TSTP Solution File: SEU290+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU290+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n005.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 16:24:08 EDT 2023
% Result : Theorem 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 52
% Syntax : Number of formulae : 92 ( 18 unt; 42 typ; 0 def)
% Number of atoms : 177 ( 56 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 198 ( 71 ~; 76 |; 33 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 27 >; 21 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 15 con; 0-3 aty)
% Number of variables : 79 ( 2 sgn; 50 !; 3 ?; 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,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_27,type,
powerset: $i > $i ).
tff(decl_28,type,
element: ( $i * $i ) > $o ).
tff(decl_29,type,
one_to_one: $i > $o ).
tff(decl_30,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
empty_set: $i ).
tff(decl_32,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff(decl_33,type,
relation_dom_as_subset: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
relation_rng: $i > $i ).
tff(decl_35,type,
relation_dom: $i > $i ).
tff(decl_36,type,
apply: ( $i * $i ) > $i ).
tff(decl_37,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
relation_empty_yielding: $i > $o ).
tff(decl_39,type,
subset: ( $i * $i ) > $o ).
tff(decl_40,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk5_1: $i > $i ).
tff(decl_45,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk7_0: $i ).
tff(decl_47,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk9_0: $i ).
tff(decl_49,type,
esk10_0: $i ).
tff(decl_50,type,
esk11_1: $i > $i ).
tff(decl_51,type,
esk12_0: $i ).
tff(decl_52,type,
esk13_0: $i ).
tff(decl_53,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk15_0: $i ).
tff(decl_55,type,
esk16_1: $i > $i ).
tff(decl_56,type,
esk17_0: $i ).
tff(decl_57,type,
esk18_0: $i ).
tff(decl_58,type,
esk19_0: $i ).
tff(decl_59,type,
esk20_0: $i ).
tff(decl_60,type,
esk21_0: $i ).
tff(decl_61,type,
esk22_0: $i ).
tff(decl_62,type,
esk23_0: $i ).
tff(decl_63,type,
esk24_0: $i ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_funct_1,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(t6_funct_2,conjecture,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| in(apply(X4,X3),relation_rng(X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_2) ).
fof(rc1_partfun1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_partfun1) ).
fof(d1_funct_2,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ( ( X2 = empty_set
=> X1 = empty_set )
=> ( quasi_total(X3,X1,X2)
<=> X1 = relation_dom_as_subset(X1,X2,X3) ) )
& ( X2 = empty_set
=> ( X1 = empty_set
| ( quasi_total(X3,X1,X2)
<=> X3 = empty_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_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/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(redefinition_k4_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(c_0_10,plain,
! [X86] :
( ~ empty(X86)
| X86 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_11,plain,
( relation(esk13_0)
& empty(esk13_0)
& function(esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
cnf(c_0_12,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
empty(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| in(apply(X4,X3),relation_rng(X4)) ) ) ),
inference(assume_negation,[status(cth)],[t6_funct_2]) ).
cnf(c_0_15,plain,
empty_set = esk13_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_16,plain,
( relation(esk9_0)
& function(esk9_0)
& one_to_one(esk9_0)
& empty(esk9_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_partfun1])]) ).
fof(c_0_17,negated_conjecture,
( function(esk24_0)
& quasi_total(esk24_0,esk21_0,esk22_0)
& relation_of2_as_subset(esk24_0,esk21_0,esk22_0)
& in(esk23_0,esk21_0)
& esk22_0 != empty_set
& ~ in(apply(esk24_0,esk23_0),relation_rng(esk24_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_18,plain,
! [X13,X14,X15] :
( ( ~ quasi_total(X15,X13,X14)
| X13 = relation_dom_as_subset(X13,X14,X15)
| X14 = empty_set
| ~ relation_of2_as_subset(X15,X13,X14) )
& ( X13 != relation_dom_as_subset(X13,X14,X15)
| quasi_total(X15,X13,X14)
| X14 = empty_set
| ~ relation_of2_as_subset(X15,X13,X14) )
& ( ~ quasi_total(X15,X13,X14)
| X13 = relation_dom_as_subset(X13,X14,X15)
| X13 != empty_set
| ~ relation_of2_as_subset(X15,X13,X14) )
& ( X13 != relation_dom_as_subset(X13,X14,X15)
| quasi_total(X15,X13,X14)
| X13 != empty_set
| ~ relation_of2_as_subset(X15,X13,X14) )
& ( ~ quasi_total(X15,X13,X14)
| X15 = empty_set
| X13 = empty_set
| X14 != empty_set
| ~ relation_of2_as_subset(X15,X13,X14) )
& ( X15 != empty_set
| quasi_total(X15,X13,X14)
| X13 = empty_set
| X14 != empty_set
| ~ relation_of2_as_subset(X15,X13,X14) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_funct_2])])]) ).
cnf(c_0_19,plain,
( X1 = esk13_0
| ~ empty(X1) ),
inference(rw,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_20,plain,
empty(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
esk22_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X29,X30,X31] :
( ~ relation_of2_as_subset(X31,X29,X30)
| element(X31,powerset(cartesian_product2(X29,X30))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
cnf(c_0_23,plain,
( X2 = relation_dom_as_subset(X2,X3,X1)
| X3 = empty_set
| ~ quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
esk13_0 = esk9_0,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
esk22_0 != esk13_0,
inference(rw,[status(thm)],[c_0_21,c_0_15]) ).
fof(c_0_26,plain,
! [X16,X17,X18,X20,X21,X22,X24] :
( ( in(esk1_3(X16,X17,X18),relation_dom(X16))
| ~ in(X18,X17)
| X17 != relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) )
& ( X18 = apply(X16,esk1_3(X16,X17,X18))
| ~ in(X18,X17)
| X17 != relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) )
& ( ~ in(X21,relation_dom(X16))
| X20 != apply(X16,X21)
| in(X20,X17)
| X17 != relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) )
& ( ~ in(esk2_2(X16,X22),X22)
| ~ in(X24,relation_dom(X16))
| esk2_2(X16,X22) != apply(X16,X24)
| X22 = relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) )
& ( in(esk3_2(X16,X22),relation_dom(X16))
| in(esk2_2(X16,X22),X22)
| X22 = relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) )
& ( esk2_2(X16,X22) = apply(X16,esk3_2(X16,X22))
| in(esk2_2(X16,X22),X22)
| X22 = relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) ) ),
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_27,plain,
! [X9,X10,X11] :
( ~ element(X11,powerset(cartesian_product2(X9,X10)))
| relation(X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
cnf(c_0_28,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
relation_of2_as_subset(esk24_0,esk21_0,esk22_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_30,plain,
! [X67,X68,X69] :
( ~ relation_of2(X69,X67,X68)
| relation_dom_as_subset(X67,X68,X69) = relation_dom(X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])]) ).
cnf(c_0_31,plain,
( relation_dom_as_subset(X1,X2,X3) = X1
| X2 = esk9_0
| ~ quasi_total(X3,X1,X2)
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_15]),c_0_24]) ).
cnf(c_0_32,negated_conjecture,
quasi_total(esk24_0,esk21_0,esk22_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,negated_conjecture,
esk22_0 != esk9_0,
inference(rw,[status(thm)],[c_0_25,c_0_24]) ).
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_26]) ).
cnf(c_0_35,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,negated_conjecture,
element(esk24_0,powerset(cartesian_product2(esk21_0,esk22_0))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,plain,
( relation_dom_as_subset(X2,X3,X1) = relation_dom(X1)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,negated_conjecture,
relation_dom_as_subset(esk21_0,esk22_0,esk24_0) = esk21_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_29])]),c_0_33]) ).
fof(c_0_39,plain,
! [X70,X71,X72] :
( ( ~ relation_of2_as_subset(X72,X70,X71)
| relation_of2(X72,X70,X71) )
& ( ~ relation_of2(X72,X70,X71)
| relation_of2_as_subset(X72,X70,X71) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_40,negated_conjecture,
~ in(apply(esk24_0,esk23_0),relation_rng(esk24_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_41,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_42,negated_conjecture,
relation(esk24_0),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,negated_conjecture,
function(esk24_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_44,negated_conjecture,
( relation_dom(esk24_0) = esk21_0
| ~ relation_of2(esk24_0,esk21_0,esk22_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,negated_conjecture,
~ in(esk23_0,relation_dom(esk24_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43])]) ).
cnf(c_0_47,negated_conjecture,
relation_dom(esk24_0) = esk21_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_29])]) ).
cnf(c_0_48,negated_conjecture,
in(esk23_0,esk21_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU290+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 13:11:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.61 % Version : CSE_E---1.5
% 0.20/0.61 % Problem : theBenchmark.p
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark.p
% 0.20/0.61 % SZS output start Proof
% See solution above
% 0.20/0.62 % Total time : 0.022000 s
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time : 0.025000 s
%------------------------------------------------------------------------------