%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU002+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 : n016.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 05:10:29 PM UTC 2026
% Result : Theorem 3.56s 3.11s
% Output : CNFRefutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 7 unt; 0 def)
% Number of atoms : 183 ( 21 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 255 ( 104 ~; 105 |; 29 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 69 ( 0 sgn 36 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(t22_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
=> apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
fof(t21_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(fc1_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(t25_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_rng(relation_composition(X3,X2)))
=> in(X1,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_1) ).
fof(c_0_6,plain,
! [X70,X71,X72,X74,X75,X76,X78] :
( ( in(esk1_3(X70,X71,X72),relation_dom(X70))
| ~ in(X72,X71)
| X71 != relation_rng(X70)
| ~ relation(X70)
| ~ function(X70) )
& ( X72 = apply(X70,esk1_3(X70,X71,X72))
| ~ in(X72,X71)
| X71 != relation_rng(X70)
| ~ relation(X70)
| ~ function(X70) )
& ( ~ in(X75,relation_dom(X70))
| X74 != apply(X70,X75)
| in(X74,X71)
| X71 != relation_rng(X70)
| ~ relation(X70)
| ~ function(X70) )
& ( ~ in(esk2_2(X70,X76),X76)
| ~ in(X78,relation_dom(X70))
| esk2_2(X70,X76) != apply(X70,X78)
| X76 = relation_rng(X70)
| ~ relation(X70)
| ~ function(X70) )
& ( in(esk3_2(X70,X76),relation_dom(X70))
| in(esk2_2(X70,X76),X76)
| X76 = relation_rng(X70)
| ~ relation(X70)
| ~ function(X70) )
& ( esk2_2(X70,X76) = apply(X70,esk3_2(X70,X76))
| in(esk2_2(X70,X76),X76)
| X76 = relation_rng(X70)
| ~ relation(X70)
| ~ function(X70) ) ),
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])])])])])]) ).
cnf(c_0_7,plain,
( in(X3,X4)
| ~ in(X1,relation_dom(X2))
| X3 != apply(X2,X1)
| X4 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_8,plain,
! [X111,X112,X113] :
( ~ relation(X112)
| ~ function(X112)
| ~ relation(X113)
| ~ function(X113)
| ~ in(X111,relation_dom(relation_composition(X113,X112)))
| apply(relation_composition(X113,X112),X111) = apply(X112,apply(X113,X111)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_funct_1])])]) ).
fof(c_0_9,plain,
! [X108,X109,X110] :
( ( in(X108,relation_dom(X110))
| ~ in(X108,relation_dom(relation_composition(X110,X109)))
| ~ relation(X110)
| ~ function(X110)
| ~ relation(X109)
| ~ function(X109) )
& ( in(apply(X110,X108),relation_dom(X109))
| ~ in(X108,relation_dom(relation_composition(X110,X109)))
| ~ relation(X110)
| ~ function(X110)
| ~ relation(X109)
| ~ function(X109) )
& ( ~ in(X108,relation_dom(X110))
| ~ in(apply(X110,X108),relation_dom(X109))
| in(X108,relation_dom(relation_composition(X110,X109)))
| ~ relation(X110)
| ~ function(X110)
| ~ relation(X109)
| ~ function(X109) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_funct_1])])])]) ).
cnf(c_0_10,plain,
( in(apply(X1,X2),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_7])]) ).
cnf(c_0_11,plain,
( apply(relation_composition(X2,X1),X3) = apply(X1,apply(X2,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( in(apply(X1,X2),relation_dom(X3))
| ~ in(X2,relation_dom(relation_composition(X1,X3)))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,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_6]) ).
cnf(c_0_14,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_6]) ).
fof(c_0_15,plain,
! [X86,X87] :
( ( relation(relation_composition(X86,X87))
| ~ relation(X86)
| ~ function(X86)
| ~ relation(X87)
| ~ function(X87) )
& ( function(relation_composition(X86,X87))
| ~ relation(X86)
| ~ function(X86)
| ~ relation(X87)
| ~ function(X87) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).
fof(c_0_16,plain,
! [X80,X81] :
( ~ relation(X80)
| ~ relation(X81)
| relation(relation_composition(X80,X81)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_rng(relation_composition(X3,X2)))
=> in(X1,relation_rng(X2)) ) ) ),
inference(assume_negation,[status(cth)],[t25_funct_1]) ).
cnf(c_0_18,plain,
( in(apply(relation_composition(X1,X2),X3),relation_rng(X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X2)
| ~ function(X1)
| ~ in(X3,relation_dom(relation_composition(X1,X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_19,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_13]) ).
cnf(c_0_20,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_14]) ).
cnf(c_0_21,plain,
( function(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_23,negated_conjecture,
( relation(esk14_0)
& function(esk14_0)
& relation(esk15_0)
& function(esk15_0)
& in(esk13_0,relation_rng(relation_composition(esk15_0,esk14_0)))
& ~ in(esk13_0,relation_rng(esk14_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
cnf(c_0_24,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X2)
| ~ function(X3)
| ~ in(X1,relation_rng(relation_composition(X3,X2))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21]),c_0_22]) ).
cnf(c_0_25,negated_conjecture,
in(esk13_0,relation_rng(relation_composition(esk15_0,esk14_0))),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_26,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
function(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,negated_conjecture,
~ in(esk13_0,relation_rng(esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,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(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU002+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n016.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:41:21 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 3.56/3.11 % Version : CSE_E---1.7
% 3.56/3.11 % Problem : theBenchmark.p
% 3.56/3.11 % SZS status Theorem for theBenchmark.p
% 3.56/3.11 % SZS output start CNFRefutation
% See solution above
% 3.56/3.12 % Total time : 2.372s
%------------------------------------------------------------------------------