%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU044+1 : 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 : n023.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 05:10:32 PM UTC 2026
% Result : Theorem 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 6 unt; 0 def)
% Number of atoms : 177 ( 19 equ)
% Maximal formula atoms : 79 ( 6 avg)
% Number of connectives : 255 ( 105 ~; 115 |; 24 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 50 ( 4 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t85_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_rng_restriction(X1,X3)
<=> ( ! [X4] :
( in(X4,relation_dom(X2))
<=> ( in(X4,relation_dom(X3))
& in(apply(X3,X4),X1) ) )
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).
fof(dt_k8_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(fc5_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( relation(relation_rng_restriction(X1,X2))
& function(relation_rng_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(t86_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_rng_restriction(X1,X3)))
<=> ( in(X2,relation_dom(X3))
& in(apply(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_funct_1) ).
fof(c_0_4,plain,
! [X105,X106,X107,X108,X109,X110] :
( ( in(X108,relation_dom(X107))
| ~ in(X108,relation_dom(X106))
| X106 != relation_rng_restriction(X105,X107)
| ~ relation(X107)
| ~ function(X107)
| ~ relation(X106)
| ~ function(X106) )
& ( in(apply(X107,X108),X105)
| ~ in(X108,relation_dom(X106))
| X106 != relation_rng_restriction(X105,X107)
| ~ relation(X107)
| ~ function(X107)
| ~ relation(X106)
| ~ function(X106) )
& ( ~ in(X109,relation_dom(X107))
| ~ in(apply(X107,X109),X105)
| in(X109,relation_dom(X106))
| X106 != relation_rng_restriction(X105,X107)
| ~ relation(X107)
| ~ function(X107)
| ~ relation(X106)
| ~ function(X106) )
& ( ~ in(X110,relation_dom(X106))
| apply(X106,X110) = apply(X107,X110)
| X106 != relation_rng_restriction(X105,X107)
| ~ relation(X107)
| ~ function(X107)
| ~ relation(X106)
| ~ function(X106) )
& ( in(esk16_3(X105,X106,X107),relation_dom(X106))
| ~ in(esk15_3(X105,X106,X107),relation_dom(X106))
| ~ in(esk15_3(X105,X106,X107),relation_dom(X107))
| ~ in(apply(X107,esk15_3(X105,X106,X107)),X105)
| X106 = relation_rng_restriction(X105,X107)
| ~ relation(X107)
| ~ function(X107)
| ~ relation(X106)
| ~ function(X106) )
& ( apply(X106,esk16_3(X105,X106,X107)) != apply(X107,esk16_3(X105,X106,X107))
| ~ in(esk15_3(X105,X106,X107),relation_dom(X106))
| ~ in(esk15_3(X105,X106,X107),relation_dom(X107))
| ~ in(apply(X107,esk15_3(X105,X106,X107)),X105)
| X106 = relation_rng_restriction(X105,X107)
| ~ relation(X107)
| ~ function(X107)
| ~ relation(X106)
| ~ function(X106) )
& ( in(esk16_3(X105,X106,X107),relation_dom(X106))
| in(esk15_3(X105,X106,X107),relation_dom(X107))
| in(esk15_3(X105,X106,X107),relation_dom(X106))
| X106 = relation_rng_restriction(X105,X107)
| ~ relation(X107)
| ~ function(X107)
| ~ relation(X106)
| ~ function(X106) )
& ( apply(X106,esk16_3(X105,X106,X107)) != apply(X107,esk16_3(X105,X106,X107))
| in(esk15_3(X105,X106,X107),relation_dom(X107))
| in(esk15_3(X105,X106,X107),relation_dom(X106))
| X106 = relation_rng_restriction(X105,X107)
| ~ relation(X107)
| ~ function(X107)
| ~ relation(X106)
| ~ function(X106) )
& ( in(esk16_3(X105,X106,X107),relation_dom(X106))
| in(apply(X107,esk15_3(X105,X106,X107)),X105)
| in(esk15_3(X105,X106,X107),relation_dom(X106))
| X106 = relation_rng_restriction(X105,X107)
| ~ relation(X107)
| ~ function(X107)
| ~ relation(X106)
| ~ function(X106) )
& ( apply(X106,esk16_3(X105,X106,X107)) != apply(X107,esk16_3(X105,X106,X107))
| in(apply(X107,esk15_3(X105,X106,X107)),X105)
| in(esk15_3(X105,X106,X107),relation_dom(X106))
| X106 = relation_rng_restriction(X105,X107)
| ~ relation(X107)
| ~ function(X107)
| ~ relation(X106)
| ~ function(X106) ) ),
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)],[t85_funct_1])])])])])]) ).
fof(c_0_5,plain,
! [X82,X83] :
( ~ relation(X83)
| relation(relation_rng_restriction(X82,X83)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_relat_1])]) ).
fof(c_0_6,plain,
! [X84,X85] :
( ( relation(relation_rng_restriction(X84,X85))
| ~ relation(X85)
| ~ function(X85) )
& ( function(relation_rng_restriction(X84,X85))
| ~ relation(X85)
| ~ function(X85) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc5_funct_1])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_rng_restriction(X1,X3)))
<=> ( in(X2,relation_dom(X3))
& in(apply(X3,X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[t86_funct_1]) ).
cnf(c_0_8,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(X3))
| X3 != relation_rng_restriction(X4,X2)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( function(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
( relation(esk14_0)
& function(esk14_0)
& ( ~ in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0)))
| ~ in(esk13_0,relation_dom(esk14_0))
| ~ in(apply(esk14_0,esk13_0),esk12_0) )
& ( in(esk13_0,relation_dom(esk14_0))
| in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0))) )
& ( in(apply(esk14_0,esk13_0),esk12_0)
| in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_12,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_rng_restriction(X3,X2)))
| ~ function(X2)
| ~ relation(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_8]),c_0_9]),c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( in(esk13_0,relation_dom(esk14_0))
| in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
function(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,relation_dom(X4))
| X4 != relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_17,negated_conjecture,
( ~ in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0)))
| ~ in(esk13_0,relation_dom(esk14_0))
| ~ in(apply(esk14_0,esk13_0),esk12_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
in(esk13_0,relation_dom(esk14_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_19,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,relation_dom(relation_rng_restriction(X3,X1)))
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_9]),c_0_10]) ).
cnf(c_0_20,negated_conjecture,
( in(apply(esk14_0,esk13_0),esk12_0)
| in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
( ~ in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0)))
| ~ in(apply(esk14_0,esk13_0),esk12_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_22,negated_conjecture,
in(apply(esk14_0,esk13_0),esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_14]),c_0_15])]) ).
cnf(c_0_23,plain,
( in(X1,relation_dom(X4))
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),X3)
| X4 != relation_rng_restriction(X3,X2)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_24,negated_conjecture,
~ in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
cnf(c_0_25,plain,
( in(X1,relation_dom(relation_rng_restriction(X2,X3)))
| ~ in(apply(X3,X1),X2)
| ~ in(X1,relation_dom(X3))
| ~ function(X3)
| ~ relation(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_23]),c_0_9]),c_0_10]) ).
cnf(c_0_26,negated_conjecture,
$false,
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_24,c_0_25]),c_0_22]),c_0_18]),c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU044+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.15/0.33 % Computer : n023.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 02:43:08 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Theorem for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------