TSTP Solution File: SEU003+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU003+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n026.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 16:22:06 EDT 2023
% Result : Theorem 2.03s 2.19s
% Output : CNFRefutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 32
% Syntax : Number of formulae : 56 ( 9 unt; 28 typ; 0 def)
% Number of atoms : 136 ( 20 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 177 ( 69 ~; 71 |; 23 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 19 >; 10 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 49 ( 0 sgn; 28 !; 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,
subset: ( $i * $i ) > $o ).
tff(decl_27,type,
relation_rng: $i > $i ).
tff(decl_28,type,
relation_dom: $i > $i ).
tff(decl_29,type,
apply: ( $i * $i ) > $i ).
tff(decl_30,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_31,type,
element: ( $i * $i ) > $o ).
tff(decl_32,type,
empty_set: $i ).
tff(decl_33,type,
relation_empty_yielding: $i > $o ).
tff(decl_34,type,
powerset: $i > $i ).
tff(decl_35,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk5_1: $i > $i ).
tff(decl_40,type,
esk6_0: $i ).
tff(decl_41,type,
esk7_0: $i ).
tff(decl_42,type,
esk8_1: $i > $i ).
tff(decl_43,type,
esk9_0: $i ).
tff(decl_44,type,
esk10_0: $i ).
tff(decl_45,type,
esk11_1: $i > $i ).
tff(decl_46,type,
esk12_0: $i ).
tff(decl_47,type,
esk13_0: $i ).
tff(decl_48,type,
esk14_0: $i ).
tff(decl_49,type,
esk15_0: $i ).
fof(t27_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( relation_dom(relation_composition(X2,X1)) = relation_dom(X2)
=> subset(relation_rng(X2),relation_dom(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_1) ).
fof(t21_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_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(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( relation_dom(relation_composition(X2,X1)) = relation_dom(X2)
=> subset(relation_rng(X2),relation_dom(X1)) ) ) ),
inference(assume_negation,[status(cth)],[t27_funct_1]) ).
fof(c_0_5,plain,
! [X53,X54,X55] :
( ( in(X53,relation_dom(X55))
| ~ in(X53,relation_dom(relation_composition(X55,X54)))
| ~ relation(X55)
| ~ function(X55)
| ~ relation(X54)
| ~ function(X54) )
& ( in(apply(X55,X53),relation_dom(X54))
| ~ in(X53,relation_dom(relation_composition(X55,X54)))
| ~ relation(X55)
| ~ function(X55)
| ~ relation(X54)
| ~ function(X54) )
& ( ~ in(X53,relation_dom(X55))
| ~ in(apply(X55,X53),relation_dom(X54))
| in(X53,relation_dom(relation_composition(X55,X54)))
| ~ relation(X55)
| ~ function(X55)
| ~ relation(X54)
| ~ function(X54) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_funct_1])])])]) ).
fof(c_0_6,negated_conjecture,
( relation(esk14_0)
& function(esk14_0)
& relation(esk15_0)
& function(esk15_0)
& relation_dom(relation_composition(esk15_0,esk14_0)) = relation_dom(esk15_0)
& ~ subset(relation_rng(esk15_0),relation_dom(esk14_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X15,X16,X17,X19,X20,X21,X23] :
( ( in(esk2_3(X15,X16,X17),relation_dom(X15))
| ~ in(X17,X16)
| X16 != relation_rng(X15)
| ~ relation(X15)
| ~ function(X15) )
& ( X17 = apply(X15,esk2_3(X15,X16,X17))
| ~ in(X17,X16)
| X16 != relation_rng(X15)
| ~ relation(X15)
| ~ function(X15) )
& ( ~ in(X20,relation_dom(X15))
| X19 != apply(X15,X20)
| in(X19,X16)
| X16 != relation_rng(X15)
| ~ relation(X15)
| ~ function(X15) )
& ( ~ in(esk3_2(X15,X21),X21)
| ~ in(X23,relation_dom(X15))
| esk3_2(X15,X21) != apply(X15,X23)
| X21 = relation_rng(X15)
| ~ relation(X15)
| ~ function(X15) )
& ( in(esk4_2(X15,X21),relation_dom(X15))
| in(esk3_2(X15,X21),X21)
| X21 = relation_rng(X15)
| ~ relation(X15)
| ~ function(X15) )
& ( esk3_2(X15,X21) = apply(X15,esk4_2(X15,X21))
| in(esk3_2(X15,X21),X21)
| X21 = relation_rng(X15)
| ~ relation(X15)
| ~ function(X15) ) ),
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_8,plain,
( in(apply(X1,X2),relation_dom(X3))
| ~ in(X2,relation_dom(relation_composition(X1,X3)))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
relation_dom(relation_composition(esk15_0,esk14_0)) = relation_dom(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
function(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( X1 = apply(X2,esk2_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
( in(apply(esk15_0,X1),relation_dom(esk14_0))
| ~ in(X1,relation_dom(esk15_0)) ),
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_8,c_0_9]),c_0_10]),c_0_11]),c_0_12]),c_0_13])]) ).
cnf(c_0_16,plain,
( apply(X1,esk2_3(X1,relation_rng(X1),X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
( in(esk2_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_7]) ).
fof(c_0_18,plain,
! [X9,X10,X11,X12,X13] :
( ( ~ subset(X9,X10)
| ~ in(X11,X9)
| in(X11,X10) )
& ( in(esk1_2(X12,X13),X12)
| subset(X12,X13) )
& ( ~ in(esk1_2(X12,X13),X13)
| subset(X12,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)],[d3_tarski])])])])])]) ).
cnf(c_0_19,negated_conjecture,
( in(X1,relation_dom(esk14_0))
| ~ in(esk2_3(esk15_0,relation_rng(esk15_0),X1),relation_dom(esk15_0))
| ~ in(X1,relation_rng(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_11]),c_0_13])]) ).
cnf(c_0_20,plain,
( in(esk2_3(X1,relation_rng(X1),X2),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
~ subset(relation_rng(esk15_0),relation_dom(esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( in(X1,relation_dom(esk14_0))
| ~ in(X1,relation_rng(esk15_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_11]),c_0_13])]) ).
cnf(c_0_25,negated_conjecture,
in(esk1_2(relation_rng(esk15_0),relation_dom(esk14_0)),relation_rng(esk15_0)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
~ in(esk1_2(relation_rng(esk15_0),relation_dom(esk14_0)),relation_dom(esk14_0)),
inference(spm,[status(thm)],[c_0_21,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU003+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 13:00:31 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.56 start to proof: theBenchmark
% 2.03/2.19 % Version : CSE_E---1.5
% 2.03/2.19 % Problem : theBenchmark.p
% 2.03/2.19 % Proof found
% 2.03/2.19 % SZS status Theorem for theBenchmark.p
% 2.03/2.19 % SZS output start Proof
% See solution above
% 2.03/2.19 % Total time : 1.621000 s
% 2.03/2.19 % SZS output end Proof
% 2.03/2.19 % Total time : 1.623000 s
%------------------------------------------------------------------------------