%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU032+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 : n008.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 1.40s 1.76s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 5 unt; 0 def)
% Number of atoms : 116 ( 27 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 148 ( 59 ~; 56 |; 19 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t63_funct_1,axiom,
! [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(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(t62_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_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(t65_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(function_inverse(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_1) ).
fof(c_0_6,plain,
! [X115,X116] :
( ~ relation(X115)
| ~ function(X115)
| ~ relation(X116)
| ~ function(X116)
| ~ one_to_one(X115)
| relation_rng(X115) != relation_dom(X116)
| relation_composition(X115,X116) != identity_relation(relation_dom(X115))
| X116 = function_inverse(X115) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_funct_1])])]) ).
fof(c_0_7,plain,
! [X113] :
( ( relation_composition(X113,function_inverse(X113)) = identity_relation(relation_dom(X113))
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) )
& ( relation_composition(function_inverse(X113),X113) = identity_relation(relation_rng(X113))
| ~ one_to_one(X113)
| ~ relation(X113)
| ~ function(X113) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t61_funct_1])])]) ).
fof(c_0_8,plain,
! [X69] :
( ( relation(function_inverse(X69))
| ~ relation(X69)
| ~ function(X69) )
& ( function(function_inverse(X69))
| ~ relation(X69)
| ~ function(X69) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
fof(c_0_9,plain,
! [X114] :
( ~ relation(X114)
| ~ function(X114)
| ~ one_to_one(X114)
| one_to_one(function_inverse(X114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t62_funct_1])]) ).
fof(c_0_10,plain,
! [X109] :
( ( relation_rng(X109) = relation_dom(function_inverse(X109))
| ~ one_to_one(X109)
| ~ relation(X109)
| ~ function(X109) )
& ( relation_dom(X109) = relation_rng(function_inverse(X109))
| ~ one_to_one(X109)
| ~ relation(X109)
| ~ function(X109) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_funct_1])])]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(function_inverse(X1)) = X1 ) ),
inference(assume_negation,[status(cth)],[t65_funct_1]) ).
cnf(c_0_12,plain,
( X2 = function_inverse(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| relation_rng(X1) != relation_dom(X2)
| relation_composition(X1,X2) != identity_relation(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,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_14,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
( one_to_one(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_18,negated_conjecture,
( relation(esk12_0)
& function(esk12_0)
& one_to_one(esk12_0)
& function_inverse(function_inverse(esk12_0)) != esk12_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_19,plain,
( function_inverse(function_inverse(X1)) = X1
| identity_relation(relation_dom(function_inverse(X1))) != identity_relation(relation_rng(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]),c_0_16]),c_0_17]) ).
cnf(c_0_20,plain,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
function_inverse(function_inverse(esk12_0)) != esk12_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( function_inverse(function_inverse(X1)) = X1
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
one_to_one(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
function(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
$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_23]),c_0_24]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU032+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
% 0.16/0.33 % Computer : n008.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 02:41:28 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.40/1.76 % Version : CSE_E---1.7
% 1.40/1.76 % Problem : theBenchmark.p
% 1.40/1.76 % SZS status Theorem for theBenchmark.p
% 1.40/1.76 % SZS output start CNFRefutation
% See solution above
% 1.40/1.76 % Total time : 1.369s
%------------------------------------------------------------------------------