%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU010+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 05:10:29 PM UTC 2026
% Result : Theorem 1.62s 1.83s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 42 ( 17 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 40 ( 16 ~; 12 |; 6 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 20 ( 1 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t42_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation_composition(identity_relation(relation_dom(X1)),X1) = X1
& relation_composition(X1,identity_relation(relation_rng(X1))) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_funct_1) ).
fof(t79_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> ( subset(relation_rng(X2),X1)
=> relation_composition(X2,identity_relation(X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_relat_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t77_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> ( subset(relation_dom(X2),X1)
=> relation_composition(identity_relation(X1),X2) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_relat_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation_composition(identity_relation(relation_dom(X1)),X1) = X1
& relation_composition(X1,identity_relation(relation_rng(X1))) = X1 ) ),
inference(assume_negation,[status(cth)],[t42_funct_1]) ).
fof(c_0_5,plain,
! [X111,X112] :
( ~ relation(X112)
| ~ subset(relation_rng(X112),X111)
| relation_composition(X112,identity_relation(X111)) = X112 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t79_relat_1])]) ).
fof(c_0_6,plain,
! [X89] : subset(X89,X89),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_7,negated_conjecture,
( relation(esk10_0)
& function(esk10_0)
& ( relation_composition(identity_relation(relation_dom(esk10_0)),esk10_0) != esk10_0
| relation_composition(esk10_0,identity_relation(relation_rng(esk10_0))) != esk10_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_8,plain,
( relation_composition(X1,identity_relation(X2)) = X1
| ~ relation(X1)
| ~ subset(relation_rng(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X109,X110] :
( ~ relation(X110)
| ~ subset(relation_dom(X110),X109)
| relation_composition(identity_relation(X109),X110) = X110 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t77_relat_1])]) ).
cnf(c_0_11,negated_conjecture,
( relation_composition(identity_relation(relation_dom(esk10_0)),esk10_0) != esk10_0
| relation_composition(esk10_0,identity_relation(relation_rng(esk10_0))) != esk10_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( relation_composition(X1,identity_relation(relation_rng(X1))) = X1
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( relation_composition(identity_relation(X2),X1) = X1
| ~ relation(X1)
| ~ subset(relation_dom(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
relation_composition(identity_relation(relation_dom(esk10_0)),esk10_0) != esk10_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_16,plain,
( relation_composition(identity_relation(relation_dom(X1)),X1) = X1
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU010+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 02:41:39 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.62/1.83 % Version : CSE_E---1.7
% 1.62/1.83 % Problem : theBenchmark.p
% 1.62/1.83 % SZS status Theorem for theBenchmark.p
% 1.62/1.83 % SZS output start CNFRefutation
% See solution above
% 1.62/1.84 % Total time : 1.369s
%------------------------------------------------------------------------------