TSTP Solution File: SEU077+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU077+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 : n007.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 16:22:22 EDT 2023
% Result : Theorem 0.20s 0.68s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 37
% Syntax : Number of formulae : 67 ( 8 unt; 33 typ; 0 def)
% Number of atoms : 170 ( 25 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 230 ( 94 ~; 100 |; 24 &)
% ( 5 <=>; 7 =>; 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 ( 21 >; 12 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 12 con; 0-3 aty)
% Number of variables : 75 ( 0 sgn; 35 !; 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_inverse_image: ( $i * $i ) > $i ).
tff(decl_28,type,
relation_dom: $i > $i ).
tff(decl_29,type,
apply: ( $i * $i ) > $i ).
tff(decl_30,type,
subset: ( $i * $i ) > $o ).
tff(decl_31,type,
relation_rng: $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,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk4_2: ( $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 ).
tff(decl_54,type,
esk19_0: $i ).
fof(t158_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( ( subset(relation_inverse_image(X3,X1),relation_inverse_image(X3,X2))
& subset(X1,relation_rng(X3)) )
=> subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_1) ).
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(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(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(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( ( subset(relation_inverse_image(X3,X1),relation_inverse_image(X3,X2))
& subset(X1,relation_rng(X3)) )
=> subset(X1,X2) ) ),
inference(assume_negation,[status(cth)],[t158_funct_1]) ).
fof(c_0_5,plain,
! [X10,X11,X12,X13,X14,X15,X16] :
( ( in(X13,relation_dom(X10))
| ~ in(X13,X12)
| X12 != relation_inverse_image(X10,X11)
| ~ relation(X10)
| ~ function(X10) )
& ( in(apply(X10,X13),X11)
| ~ in(X13,X12)
| X12 != relation_inverse_image(X10,X11)
| ~ relation(X10)
| ~ function(X10) )
& ( ~ in(X14,relation_dom(X10))
| ~ in(apply(X10,X14),X11)
| in(X14,X12)
| X12 != relation_inverse_image(X10,X11)
| ~ relation(X10)
| ~ function(X10) )
& ( ~ in(esk1_3(X10,X15,X16),X16)
| ~ in(esk1_3(X10,X15,X16),relation_dom(X10))
| ~ in(apply(X10,esk1_3(X10,X15,X16)),X15)
| X16 = relation_inverse_image(X10,X15)
| ~ relation(X10)
| ~ function(X10) )
& ( in(esk1_3(X10,X15,X16),relation_dom(X10))
| in(esk1_3(X10,X15,X16),X16)
| X16 = relation_inverse_image(X10,X15)
| ~ relation(X10)
| ~ function(X10) )
& ( in(apply(X10,esk1_3(X10,X15,X16)),X15)
| in(esk1_3(X10,X15,X16),X16)
| X16 = relation_inverse_image(X10,X15)
| ~ 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)],[d13_funct_1])])])])])]) ).
fof(c_0_6,plain,
! [X18,X19,X20,X21,X22] :
( ( ~ subset(X18,X19)
| ~ in(X20,X18)
| in(X20,X19) )
& ( in(esk2_2(X21,X22),X21)
| subset(X21,X22) )
& ( ~ in(esk2_2(X21,X22),X22)
| subset(X21,X22) ) ),
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_7,negated_conjecture,
( relation(esk19_0)
& function(esk19_0)
& subset(relation_inverse_image(esk19_0,esk17_0),relation_inverse_image(esk19_0,esk18_0))
& subset(esk17_0,relation_rng(esk19_0))
& ~ subset(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(apply(X1,X2),X3)
| ~ in(X2,X4)
| X4 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
subset(relation_inverse_image(esk19_0,esk17_0),relation_inverse_image(esk19_0,esk18_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X24,X25,X26,X28,X29,X30,X32] :
( ( in(esk3_3(X24,X25,X26),relation_dom(X24))
| ~ in(X26,X25)
| X25 != relation_rng(X24)
| ~ relation(X24)
| ~ function(X24) )
& ( X26 = apply(X24,esk3_3(X24,X25,X26))
| ~ in(X26,X25)
| X25 != relation_rng(X24)
| ~ relation(X24)
| ~ function(X24) )
& ( ~ in(X29,relation_dom(X24))
| X28 != apply(X24,X29)
| in(X28,X25)
| X25 != relation_rng(X24)
| ~ relation(X24)
| ~ function(X24) )
& ( ~ in(esk4_2(X24,X30),X30)
| ~ in(X32,relation_dom(X24))
| esk4_2(X24,X30) != apply(X24,X32)
| X30 = relation_rng(X24)
| ~ relation(X24)
| ~ function(X24) )
& ( in(esk5_2(X24,X30),relation_dom(X24))
| in(esk4_2(X24,X30),X30)
| X30 = relation_rng(X24)
| ~ relation(X24)
| ~ function(X24) )
& ( esk4_2(X24,X30) = apply(X24,esk5_2(X24,X30))
| in(esk4_2(X24,X30),X30)
| X30 = relation_rng(X24)
| ~ relation(X24)
| ~ function(X24) ) ),
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])])])])])]) ).
cnf(c_0_12,plain,
( in(apply(X1,X2),X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( in(X1,relation_inverse_image(esk19_0,esk18_0))
| ~ in(X1,relation_inverse_image(esk19_0,esk17_0)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
relation(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
function(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
( X1 = apply(X2,esk3_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( in(X1,X4)
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),X3)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,plain,
( in(esk3_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_11]) ).
cnf(c_0_19,negated_conjecture,
( in(apply(esk19_0,X1),esk18_0)
| ~ in(X1,relation_inverse_image(esk19_0,esk17_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_20,plain,
( apply(X1,esk3_3(X1,relation_rng(X1),X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( in(X1,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ function(X2)
| ~ in(apply(X2,X1),X3)
| ~ in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( in(esk3_3(X1,relation_rng(X1),X2),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
subset(esk17_0,relation_rng(esk19_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
~ subset(esk17_0,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,plain,
( subset(X1,X2)
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_26,negated_conjecture,
( in(X1,esk18_0)
| ~ in(esk3_3(esk19_0,relation_rng(esk19_0),X1),relation_inverse_image(esk19_0,esk17_0))
| ~ in(X1,relation_rng(esk19_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_14]),c_0_15])]) ).
cnf(c_0_27,plain,
( in(esk3_3(X1,relation_rng(X1),X2),relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1))
| ~ in(X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( in(X1,relation_rng(esk19_0))
| ~ in(X1,esk17_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_23]) ).
cnf(c_0_29,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_30,negated_conjecture,
~ in(esk2_2(esk17_0,esk18_0),esk18_0),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( in(X1,esk18_0)
| ~ in(X1,esk17_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_14]),c_0_15])]),c_0_28]) ).
cnf(c_0_32,negated_conjecture,
in(esk2_2(esk17_0,esk18_0),esk17_0),
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU077+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n007.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 18:01:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.68 % Version : CSE_E---1.5
% 0.20/0.68 % Problem : theBenchmark.p
% 0.20/0.68 % Proof found
% 0.20/0.68 % SZS status Theorem for theBenchmark.p
% 0.20/0.68 % SZS output start Proof
% See solution above
% 0.20/0.69 % Total time : 0.090000 s
% 0.20/0.69 % SZS output end Proof
% 0.20/0.69 % Total time : 0.093000 s
%------------------------------------------------------------------------------