%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU219+3 : TPTP v9.2.1. Released v3.2.0.
% 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 : n024.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 1.11s 1.82s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 5 unt; 0 def)
% Number of atoms : 47 ( 20 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 48 ( 18 ~; 13 |; 10 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 9 ( 0 sgn 6 !; 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(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(t37_relat_1,axiom,
! [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(c_0_3,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_4,negated_conjecture,
( relation(esk12_0)
& function(esk12_0)
& one_to_one(esk12_0)
& ( relation_rng(esk12_0) != relation_dom(function_inverse(esk12_0))
| relation_dom(esk12_0) != relation_rng(function_inverse(esk12_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_5,plain,
! [X60] :
( ~ relation(X60)
| ~ function(X60)
| ~ one_to_one(X60)
| function_inverse(X60) = relation_inverse(X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_funct_1])]) ).
cnf(c_0_6,negated_conjecture,
( relation_rng(esk12_0) != relation_dom(function_inverse(esk12_0))
| relation_dom(esk12_0) != relation_rng(function_inverse(esk12_0)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( function_inverse(X1) = relation_inverse(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
one_to_one(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,negated_conjecture,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
function(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_11,plain,
! [X90] :
( ( relation_rng(X90) = relation_dom(relation_inverse(X90))
| ~ relation(X90) )
& ( relation_dom(X90) = relation_rng(relation_inverse(X90))
| ~ relation(X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_relat_1])])]) ).
cnf(c_0_12,negated_conjecture,
( relation_rng(relation_inverse(esk12_0)) != relation_dom(esk12_0)
| relation_dom(relation_inverse(esk12_0)) != relation_rng(esk12_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]),c_0_9]),c_0_10])]) ).
cnf(c_0_13,plain,
( relation_dom(X1) = relation_rng(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
relation_dom(relation_inverse(esk12_0)) != relation_rng(esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_9])]) ).
cnf(c_0_15,plain,
( relation_rng(X1) = relation_dom(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_9])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SEU219+3 : TPTP v9.2.1. Released v3.2.0.
% 0.03/0.14 % 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
% 0.06/0.40 % Computer : n024.cluster.edu
% 0.06/0.40 % Model : x86_64 x86_64
% 0.06/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.40 % Memory : 8042.1875MB
% 0.06/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.40 % CPULimit : 300
% 0.06/0.40 % WCLimit : 300
% 0.06/0.40 % DateTime : Mon May 4 21:49:27 EDT 2026
% 0.06/0.40 % CPUTime :
% 0.06/0.43 % start to proof: theBenchmark
% 1.11/1.82 % Version : CSE_E---1.7
% 1.11/1.82 % Problem : theBenchmark.p
% 1.11/1.82 % SZS status Theorem for theBenchmark.p
% 1.11/1.82 % SZS output start CNFRefutation
% See solution above
% 1.11/1.82 % Total time : 1.387s
%------------------------------------------------------------------------------