TSTP Solution File: SEU226+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU226+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n008.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 16:23:32 EDT 2023
% Result : Theorem 2.34s 2.43s
% Output : CNFRefutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 36
% Syntax : Number of formulae : 56 ( 4 unt; 32 typ; 0 def)
% Number of atoms : 158 ( 27 equ)
% Maximal formula atoms : 44 ( 6 avg)
% Number of connectives : 225 ( 91 ~; 101 |; 23 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 21 >; 16 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 11 con; 0-4 aty)
% Number of variables : 73 ( 0 sgn; 36 !; 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_image: ( $i * $i ) > $i ).
tff(decl_28,type,
relation_dom: $i > $i ).
tff(decl_29,type,
apply: ( $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,
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,
esk1_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_37,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk6_1: $i > $i ).
tff(decl_42,type,
esk7_0: $i ).
tff(decl_43,type,
esk8_0: $i ).
tff(decl_44,type,
esk9_1: $i > $i ).
tff(decl_45,type,
esk10_0: $i ).
tff(decl_46,type,
esk11_0: $i ).
tff(decl_47,type,
esk12_0: $i ).
tff(decl_48,type,
esk13_1: $i > $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 ).
fof(d13_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(d12_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,relation_dom(X1))
& in(X5,X2)
& X4 = apply(X1,X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_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(t145_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> subset(relation_image(X2,relation_inverse_image(X2,X1)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
fof(c_0_4,plain,
! [X23,X24,X25,X26,X27,X28,X29] :
( ( in(X26,relation_dom(X23))
| ~ in(X26,X25)
| X25 != relation_inverse_image(X23,X24)
| ~ relation(X23)
| ~ function(X23) )
& ( in(apply(X23,X26),X24)
| ~ in(X26,X25)
| X25 != relation_inverse_image(X23,X24)
| ~ relation(X23)
| ~ function(X23) )
& ( ~ in(X27,relation_dom(X23))
| ~ in(apply(X23,X27),X24)
| in(X27,X25)
| X25 != relation_inverse_image(X23,X24)
| ~ relation(X23)
| ~ function(X23) )
& ( ~ in(esk4_3(X23,X28,X29),X29)
| ~ in(esk4_3(X23,X28,X29),relation_dom(X23))
| ~ in(apply(X23,esk4_3(X23,X28,X29)),X28)
| X29 = relation_inverse_image(X23,X28)
| ~ relation(X23)
| ~ function(X23) )
& ( in(esk4_3(X23,X28,X29),relation_dom(X23))
| in(esk4_3(X23,X28,X29),X29)
| X29 = relation_inverse_image(X23,X28)
| ~ relation(X23)
| ~ function(X23) )
& ( in(apply(X23,esk4_3(X23,X28,X29)),X28)
| in(esk4_3(X23,X28,X29),X29)
| X29 = relation_inverse_image(X23,X28)
| ~ relation(X23)
| ~ function(X23) ) ),
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_funct_1])])])])])]) ).
cnf(c_0_5,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,X4)
| X4 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_6,plain,
! [X11,X12,X13,X14,X16,X17,X18,X19,X21] :
( ( in(esk1_4(X11,X12,X13,X14),relation_dom(X11))
| ~ in(X14,X13)
| X13 != relation_image(X11,X12)
| ~ relation(X11)
| ~ function(X11) )
& ( in(esk1_4(X11,X12,X13,X14),X12)
| ~ in(X14,X13)
| X13 != relation_image(X11,X12)
| ~ relation(X11)
| ~ function(X11) )
& ( X14 = apply(X11,esk1_4(X11,X12,X13,X14))
| ~ in(X14,X13)
| X13 != relation_image(X11,X12)
| ~ relation(X11)
| ~ function(X11) )
& ( ~ in(X17,relation_dom(X11))
| ~ in(X17,X12)
| X16 != apply(X11,X17)
| in(X16,X13)
| X13 != relation_image(X11,X12)
| ~ relation(X11)
| ~ function(X11) )
& ( ~ in(esk2_3(X11,X18,X19),X19)
| ~ in(X21,relation_dom(X11))
| ~ in(X21,X18)
| esk2_3(X11,X18,X19) != apply(X11,X21)
| X19 = relation_image(X11,X18)
| ~ relation(X11)
| ~ function(X11) )
& ( in(esk3_3(X11,X18,X19),relation_dom(X11))
| in(esk2_3(X11,X18,X19),X19)
| X19 = relation_image(X11,X18)
| ~ relation(X11)
| ~ function(X11) )
& ( in(esk3_3(X11,X18,X19),X18)
| in(esk2_3(X11,X18,X19),X19)
| X19 = relation_image(X11,X18)
| ~ relation(X11)
| ~ function(X11) )
& ( esk2_3(X11,X18,X19) = apply(X11,esk3_3(X11,X18,X19))
| in(esk2_3(X11,X18,X19),X19)
| X19 = relation_image(X11,X18)
| ~ relation(X11)
| ~ function(X11) ) ),
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)],[d12_funct_1])])])])])]) ).
cnf(c_0_7,plain,
( in(apply(X1,X2),X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(er,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( in(esk1_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( in(apply(X1,esk1_4(X2,relation_inverse_image(X1,X3),X4,X5)),X3)
| X4 != relation_image(X2,relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X1)
| ~ function(X2)
| ~ in(X5,X4) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
( X1 = apply(X2,esk1_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( in(X1,X2)
| X3 != relation_image(X4,relation_inverse_image(X4,X2))
| ~ relation(X4)
| ~ function(X4)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_12,plain,
! [X31,X32,X33,X34,X35] :
( ( ~ subset(X31,X32)
| ~ in(X33,X31)
| in(X33,X32) )
& ( in(esk5_2(X34,X35),X34)
| subset(X34,X35) )
& ( ~ in(esk5_2(X34,X35),X35)
| subset(X34,X35) ) ),
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_13,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> subset(relation_image(X2,relation_inverse_image(X2,X1)),X1) ),
inference(assume_negation,[status(cth)],[t145_funct_1]) ).
cnf(c_0_14,plain,
( in(X1,X2)
| ~ relation(X3)
| ~ function(X3)
| ~ in(X1,relation_image(X3,relation_inverse_image(X3,X2))) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( in(esk5_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,negated_conjecture,
( relation(esk18_0)
& function(esk18_0)
& ~ subset(relation_image(esk18_0,relation_inverse_image(esk18_0,esk17_0)),esk17_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| ~ in(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( subset(relation_image(X1,relation_inverse_image(X1,X2)),X3)
| in(esk5_2(relation_image(X1,relation_inverse_image(X1,X2)),X3),X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
~ subset(relation_image(esk18_0,relation_inverse_image(esk18_0,esk17_0)),esk17_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( subset(relation_image(X1,relation_inverse_image(X1,X2)),X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
relation(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
function(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU226+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 16:45:48 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.59 start to proof: theBenchmark
% 2.34/2.43 % Version : CSE_E---1.5
% 2.34/2.43 % Problem : theBenchmark.p
% 2.34/2.43 % Proof found
% 2.34/2.43 % SZS status Theorem for theBenchmark.p
% 2.34/2.43 % SZS output start Proof
% See solution above
% 2.34/2.43 % Total time : 1.827000 s
% 2.34/2.43 % SZS output end Proof
% 2.34/2.43 % Total time : 1.829000 s
%------------------------------------------------------------------------------