TSTP Solution File: SEU019+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU019+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 : n031.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 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 31
% Syntax : Number of formulae : 57 ( 11 unt; 26 typ; 0 def)
% Number of atoms : 111 ( 31 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 130 ( 50 ~; 60 |; 14 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 18 >; 5 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 3 sgn; 18 !; 0 ?; 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,
one_to_one: $i > $o ).
tff(decl_27,type,
relation_dom: $i > $i ).
tff(decl_28,type,
apply: ( $i * $i ) > $i ).
tff(decl_29,type,
identity_relation: $i > $i ).
tff(decl_30,type,
element: ( $i * $i ) > $o ).
tff(decl_31,type,
empty_set: $i ).
tff(decl_32,type,
relation_empty_yielding: $i > $o ).
tff(decl_33,type,
powerset: $i > $i ).
tff(decl_34,type,
subset: ( $i * $i ) > $o ).
tff(decl_35,type,
esk1_1: $i > $i ).
tff(decl_36,type,
esk2_1: $i > $i ).
tff(decl_37,type,
esk3_1: $i > $i ).
tff(decl_38,type,
esk4_0: $i ).
tff(decl_39,type,
esk5_0: $i ).
tff(decl_40,type,
esk6_1: $i > $i ).
tff(decl_41,type,
esk7_0: $i ).
tff(decl_42,type,
esk8_0: $i ).
tff(decl_43,type,
esk9_1: $i > $i ).
tff(decl_44,type,
esk10_0: $i ).
tff(decl_45,type,
esk11_0: $i ).
tff(decl_46,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk13_0: $i ).
fof(t34_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(d8_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(t52_funct_1,conjecture,
! [X1] : one_to_one(identity_relation(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_1) ).
fof(c_0_5,plain,
! [X35,X36,X37] :
( ( relation_dom(X36) = X35
| X36 != identity_relation(X35)
| ~ relation(X36)
| ~ function(X36) )
& ( ~ in(X37,X35)
| apply(X36,X37) = X37
| X36 != identity_relation(X35)
| ~ relation(X36)
| ~ function(X36) )
& ( in(esk12_2(X35,X36),X35)
| relation_dom(X36) != X35
| X36 = identity_relation(X35)
| ~ relation(X36)
| ~ function(X36) )
& ( apply(X36,esk12_2(X35,X36)) != esk12_2(X35,X36)
| relation_dom(X36) != X35
| X36 = identity_relation(X35)
| ~ relation(X36)
| ~ function(X36) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).
fof(c_0_6,plain,
! [X13] : relation(identity_relation(X13)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_7,plain,
! [X17] :
( relation(identity_relation(X17))
& function(identity_relation(X17)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(c_0_8,plain,
! [X8,X9,X10] :
( ( ~ one_to_one(X8)
| ~ in(X9,relation_dom(X8))
| ~ in(X10,relation_dom(X8))
| apply(X8,X9) != apply(X8,X10)
| X9 = X10
| ~ relation(X8)
| ~ function(X8) )
& ( in(esk1_1(X8),relation_dom(X8))
| one_to_one(X8)
| ~ relation(X8)
| ~ function(X8) )
& ( in(esk2_1(X8),relation_dom(X8))
| one_to_one(X8)
| ~ relation(X8)
| ~ function(X8) )
& ( apply(X8,esk1_1(X8)) = apply(X8,esk2_1(X8))
| one_to_one(X8)
| ~ relation(X8)
| ~ function(X8) )
& ( esk1_1(X8) != esk2_1(X8)
| one_to_one(X8)
| ~ relation(X8)
| ~ function(X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])]) ).
cnf(c_0_9,plain,
( relation_dom(X1) = X2
| X1 != identity_relation(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( apply(X3,X1) = X1
| ~ in(X1,X2)
| X3 != identity_relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
( in(esk2_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
relation_dom(identity_relation(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_9]),c_0_10]),c_0_11])]) ).
cnf(c_0_15,plain,
( in(esk1_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
( apply(X1,esk1_1(X1)) = apply(X1,esk2_1(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,plain,
( apply(identity_relation(X1),X2) = X2
| ~ in(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_12]),c_0_10]),c_0_11])]) ).
cnf(c_0_18,plain,
( one_to_one(identity_relation(X1))
| in(esk2_1(identity_relation(X1)),X1) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_10]),c_0_11])]),c_0_14]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1] : one_to_one(identity_relation(X1)),
inference(assume_negation,[status(cth)],[t52_funct_1]) ).
cnf(c_0_20,plain,
( one_to_one(identity_relation(X1))
| in(esk1_1(identity_relation(X1)),X1) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_10]),c_0_11])]),c_0_14]) ).
cnf(c_0_21,plain,
( apply(identity_relation(X1),esk2_1(identity_relation(X1))) = apply(identity_relation(X1),esk1_1(identity_relation(X1)))
| one_to_one(identity_relation(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_10]),c_0_11])]) ).
cnf(c_0_22,plain,
( apply(identity_relation(X1),esk2_1(identity_relation(X1))) = esk2_1(identity_relation(X1))
| one_to_one(identity_relation(X1)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( one_to_one(X1)
| esk1_1(X1) != esk2_1(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_24,negated_conjecture,
~ one_to_one(identity_relation(esk13_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_25,plain,
( apply(identity_relation(X1),esk1_1(identity_relation(X1))) = esk1_1(identity_relation(X1))
| one_to_one(identity_relation(X1)) ),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_26,plain,
( apply(identity_relation(X1),esk1_1(identity_relation(X1))) = esk2_1(identity_relation(X1))
| one_to_one(identity_relation(X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( one_to_one(identity_relation(X1))
| esk2_1(identity_relation(X1)) != esk1_1(identity_relation(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_10]),c_0_11])]) ).
cnf(c_0_28,negated_conjecture,
~ one_to_one(identity_relation(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
one_to_one(identity_relation(X1)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU019+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n031.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 17:23:35 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.59 % Version : CSE_E---1.5
% 0.19/0.59 % Problem : theBenchmark.p
% 0.19/0.59 % Proof found
% 0.19/0.59 % SZS status Theorem for theBenchmark.p
% 0.19/0.59 % SZS output start Proof
% See solution above
% 0.19/0.60 % Total time : 0.012000 s
% 0.19/0.60 % SZS output end Proof
% 0.19/0.60 % Total time : 0.015000 s
%------------------------------------------------------------------------------