%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU012+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 : n020.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 05:10:30 PM UTC 2026
% Result : Theorem 4.01s 3.25s
% Output : CNFRefutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 153 ( 54 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 201 ( 78 ~; 82 |; 26 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-3 aty)
% Number of variables : 49 ( 0 sgn 26 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t44_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( relation_rng(X1) = relation_dom(X2)
& relation_composition(X1,X2) = X1 )
=> X2 = identity_relation(relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_1) ).
fof(d5_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(t23_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(t34_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( relation_rng(X1) = relation_dom(X2)
& relation_composition(X1,X2) = X1 )
=> X2 = identity_relation(relation_dom(X2)) ) ) ),
inference(assume_negation,[status(cth)],[t44_funct_1]) ).
fof(c_0_5,plain,
! [X71,X72,X73,X75,X76,X77,X79] :
( ( in(esk1_3(X71,X72,X73),relation_dom(X71))
| ~ in(X73,X72)
| X72 != relation_rng(X71)
| ~ relation(X71)
| ~ function(X71) )
& ( X73 = apply(X71,esk1_3(X71,X72,X73))
| ~ in(X73,X72)
| X72 != relation_rng(X71)
| ~ relation(X71)
| ~ function(X71) )
& ( ~ in(X76,relation_dom(X71))
| X75 != apply(X71,X76)
| in(X75,X72)
| X72 != relation_rng(X71)
| ~ relation(X71)
| ~ function(X71) )
& ( ~ in(esk2_2(X71,X77),X77)
| ~ in(X79,relation_dom(X71))
| esk2_2(X71,X77) != apply(X71,X79)
| X77 = relation_rng(X71)
| ~ relation(X71)
| ~ function(X71) )
& ( in(esk3_2(X71,X77),relation_dom(X71))
| in(esk2_2(X71,X77),X77)
| X77 = relation_rng(X71)
| ~ relation(X71)
| ~ function(X71) )
& ( esk2_2(X71,X77) = apply(X71,esk3_2(X71,X77))
| in(esk2_2(X71,X77),X77)
| X77 = relation_rng(X71)
| ~ relation(X71)
| ~ function(X71) ) ),
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)],[d5_funct_1])])])])])]) ).
fof(c_0_6,plain,
! [X111,X112,X113] :
( ~ relation(X112)
| ~ function(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ in(X111,relation_dom(X112))
| apply(relation_composition(X112,X113),X111) = apply(X113,apply(X112,X111)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
fof(c_0_7,negated_conjecture,
( relation(esk14_0)
& function(esk14_0)
& relation(esk15_0)
& function(esk15_0)
& relation_rng(esk14_0) = relation_dom(esk15_0)
& relation_composition(esk14_0,esk15_0) = esk14_0
& esk15_0 != identity_relation(relation_dom(esk15_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_8,plain,
( in(esk1_3(X1,X2,X3),relation_dom(X1))
| ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
relation_composition(esk14_0,esk15_0) = esk14_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
function(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( X1 = apply(X2,esk1_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,plain,
( in(esk1_3(X1,relation_rng(X1),X2),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
relation_rng(esk14_0) = relation_dom(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_18,plain,
! [X116,X117,X118] :
( ( relation_dom(X117) = X116
| X117 != identity_relation(X116)
| ~ relation(X117)
| ~ function(X117) )
& ( ~ in(X118,X116)
| apply(X117,X118) = X118
| X117 != identity_relation(X116)
| ~ relation(X117)
| ~ function(X117) )
& ( in(esk13_2(X116,X117),X116)
| relation_dom(X117) != X116
| X117 = identity_relation(X116)
| ~ relation(X117)
| ~ function(X117) )
& ( apply(X117,esk13_2(X116,X117)) != esk13_2(X116,X117)
| relation_dom(X117) != X116
| X117 = identity_relation(X116)
| ~ relation(X117)
| ~ function(X117) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).
cnf(c_0_19,negated_conjecture,
( apply(esk15_0,apply(esk14_0,X1)) = apply(esk14_0,X1)
| ~ in(X1,relation_dom(esk14_0)) ),
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_9,c_0_10]),c_0_11]),c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_20,plain,
( apply(X1,esk1_3(X1,relation_rng(X1),X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( in(esk1_3(esk14_0,relation_dom(esk15_0),X1),relation_dom(esk14_0))
| ~ in(X1,relation_dom(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_12]),c_0_14])]) ).
cnf(c_0_22,plain,
( in(esk13_2(X1,X2),X1)
| X2 = identity_relation(X1)
| relation_dom(X2) != X1
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( X1 = identity_relation(X2)
| apply(X1,esk13_2(X2,X1)) != esk13_2(X2,X1)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( apply(esk15_0,X1) = X1
| ~ in(X1,relation_dom(esk15_0)) ),
inference(csr,[status(thm)],[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_19,c_0_20]),c_0_17]),c_0_12]),c_0_14]),c_0_17])]),c_0_21]) ).
cnf(c_0_25,plain,
( identity_relation(relation_dom(X1)) = X1
| in(esk13_2(relation_dom(X1),X1),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
esk15_0 != identity_relation(relation_dom(esk15_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,plain,
( identity_relation(relation_dom(X1)) = X1
| apply(X1,esk13_2(relation_dom(X1),X1)) != esk13_2(relation_dom(X1),X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
apply(esk15_0,esk13_2(relation_dom(esk15_0),esk15_0)) = esk13_2(relation_dom(esk15_0),esk15_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_11]),c_0_13])]),c_0_26]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_11]),c_0_13])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU012+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 : n020.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 02:42:05 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.01/3.25 % Version : CSE_E---1.7
% 4.01/3.25 % Problem : theBenchmark.p
% 4.01/3.25 % SZS status Theorem for theBenchmark.p
% 4.01/3.25 % SZS output start CNFRefutation
% See solution above
% 4.01/3.26 % Total time : 2.370s
%------------------------------------------------------------------------------