TSTP Solution File: SEU020+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU020+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 16:22:09 EDT 2023
% Result : Theorem 0.18s 0.60s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 30
% Syntax : Number of formulae : 48 ( 12 unt; 25 typ; 0 def)
% Number of atoms : 73 ( 12 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 75 ( 25 ~; 22 |; 18 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 16 >; 4 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 22 ( 1 sgn; 14 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
function: $i > $o ).
tff(decl_25,type,
relation: $i > $o ).
tff(decl_26,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_27,type,
identity_relation: $i > $i ).
tff(decl_28,type,
element: ( $i * $i ) > $o ).
tff(decl_29,type,
empty_set: $i ).
tff(decl_30,type,
relation_empty_yielding: $i > $o ).
tff(decl_31,type,
powerset: $i > $i ).
tff(decl_32,type,
relation_dom: $i > $i ).
tff(decl_33,type,
relation_rng: $i > $i ).
tff(decl_34,type,
subset: ( $i * $i ) > $o ).
tff(decl_35,type,
one_to_one: $i > $o ).
tff(decl_36,type,
esk1_1: $i > $i ).
tff(decl_37,type,
esk2_0: $i ).
tff(decl_38,type,
esk3_0: $i ).
tff(decl_39,type,
esk4_1: $i > $i ).
tff(decl_40,type,
esk5_0: $i ).
tff(decl_41,type,
esk6_0: $i ).
tff(decl_42,type,
esk7_1: $i > $i ).
tff(decl_43,type,
esk8_0: $i ).
tff(decl_44,type,
esk9_0: $i ).
tff(decl_45,type,
esk10_0: $i ).
tff(decl_46,type,
esk11_0: $i ).
fof(t53_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ? [X2] :
( relation(X2)
& function(X2)
& relation_composition(X1,X2) = identity_relation(relation_dom(X1)) )
=> one_to_one(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funct_1) ).
fof(t27_funct_1,axiom,
! [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/sandbox/benchmark/theBenchmark.p',t27_funct_1) ).
fof(t71_relat_1,axiom,
! [X1] :
( relation_dom(identity_relation(X1)) = X1
& relation_rng(identity_relation(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
fof(t47_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(relation_composition(X2,X1))
& subset(relation_rng(X2),relation_dom(X1)) )
=> one_to_one(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_funct_1) ).
fof(t52_funct_1,axiom,
! [X1] : one_to_one(identity_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ? [X2] :
( relation(X2)
& function(X2)
& relation_composition(X1,X2) = identity_relation(relation_dom(X1)) )
=> one_to_one(X1) ) ),
inference(assume_negation,[status(cth)],[t53_funct_1]) ).
fof(c_0_6,plain,
! [X38,X39] :
( ~ relation(X38)
| ~ function(X38)
| ~ relation(X39)
| ~ function(X39)
| relation_dom(relation_composition(X39,X38)) != relation_dom(X39)
| subset(relation_rng(X39),relation_dom(X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t27_funct_1])])]) ).
fof(c_0_7,negated_conjecture,
( relation(esk10_0)
& function(esk10_0)
& relation(esk11_0)
& function(esk11_0)
& relation_composition(esk10_0,esk11_0) = identity_relation(relation_dom(esk10_0))
& ~ one_to_one(esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X56] :
( relation_dom(identity_relation(X56)) = X56
& relation_rng(identity_relation(X56)) = X56 ),
inference(variable_rename,[status(thm)],[t71_relat_1]) ).
fof(c_0_9,plain,
! [X44,X45] :
( ~ relation(X44)
| ~ function(X44)
| ~ relation(X45)
| ~ function(X45)
| ~ one_to_one(relation_composition(X45,X44))
| ~ subset(relation_rng(X45),relation_dom(X44))
| one_to_one(X45) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_funct_1])])]) ).
cnf(c_0_10,plain,
( subset(relation_rng(X2),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| relation_dom(relation_composition(X2,X1)) != relation_dom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
relation_composition(esk10_0,esk11_0) = identity_relation(relation_dom(esk10_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
relation_dom(identity_relation(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
function(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
function(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_17,plain,
! [X49] : one_to_one(identity_relation(X49)),
inference(variable_rename,[status(thm)],[t52_funct_1]) ).
cnf(c_0_18,plain,
( one_to_one(X2)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(relation_composition(X2,X1))
| ~ subset(relation_rng(X2),relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
subset(relation_rng(esk10_0),relation_dom(esk11_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_20,plain,
one_to_one(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
~ one_to_one(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_11]),c_0_20]),c_0_13]),c_0_14]),c_0_15]),c_0_16])]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU020+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n022.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 : Thu Aug 24 00:27:26 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.56 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 : 0.036000 s
% 0.18/0.60 % SZS output end Proof
% 0.18/0.60 % Total time : 0.039000 s
%------------------------------------------------------------------------------