%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU030+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/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 05:10:31 PM UTC 2026
% Result : Theorem 2.15s 2.00s
% Output : CNFRefutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 9 unt; 0 def)
% Number of atoms : 138 ( 43 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 179 ( 69 ~; 66 |; 29 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l72_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ! [X4] :
( ( relation(X4)
& function(X4) )
=> ( ( relation_rng(X2) = X1
& relation_composition(X2,X3) = identity_relation(relation_dom(X4))
& relation_composition(X3,X4) = identity_relation(X1) )
=> X4 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l72_funct_1) ).
fof(t61_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_composition(X1,function_inverse(X1)) = identity_relation(relation_dom(X1))
& relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_1) ).
fof(dt_k2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(t55_funct_1,axiom,
! [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/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(t63_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X1)
& relation_rng(X1) = relation_dom(X2)
& relation_composition(X1,X2) = identity_relation(relation_dom(X1)) )
=> X2 = function_inverse(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_funct_1) ).
fof(c_0_5,plain,
! [X90,X91,X92,X93] :
( ~ relation(X91)
| ~ function(X91)
| ~ relation(X92)
| ~ function(X92)
| ~ relation(X93)
| ~ function(X93)
| relation_rng(X91) != X90
| relation_composition(X91,X92) != identity_relation(relation_dom(X93))
| relation_composition(X92,X93) != identity_relation(X90)
| X93 = X91 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l72_funct_1])])]) ).
cnf(c_0_6,plain,
( X3 = X1
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X3)
| ~ function(X3)
| relation_rng(X1) != X4
| relation_composition(X1,X2) != identity_relation(relation_dom(X3))
| relation_composition(X2,X3) != identity_relation(X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X120] :
( ( relation_composition(X120,function_inverse(X120)) = identity_relation(relation_dom(X120))
| ~ one_to_one(X120)
| ~ relation(X120)
| ~ function(X120) )
& ( relation_composition(function_inverse(X120),X120) = identity_relation(relation_rng(X120))
| ~ one_to_one(X120)
| ~ relation(X120)
| ~ function(X120) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t61_funct_1])])]) ).
fof(c_0_8,plain,
! [X72] :
( ( relation(function_inverse(X72))
| ~ relation(X72)
| ~ function(X72) )
& ( function(function_inverse(X72))
| ~ relation(X72)
| ~ function(X72) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
cnf(c_0_9,plain,
( X1 = X2
| relation_composition(X1,X3) != identity_relation(relation_dom(X2))
| relation_composition(X3,X2) != identity_relation(relation_rng(X1))
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ function(X2)
| ~ function(X3)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X116] :
( ( relation_rng(X116) = relation_dom(function_inverse(X116))
| ~ one_to_one(X116)
| ~ relation(X116)
| ~ function(X116) )
& ( relation_dom(X116) = relation_rng(function_inverse(X116))
| ~ one_to_one(X116)
| ~ relation(X116)
| ~ function(X116) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_funct_1])])]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X1)
& relation_rng(X1) = relation_dom(X2)
& relation_composition(X1,X2) = identity_relation(relation_dom(X1)) )
=> X2 = function_inverse(X1) ) ) ),
inference(assume_negation,[status(cth)],[t63_funct_1]) ).
cnf(c_0_15,plain,
( function_inverse(X1) = X2
| relation_composition(X1,X2) != identity_relation(relation_rng(function_inverse(X1)))
| identity_relation(relation_rng(X1)) != identity_relation(relation_dom(X2))
| ~ one_to_one(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X2)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]) ).
cnf(c_0_16,plain,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,negated_conjecture,
( relation(esk12_0)
& function(esk12_0)
& relation(esk13_0)
& function(esk13_0)
& one_to_one(esk12_0)
& relation_rng(esk12_0) = relation_dom(esk13_0)
& relation_composition(esk12_0,esk13_0) = identity_relation(relation_dom(esk12_0))
& esk13_0 != function_inverse(esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_18,plain,
( function_inverse(X1) = X2
| identity_relation(relation_rng(X1)) != identity_relation(relation_dom(X2))
| relation_composition(X1,X2) != identity_relation(relation_dom(X1))
| ~ one_to_one(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X2)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
relation_composition(esk12_0,esk13_0) = identity_relation(relation_dom(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,negated_conjecture,
relation_rng(esk12_0) = relation_dom(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
one_to_one(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
function(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
function(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
esk13_0 != function_inverse(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,negated_conjecture,
$false,
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU030+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n018.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:41:32 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.15/2.00 % Version : CSE_E---1.7
% 2.15/2.00 % Problem : theBenchmark.p
% 2.15/2.00 % SZS status Theorem for theBenchmark.p
% 2.15/2.00 % SZS output start CNFRefutation
% See solution above
% 2.15/2.01 % Total time : 1.369s
%------------------------------------------------------------------------------