TSTP Solution File: SEU075+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU075+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 : n009.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 16:22:21 EDT 2023
% Result : Theorem 138.96s 139.26s
% Output : CNFRefutation 138.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 37
% Syntax : Number of formulae : 70 ( 17 unt; 33 typ; 0 def)
% Number of atoms : 172 ( 59 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 213 ( 78 ~; 82 |; 35 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 20 >; 10 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 13 con; 0-3 aty)
% Number of variables : 51 ( 0 sgn; 29 !; 1 ?; 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_rng: $i > $i ).
tff(decl_28,type,
relation_dom: $i > $i ).
tff(decl_29,type,
apply: ( $i * $i ) > $i ).
tff(decl_30,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_31,type,
element: ( $i * $i ) > $o ).
tff(decl_32,type,
empty_set: $i ).
tff(decl_33,type,
relation_empty_yielding: $i > $o ).
tff(decl_34,type,
powerset: $i > $i ).
tff(decl_35,type,
subset: ( $i * $i ) > $o ).
tff(decl_36,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk3_2: ( $i * $i ) > $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_1: $i > $i ).
tff(decl_47,type,
esk12_0: $i ).
tff(decl_48,type,
esk13_0: $i ).
tff(decl_49,type,
esk14_0: $i ).
tff(decl_50,type,
esk15_0: $i ).
tff(decl_51,type,
esk16_0: $i ).
tff(decl_52,type,
esk17_0: $i ).
tff(decl_53,type,
esk18_0: $i ).
tff(decl_54,type,
esk19_2: ( $i * $i ) > $i ).
fof(t156_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ! [X4] :
( ( relation(X4)
& function(X4) )
=> ( ( X1 = relation_rng(X2)
& relation_dom(X3) = X1
& relation_dom(X4) = X1
& relation_composition(X2,X3) = relation_composition(X2,X4) )
=> X3 = X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_funct_1) ).
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(t9_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( relation_dom(X1) = relation_dom(X2)
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
fof(t23_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ! [X4] :
( ( relation(X4)
& function(X4) )
=> ( ( X1 = relation_rng(X2)
& relation_dom(X3) = X1
& relation_dom(X4) = X1
& relation_composition(X2,X3) = relation_composition(X2,X4) )
=> X3 = X4 ) ) ) ),
inference(assume_negation,[status(cth)],[t156_funct_1]) ).
fof(c_0_5,plain,
! [X10,X11,X12,X14,X15,X16,X18] :
( ( in(esk1_3(X10,X11,X12),relation_dom(X10))
| ~ in(X12,X11)
| X11 != relation_rng(X10)
| ~ relation(X10)
| ~ function(X10) )
& ( X12 = apply(X10,esk1_3(X10,X11,X12))
| ~ in(X12,X11)
| X11 != relation_rng(X10)
| ~ relation(X10)
| ~ function(X10) )
& ( ~ in(X15,relation_dom(X10))
| X14 != apply(X10,X15)
| in(X14,X11)
| X11 != relation_rng(X10)
| ~ relation(X10)
| ~ function(X10) )
& ( ~ in(esk2_2(X10,X16),X16)
| ~ in(X18,relation_dom(X10))
| esk2_2(X10,X16) != apply(X10,X18)
| X16 = relation_rng(X10)
| ~ relation(X10)
| ~ function(X10) )
& ( in(esk3_2(X10,X16),relation_dom(X10))
| in(esk2_2(X10,X16),X16)
| X16 = relation_rng(X10)
| ~ relation(X10)
| ~ function(X10) )
& ( esk2_2(X10,X16) = apply(X10,esk3_2(X10,X16))
| in(esk2_2(X10,X16),X16)
| X16 = relation_rng(X10)
| ~ relation(X10)
| ~ function(X10) ) ),
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_6,plain,
! [X72,X73] :
( ( in(esk19_2(X72,X73),relation_dom(X72))
| relation_dom(X72) != relation_dom(X73)
| X72 = X73
| ~ relation(X73)
| ~ function(X73)
| ~ relation(X72)
| ~ function(X72) )
& ( apply(X72,esk19_2(X72,X73)) != apply(X73,esk19_2(X72,X73))
| relation_dom(X72) != relation_dom(X73)
| X72 = X73
| ~ relation(X73)
| ~ function(X73)
| ~ relation(X72)
| ~ function(X72) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_funct_1])])])])]) ).
fof(c_0_7,negated_conjecture,
( relation(esk16_0)
& function(esk16_0)
& relation(esk17_0)
& function(esk17_0)
& relation(esk18_0)
& function(esk18_0)
& esk15_0 = relation_rng(esk16_0)
& relation_dom(esk17_0) = esk15_0
& relation_dom(esk18_0) = esk15_0
& relation_composition(esk16_0,esk17_0) = relation_composition(esk16_0,esk18_0)
& esk17_0 != esk18_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_8,plain,
( in(esk1_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_5]) ).
cnf(c_0_9,plain,
( in(esk19_2(X1,X2),relation_dom(X1))
| X1 = X2
| relation_dom(X1) != relation_dom(X2)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
relation_dom(esk18_0) = esk15_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
relation(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
function(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( X1 = apply(X2,esk1_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,plain,
( in(esk1_3(X1,relation_rng(X1),X2),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
esk15_0 = relation_rng(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
function(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
( esk18_0 = X1
| in(esk19_2(esk18_0,X1),esk15_0)
| relation_dom(X1) != esk15_0
| ~ relation(X1)
| ~ function(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12])]) ).
cnf(c_0_19,negated_conjecture,
relation_dom(esk17_0) = esk15_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,negated_conjecture,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,negated_conjecture,
function(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
esk17_0 != esk18_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,plain,
( apply(X1,esk1_3(X1,relation_rng(X1),X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_13]) ).
fof(c_0_24,plain,
! [X54,X55,X56] :
( ~ relation(X55)
| ~ function(X55)
| ~ relation(X56)
| ~ function(X56)
| ~ in(X54,relation_dom(X55))
| apply(relation_composition(X55,X56),X54) = apply(X56,apply(X55,X54)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
cnf(c_0_25,negated_conjecture,
( in(esk1_3(esk16_0,esk15_0,X1),relation_dom(esk16_0))
| ~ in(X1,esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_26,negated_conjecture,
in(esk19_2(esk18_0,esk17_0),esk15_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( apply(esk16_0,esk1_3(esk16_0,esk15_0,X1)) = X1
| ~ in(X1,esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_28,plain,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
in(esk1_3(esk16_0,esk15_0,esk19_2(esk18_0,esk17_0)),relation_dom(esk16_0)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
apply(esk16_0,esk1_3(esk16_0,esk15_0,esk19_2(esk18_0,esk17_0))) = esk19_2(esk18_0,esk17_0),
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( apply(relation_composition(esk16_0,X1),esk1_3(esk16_0,esk15_0,esk19_2(esk18_0,esk17_0))) = apply(X1,esk19_2(esk18_0,esk17_0))
| ~ relation(X1)
| ~ function(X1) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_16]),c_0_17])]),c_0_30]) ).
cnf(c_0_32,negated_conjecture,
relation_composition(esk16_0,esk17_0) = relation_composition(esk16_0,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_33,negated_conjecture,
apply(relation_composition(esk16_0,esk17_0),esk1_3(esk16_0,esk15_0,esk19_2(esk18_0,esk17_0))) = apply(esk18_0,esk19_2(esk18_0,esk17_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_11]),c_0_12])]) ).
cnf(c_0_34,plain,
( X1 = X2
| apply(X1,esk19_2(X1,X2)) != apply(X2,esk19_2(X1,X2))
| relation_dom(X1) != relation_dom(X2)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_35,negated_conjecture,
apply(esk18_0,esk19_2(esk18_0,esk17_0)) = apply(esk17_0,esk19_2(esk18_0,esk17_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_33]),c_0_20]),c_0_21])]) ).
cnf(c_0_36,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_34,c_0_35]),c_0_10]),c_0_19]),c_0_20]),c_0_11]),c_0_21]),c_0_12])]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU075+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n009.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 22:28:36 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 138.96/139.26 % Version : CSE_E---1.5
% 138.96/139.26 % Problem : theBenchmark.p
% 138.96/139.26 % Proof found
% 138.96/139.26 % SZS status Theorem for theBenchmark.p
% 138.96/139.26 % SZS output start Proof
% See solution above
% 138.96/139.26 % Total time : 138.671000 s
% 138.96/139.26 % SZS output end Proof
% 138.96/139.26 % Total time : 138.680000 s
%------------------------------------------------------------------------------