: theBenchmark
% 1.57/2.07 % Version : CSE_E---1.7
% 1.57/2.07 % Problem : theBenchmark.p
% 1.57/2.07 % SZS status Theorem for theBenchmark.p
% 1.57/2.07 % SZS output start CNFRefutation
% See solution above
% 1.57/2.07 % Total time : 1.432s
%------------------------------------------------------------------------------