TSTP Solution File: SEU017+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU017+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 : n029.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 3.48s 3.72s
% Output : CNFRefutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 42
% Syntax : Number of formulae : 86 ( 15 unt; 33 typ; 0 def)
% Number of atoms : 241 ( 68 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 305 ( 117 ~; 122 |; 45 &)
% ( 5 <=>; 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 : 33 ( 23 >; 10 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 10 con; 0-3 aty)
% Number of variables : 89 ( 1 sgn; 52 !; 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,
relation_rng: $i > $i ).
tff(decl_27,type,
relation_dom: $i > $i ).
tff(decl_28,type,
apply: ( $i * $i ) > $i ).
tff(decl_29,type,
one_to_one: $i > $o ).
tff(decl_30,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_31,type,
identity_relation: $i > $i ).
tff(decl_32,type,
element: ( $i * $i ) > $o ).
tff(decl_33,type,
empty_set: $i ).
tff(decl_34,type,
relation_empty_yielding: $i > $o ).
tff(decl_35,type,
powerset: $i > $i ).
tff(decl_36,type,
subset: ( $i * $i ) > $o ).
tff(decl_37,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk4_1: $i > $i ).
tff(decl_41,type,
esk5_1: $i > $i ).
tff(decl_42,type,
esk6_1: $i > $i ).
tff(decl_43,type,
esk7_0: $i ).
tff(decl_44,type,
esk8_0: $i ).
tff(decl_45,type,
esk9_1: $i > $i ).
tff(decl_46,type,
esk10_0: $i ).
tff(decl_47,type,
esk11_0: $i ).
tff(decl_48,type,
esk12_1: $i > $i ).
tff(decl_49,type,
esk13_0: $i ).
tff(decl_50,type,
esk14_0: $i ).
tff(decl_51,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk16_0: $i ).
tff(decl_53,type,
esk17_0: $i ).
tff(decl_54,type,
esk18_0: $i ).
fof(t50_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( relation_dom(X2) = X1
& relation_dom(X3) = X1
& subset(relation_rng(X3),X1)
& one_to_one(X2)
& relation_composition(X3,X2) = X2 )
=> X3 = identity_relation(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_funct_1) ).
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(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
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(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(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_9,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( relation_dom(X2) = X1
& relation_dom(X3) = X1
& subset(relation_rng(X3),X1)
& one_to_one(X2)
& relation_composition(X3,X2) = X2 )
=> X3 = identity_relation(X1) ) ) ),
inference(assume_negation,[status(cth)],[t50_funct_1]) ).
fof(c_0_10,plain,
! [X59,X60,X61] :
( ( relation_dom(X60) = X59
| X60 != identity_relation(X59)
| ~ relation(X60)
| ~ function(X60) )
& ( ~ in(X61,X59)
| apply(X60,X61) = X61
| X60 != identity_relation(X59)
| ~ relation(X60)
| ~ function(X60) )
& ( in(esk15_2(X59,X60),X59)
| relation_dom(X60) != X59
| X60 = identity_relation(X59)
| ~ relation(X60)
| ~ function(X60) )
& ( apply(X60,esk15_2(X59,X60)) != esk15_2(X59,X60)
| relation_dom(X60) != X59
| X60 = identity_relation(X59)
| ~ relation(X60)
| ~ function(X60) ) ),
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_11,plain,
! [X63,X64] :
( ( ~ element(X63,powerset(X64))
| subset(X63,X64) )
& ( ~ subset(X63,X64)
| element(X63,powerset(X64)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_12,negated_conjecture,
( relation(esk17_0)
& function(esk17_0)
& relation(esk18_0)
& function(esk18_0)
& relation_dom(esk17_0) = esk16_0
& relation_dom(esk18_0) = esk16_0
& subset(relation_rng(esk18_0),esk16_0)
& one_to_one(esk17_0)
& relation_composition(esk18_0,esk17_0) = esk17_0
& esk18_0 != identity_relation(esk16_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_13,plain,
( in(esk15_2(X1,X2),X1)
| X2 = identity_relation(X1)
| relation_dom(X2) != X1
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X65,X66,X67] :
( ~ in(X65,X66)
| ~ element(X66,powerset(X67))
| element(X65,X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
cnf(c_0_15,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
subset(relation_rng(esk18_0),esk16_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X75,X76] :
( ~ in(X75,X76)
| ~ empty(X76) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_18,plain,
( identity_relation(relation_dom(X1)) = X1
| in(esk15_2(relation_dom(X1),X1),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
relation(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
relation_dom(esk18_0) = esk16_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,negated_conjecture,
function(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,negated_conjecture,
esk18_0 != identity_relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_23,plain,
! [X57,X58] :
( ~ element(X57,X58)
| empty(X58)
| in(X57,X58) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_24,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,negated_conjecture,
element(relation_rng(esk18_0),powerset(esk16_0)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_26,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,negated_conjecture,
in(esk15_2(esk16_0,esk18_0),esk16_0),
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(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_20]),c_0_20]),c_0_21])]),c_0_22]) ).
fof(c_0_28,plain,
! [X9,X10,X11,X13,X14,X15,X17] :
( ( in(esk1_3(X9,X10,X11),relation_dom(X9))
| ~ in(X11,X10)
| X10 != relation_rng(X9)
| ~ relation(X9)
| ~ function(X9) )
& ( X11 = apply(X9,esk1_3(X9,X10,X11))
| ~ in(X11,X10)
| X10 != relation_rng(X9)
| ~ relation(X9)
| ~ function(X9) )
& ( ~ in(X14,relation_dom(X9))
| X13 != apply(X9,X14)
| in(X13,X10)
| X10 != relation_rng(X9)
| ~ relation(X9)
| ~ function(X9) )
& ( ~ in(esk2_2(X9,X15),X15)
| ~ in(X17,relation_dom(X9))
| esk2_2(X9,X15) != apply(X9,X17)
| X15 = relation_rng(X9)
| ~ relation(X9)
| ~ function(X9) )
& ( in(esk3_2(X9,X15),relation_dom(X9))
| in(esk2_2(X9,X15),X15)
| X15 = relation_rng(X9)
| ~ relation(X9)
| ~ function(X9) )
& ( esk2_2(X9,X15) = apply(X9,esk3_2(X9,X15))
| in(esk2_2(X9,X15),X15)
| X15 = relation_rng(X9)
| ~ relation(X9)
| ~ function(X9) ) ),
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_29,plain,
! [X19,X20,X21] :
( ( ~ one_to_one(X19)
| ~ in(X20,relation_dom(X19))
| ~ in(X21,relation_dom(X19))
| apply(X19,X20) != apply(X19,X21)
| X20 = X21
| ~ relation(X19)
| ~ function(X19) )
& ( in(esk4_1(X19),relation_dom(X19))
| one_to_one(X19)
| ~ relation(X19)
| ~ function(X19) )
& ( in(esk5_1(X19),relation_dom(X19))
| one_to_one(X19)
| ~ relation(X19)
| ~ function(X19) )
& ( apply(X19,esk4_1(X19)) = apply(X19,esk5_1(X19))
| one_to_one(X19)
| ~ relation(X19)
| ~ function(X19) )
& ( esk4_1(X19) != esk5_1(X19)
| one_to_one(X19)
| ~ relation(X19)
| ~ function(X19) ) ),
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])])])])]) ).
fof(c_0_30,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_31,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,negated_conjecture,
( element(X1,esk16_0)
| ~ in(X1,relation_rng(esk18_0)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,negated_conjecture,
~ empty(esk16_0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
( in(X3,X4)
| ~ in(X1,relation_dom(X2))
| X3 != apply(X2,X1)
| X4 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
( X2 = X3
| ~ one_to_one(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X3,relation_dom(X1))
| apply(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,negated_conjecture,
relation_dom(esk17_0) = esk16_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_37,negated_conjecture,
one_to_one(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_38,negated_conjecture,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_39,negated_conjecture,
function(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_40,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_30]) ).
cnf(c_0_41,negated_conjecture,
relation_composition(esk18_0,esk17_0) = esk17_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_42,negated_conjecture,
( in(X1,esk16_0)
| ~ in(X1,relation_rng(esk18_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_43,plain,
( in(apply(X1,X2),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_34])]) ).
cnf(c_0_44,plain,
( X1 = identity_relation(X2)
| apply(X1,esk15_2(X2,X1)) != esk15_2(X2,X1)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_45,negated_conjecture,
( X1 = X2
| apply(esk17_0,X1) != apply(esk17_0,X2)
| ~ in(X2,esk16_0)
| ~ in(X1,esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38]),c_0_39])]) ).
cnf(c_0_46,negated_conjecture,
( apply(esk17_0,apply(esk18_0,X1)) = apply(esk17_0,X1)
| ~ in(X1,esk16_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_40,c_0_41]),c_0_38]),c_0_19]),c_0_39]),c_0_21]),c_0_20])]) ).
cnf(c_0_47,negated_conjecture,
( in(apply(esk18_0,X1),esk16_0)
| ~ in(X1,esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_19]),c_0_21]),c_0_20])]) ).
cnf(c_0_48,plain,
( identity_relation(relation_dom(X1)) = X1
| apply(X1,esk15_2(relation_dom(X1),X1)) != esk15_2(relation_dom(X1),X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_44]) ).
cnf(c_0_49,negated_conjecture,
( apply(esk18_0,X1) = X2
| apply(esk17_0,X1) != apply(esk17_0,X2)
| ~ in(X2,esk16_0)
| ~ in(X1,esk16_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_50,negated_conjecture,
apply(esk18_0,esk15_2(esk16_0,esk18_0)) != esk15_2(esk16_0,esk18_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_20]),c_0_19]),c_0_21])]),c_0_22]) ).
cnf(c_0_51,negated_conjecture,
( apply(esk18_0,X1) = X1
| ~ in(X1,esk16_0) ),
inference(er,[status(thm)],[c_0_49]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU017+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
% 0.15/0.33 % Computer : n029.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
% 0.19/0.33 % CPULimit : 300
% 0.19/0.33 % WCLimit : 300
% 0.19/0.33 % DateTime : Wed Aug 23 15:27:07 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.53 start to proof: theBenchmark
% 3.48/3.72 % Version : CSE_E---1.5
% 3.48/3.72 % Problem : theBenchmark.p
% 3.48/3.72 % Proof found
% 3.48/3.72 % SZS status Theorem for theBenchmark.p
% 3.48/3.72 % SZS output start Proof
% See solution above
% 3.48/3.73 % Total time : 3.191000 s
% 3.48/3.73 % SZS output end Proof
% 3.48/3.73 % Total time : 3.194000 s
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