TSTP Solution File: SEU227+3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU227+3 : 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 : n020.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 16:23:34 EDT 2023
% Result : Theorem 265.34s 265.50s
% Output : CNFRefutation 265.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 46
% Syntax : Number of formulae : 82 ( 10 unt; 39 typ; 0 def)
% Number of atoms : 207 ( 46 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 285 ( 121 ~; 130 |; 19 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 54 ( 28 >; 26 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 31 ( 31 usr; 11 con; 0-4 aty)
% Number of variables : 142 ( 0 sgn; 56 !; 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,
one_to_one: $i > $o ).
tff(decl_27,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
relation_image: ( $i * $i ) > $i ).
tff(decl_29,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_30,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff(decl_31,type,
subset: ( $i * $i ) > $o ).
tff(decl_32,type,
relation_dom: $i > $i ).
tff(decl_33,type,
singleton: $i > $i ).
tff(decl_34,type,
element: ( $i * $i ) > $o ).
tff(decl_35,type,
empty_set: $i ).
tff(decl_36,type,
relation_empty_yielding: $i > $o ).
tff(decl_37,type,
powerset: $i > $i ).
tff(decl_38,type,
esk1_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_39,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_42,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk11_1: $i > $i ).
tff(decl_49,type,
esk12_0: $i ).
tff(decl_50,type,
esk13_0: $i ).
tff(decl_51,type,
esk14_1: $i > $i ).
tff(decl_52,type,
esk15_0: $i ).
tff(decl_53,type,
esk16_0: $i ).
tff(decl_54,type,
esk17_0: $i ).
tff(decl_55,type,
esk18_1: $i > $i ).
tff(decl_56,type,
esk19_0: $i ).
tff(decl_57,type,
esk20_0: $i ).
tff(decl_58,type,
esk21_0: $i ).
tff(decl_59,type,
esk22_0: $i ).
tff(decl_60,type,
esk23_0: $i ).
fof(d13_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(X5,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(d14_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X4,X5),X1)
& in(X5,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t146_funct_1,conjecture,
! [X1,X2] :
( relation(X2)
=> ( subset(X1,relation_dom(X2))
=> subset(X1,relation_inverse_image(X2,relation_image(X2,X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(c_0_7,plain,
! [X13,X14,X15,X16,X18,X19,X20,X21,X23] :
( ( in(ordered_pair(esk1_4(X13,X14,X15,X16),X16),X13)
| ~ in(X16,X15)
| X15 != relation_image(X13,X14)
| ~ relation(X13) )
& ( in(esk1_4(X13,X14,X15,X16),X14)
| ~ in(X16,X15)
| X15 != relation_image(X13,X14)
| ~ relation(X13) )
& ( ~ in(ordered_pair(X19,X18),X13)
| ~ in(X19,X14)
| in(X18,X15)
| X15 != relation_image(X13,X14)
| ~ relation(X13) )
& ( ~ in(esk2_3(X13,X20,X21),X21)
| ~ in(ordered_pair(X23,esk2_3(X13,X20,X21)),X13)
| ~ in(X23,X20)
| X21 = relation_image(X13,X20)
| ~ relation(X13) )
& ( in(ordered_pair(esk3_3(X13,X20,X21),esk2_3(X13,X20,X21)),X13)
| in(esk2_3(X13,X20,X21),X21)
| X21 = relation_image(X13,X20)
| ~ relation(X13) )
& ( in(esk3_3(X13,X20,X21),X20)
| in(esk2_3(X13,X20,X21),X21)
| X21 = relation_image(X13,X20)
| ~ relation(X13) ) ),
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)],[d13_relat_1])])])])])]) ).
fof(c_0_8,plain,
! [X53,X54] : ordered_pair(X53,X54) = unordered_pair(unordered_pair(X53,X54),singleton(X53)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_9,plain,
! [X43,X44,X45,X47,X48,X49,X51] :
( ( ~ in(X45,X44)
| in(ordered_pair(X45,esk8_3(X43,X44,X45)),X43)
| X44 != relation_dom(X43)
| ~ relation(X43) )
& ( ~ in(ordered_pair(X47,X48),X43)
| in(X47,X44)
| X44 != relation_dom(X43)
| ~ relation(X43) )
& ( ~ in(esk9_2(X43,X49),X49)
| ~ in(ordered_pair(esk9_2(X43,X49),X51),X43)
| X49 = relation_dom(X43)
| ~ relation(X43) )
& ( in(esk9_2(X43,X49),X49)
| in(ordered_pair(esk9_2(X43,X49),esk10_2(X43,X49)),X43)
| X49 = relation_dom(X43)
| ~ relation(X43) ) ),
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)],[d4_relat_1])])])])])]) ).
fof(c_0_10,plain,
! [X25,X26,X27,X28,X30,X31,X32,X33,X35] :
( ( in(ordered_pair(X28,esk4_4(X25,X26,X27,X28)),X25)
| ~ in(X28,X27)
| X27 != relation_inverse_image(X25,X26)
| ~ relation(X25) )
& ( in(esk4_4(X25,X26,X27,X28),X26)
| ~ in(X28,X27)
| X27 != relation_inverse_image(X25,X26)
| ~ relation(X25) )
& ( ~ in(ordered_pair(X30,X31),X25)
| ~ in(X31,X26)
| in(X30,X27)
| X27 != relation_inverse_image(X25,X26)
| ~ relation(X25) )
& ( ~ in(esk5_3(X25,X32,X33),X33)
| ~ in(ordered_pair(esk5_3(X25,X32,X33),X35),X25)
| ~ in(X35,X32)
| X33 = relation_inverse_image(X25,X32)
| ~ relation(X25) )
& ( in(ordered_pair(esk5_3(X25,X32,X33),esk6_3(X25,X32,X33)),X25)
| in(esk5_3(X25,X32,X33),X33)
| X33 = relation_inverse_image(X25,X32)
| ~ relation(X25) )
& ( in(esk6_3(X25,X32,X33),X32)
| in(esk5_3(X25,X32,X33),X33)
| X33 = relation_inverse_image(X25,X32)
| ~ relation(X25) ) ),
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)],[d14_relat_1])])])])])]) ).
cnf(c_0_11,plain,
( in(X2,X5)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X1,X4)
| X5 != relation_image(X3,X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X11,X12] : unordered_pair(X11,X12) = unordered_pair(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_14,plain,
( in(ordered_pair(X1,esk8_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( in(X1,X5)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X2,X4)
| X5 != relation_inverse_image(X3,X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( in(X2,X5)
| X5 != relation_image(X3,X4)
| ~ relation(X3)
| ~ in(X1,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( in(unordered_pair(unordered_pair(X1,esk8_3(X3,X2,X1)),singleton(X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_19,plain,
( in(X1,X5)
| X5 != relation_inverse_image(X3,X4)
| ~ relation(X3)
| ~ in(X2,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_20,plain,
( in(X1,X2)
| X2 != relation_image(X3,X4)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X1)),X3)
| ~ in(X5,X4) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk8_3(X2,X3,X1))),X2)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_22,plain,
( in(X1,X2)
| X2 != relation_inverse_image(X3,X4)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X5)),X3)
| ~ in(X5,X4) ),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_23,plain,
( in(esk8_3(X1,X2,X3),X4)
| X4 != relation_image(X1,X5)
| X2 != relation_dom(X1)
| ~ relation(X1)
| ~ in(X3,X5)
| ~ in(X3,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_24,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> ( subset(X1,relation_dom(X2))
=> subset(X1,relation_inverse_image(X2,relation_image(X2,X1))) ) ),
inference(assume_negation,[status(cth)],[t146_funct_1]) ).
cnf(c_0_25,plain,
( in(X1,X2)
| X2 != relation_inverse_image(X3,X4)
| X5 != relation_dom(X3)
| ~ relation(X3)
| ~ in(esk8_3(X3,X5,X1),X4)
| ~ in(X1,X5) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_26,plain,
( in(esk8_3(X1,X2,X3),relation_image(X1,X4))
| X2 != relation_dom(X1)
| ~ relation(X1)
| ~ in(X3,X4)
| ~ in(X3,X2) ),
inference(er,[status(thm)],[c_0_23]) ).
fof(c_0_27,plain,
! [X37,X38,X39,X40,X41] :
( ( ~ subset(X37,X38)
| ~ in(X39,X37)
| in(X39,X38) )
& ( in(esk7_2(X40,X41),X40)
| subset(X40,X41) )
& ( ~ in(esk7_2(X40,X41),X41)
| subset(X40,X41) ) ),
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)],[d3_tarski])])])])])]) ).
fof(c_0_28,negated_conjecture,
( relation(esk23_0)
& subset(esk22_0,relation_dom(esk23_0))
& ~ subset(esk22_0,relation_inverse_image(esk23_0,relation_image(esk23_0,esk22_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
cnf(c_0_29,plain,
( in(X1,X2)
| X2 != relation_inverse_image(X3,relation_image(X3,X4))
| X5 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X5)
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,negated_conjecture,
subset(esk22_0,relation_dom(esk23_0)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,plain,
( in(X1,relation_inverse_image(X2,relation_image(X2,X3)))
| X4 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X4)
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( in(X1,relation_dom(esk23_0))
| ~ in(X1,esk22_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
( subset(X1,X2)
| ~ in(esk7_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( in(X1,relation_inverse_image(X2,relation_image(X2,X3)))
| relation_dom(esk23_0) != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,esk22_0)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( subset(X1,relation_inverse_image(X2,relation_image(X2,X3)))
| relation_dom(esk23_0) != relation_dom(X2)
| ~ relation(X2)
| ~ in(esk7_2(X1,relation_inverse_image(X2,relation_image(X2,X3))),esk22_0)
| ~ in(esk7_2(X1,relation_inverse_image(X2,relation_image(X2,X3))),X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,plain,
( in(esk7_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,negated_conjecture,
( subset(esk22_0,relation_inverse_image(X1,relation_image(X1,X2)))
| relation_dom(esk23_0) != relation_dom(X1)
| ~ relation(X1)
| ~ in(esk7_2(esk22_0,relation_inverse_image(X1,relation_image(X1,X2))),X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,negated_conjecture,
~ subset(esk22_0,relation_inverse_image(esk23_0,relation_image(esk23_0,esk22_0))),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_40,negated_conjecture,
( subset(esk22_0,relation_inverse_image(X1,relation_image(X1,esk22_0)))
| relation_dom(esk23_0) != relation_dom(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
relation(esk23_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU227+3 : 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
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 19:50:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 265.34/265.50 % Version : CSE_E---1.5
% 265.34/265.50 % Problem : theBenchmark.p
% 265.34/265.50 % Proof found
% 265.34/265.50 % SZS status Theorem for theBenchmark.p
% 265.34/265.50 % SZS output start Proof
% See solution above
% 265.34/265.51 % Total time : 264.758000 s
% 265.34/265.51 % SZS output end Proof
% 265.34/265.51 % Total time : 264.772000 s
%------------------------------------------------------------------------------