%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU003+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 : n025.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 43.55s 30.00s
% Output : CNFRefutation 43.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 7 unt; 0 def)
% Number of atoms : 141 ( 20 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 187 ( 73 ~; 77 |; 23 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 52 ( 0 sgn 28 !; 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(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(t27_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( relation_dom(relation_composition(X2,X1)) = relation_dom(X2)
=> subset(relation_rng(X2),relation_dom(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(c_0_4,plain,
! [X75,X76,X77,X79,X80,X81,X83] :
( ( in(esk2_3(X75,X76,X77),relation_dom(X75))
| ~ in(X77,X76)
| X76 != relation_rng(X75)
| ~ relation(X75)
| ~ function(X75) )
& ( X77 = apply(X75,esk2_3(X75,X76,X77))
| ~ in(X77,X76)
| X76 != relation_rng(X75)
| ~ relation(X75)
| ~ function(X75) )
& ( ~ in(X80,relation_dom(X75))
| X79 != apply(X75,X80)
| in(X79,X76)
| X76 != relation_rng(X75)
| ~ relation(X75)
| ~ function(X75) )
& ( ~ in(esk3_2(X75,X81),X81)
| ~ in(X83,relation_dom(X75))
| esk3_2(X75,X81) != apply(X75,X83)
| X81 = relation_rng(X75)
| ~ relation(X75)
| ~ function(X75) )
& ( in(esk4_2(X75,X81),relation_dom(X75))
| in(esk3_2(X75,X81),X81)
| X81 = relation_rng(X75)
| ~ relation(X75)
| ~ function(X75) )
& ( esk3_2(X75,X81) = apply(X75,esk4_2(X75,X81))
| in(esk3_2(X75,X81),X81)
| X81 = relation_rng(X75)
| ~ relation(X75)
| ~ function(X75) ) ),
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_5,plain,
! [X113,X114,X115] :
( ( in(X113,relation_dom(X115))
| ~ in(X113,relation_dom(relation_composition(X115,X114)))
| ~ relation(X115)
| ~ function(X115)
| ~ relation(X114)
| ~ function(X114) )
& ( in(apply(X115,X113),relation_dom(X114))
| ~ in(X113,relation_dom(relation_composition(X115,X114)))
| ~ relation(X115)
| ~ function(X115)
| ~ relation(X114)
| ~ function(X114) )
& ( ~ in(X113,relation_dom(X115))
| ~ in(apply(X115,X113),relation_dom(X114))
| in(X113,relation_dom(relation_composition(X115,X114)))
| ~ relation(X115)
| ~ function(X115)
| ~ relation(X114)
| ~ function(X114) ) ),
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_6,plain,
( X1 = apply(X2,esk2_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( relation_dom(relation_composition(X2,X1)) = relation_dom(X2)
=> subset(relation_rng(X2),relation_dom(X1)) ) ) ),
inference(assume_negation,[status(cth)],[t27_funct_1]) ).
cnf(c_0_8,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_5]) ).
cnf(c_0_9,plain,
( apply(X1,esk2_3(X1,relation_rng(X1),X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_6]) ).
fof(c_0_10,negated_conjecture,
( relation(esk14_0)
& function(esk14_0)
& relation(esk15_0)
& function(esk15_0)
& relation_dom(relation_composition(esk15_0,esk14_0)) = relation_dom(esk15_0)
& ~ subset(relation_rng(esk15_0),relation_dom(esk14_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_11,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X2)
| ~ function(X3)
| ~ in(esk2_3(X3,relation_rng(X3),X1),relation_dom(relation_composition(X3,X2)))
| ~ in(X1,relation_rng(X3)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
relation_dom(relation_composition(esk15_0,esk14_0)) = relation_dom(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
function(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( in(esk2_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_4]) ).
cnf(c_0_18,negated_conjecture,
( in(X1,relation_dom(esk14_0))
| ~ in(esk2_3(esk15_0,relation_rng(esk15_0),X1),relation_dom(esk15_0))
| ~ in(X1,relation_rng(esk15_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_11,c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_19,plain,
( in(esk2_3(X1,relation_rng(X1),X2),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X69,X70,X71,X72,X73] :
( ( ~ subset(X69,X70)
| ~ in(X71,X69)
| in(X71,X70) )
& ( in(esk1_2(X72,X73),X72)
| subset(X72,X73) )
& ( ~ in(esk1_2(X72,X73),X73)
| subset(X72,X73) ) ),
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)],[d3_tarski])])])])])]) ).
cnf(c_0_21,negated_conjecture,
( in(X1,relation_dom(esk14_0))
| ~ in(X1,relation_rng(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_14]),c_0_16])]) ).
cnf(c_0_22,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( subset(relation_rng(esk15_0),X1)
| in(esk1_2(relation_rng(esk15_0),X1),relation_dom(esk14_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
~ subset(relation_rng(esk15_0),relation_dom(esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU003+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 : n025.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 02:40:58 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 43.55/30.00 % Version : CSE_E---1.7
% 43.55/30.00 % Problem : theBenchmark.p
% 43.55/30.00 % SZS status Theorem for theBenchmark.p
% 43.55/30.00 % SZS output start CNFRefutation
% See solution above
% 43.94/30.31 % Total time : 18.405s
%------------------------------------------------------------------------------