TSTP Solution File: SEU010+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU010+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n024.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 : Thu Aug 31 16:22:07 EDT 2023
% Result : Theorem 0.18s 0.60s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 27
% Syntax : Number of formulae : 41 ( 6 unt; 23 typ; 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 types : 2 ( 0 usr)
% Number of type conns : 19 ( 15 >; 4 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 20 ( 1 sgn; 13 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty_set: $i ).
tff(decl_24,type,
empty: $i > $o ).
tff(decl_25,type,
relation: $i > $o ).
tff(decl_26,type,
relation_empty_yielding: $i > $o ).
tff(decl_27,type,
element: ( $i * $i ) > $o ).
tff(decl_28,type,
powerset: $i > $i ).
tff(decl_29,type,
function: $i > $o ).
tff(decl_30,type,
relation_dom: $i > $i ).
tff(decl_31,type,
relation_rng: $i > $i ).
tff(decl_32,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_33,type,
subset: ( $i * $i ) > $o ).
tff(decl_34,type,
identity_relation: $i > $i ).
tff(decl_35,type,
esk1_1: $i > $i ).
tff(decl_36,type,
esk2_0: $i ).
tff(decl_37,type,
esk3_1: $i > $i ).
tff(decl_38,type,
esk4_1: $i > $i ).
tff(decl_39,type,
esk5_0: $i ).
tff(decl_40,type,
esk6_0: $i ).
tff(decl_41,type,
esk7_0: $i ).
tff(decl_42,type,
esk8_0: $i ).
tff(decl_43,type,
esk9_0: $i ).
tff(decl_44,type,
esk10_0: $i ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t79_relat_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/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/sandbox2/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,
! [X56,X57] :
( ~ relation(X57)
| ~ subset(relation_rng(X57),X56)
| relation_composition(X57,identity_relation(X56)) = X57 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t79_relat_1])]) ).
fof(c_0_6,plain,
! [X34] : subset(X34,X34),
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,
! [X54,X55] :
( ~ relation(X55)
| ~ subset(relation_dom(X55),X54)
| relation_composition(identity_relation(X54),X55) = X55 ),
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
% 0.08/0.11 % Problem : SEU010+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 19:33:25 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.55 start to proof: theBenchmark
% 0.18/0.60 % Version : CSE_E---1.5
% 0.18/0.60 % Problem : theBenchmark.p
% 0.18/0.60 % Proof found
% 0.18/0.60 % SZS status Theorem for theBenchmark.p
% 0.18/0.60 % SZS output start Proof
% See solution above
% 0.18/0.60 % Total time : 0.040000 s
% 0.18/0.60 % SZS output end Proof
% 0.18/0.60 % Total time : 0.043000 s
%------------------------------------------------------------------------------