TSTP Solution File: SEU012+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU012+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 : n025.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 16:22:07 EDT 2023
% Result : Theorem 6.62s 6.69s
% Output : CNFRefutation 6.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 35
% Syntax : Number of formulae : 68 ( 10 unt; 29 typ; 0 def)
% Number of atoms : 193 ( 56 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 256 ( 102 ~; 105 |; 32 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 20 >; 10 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 65 ( 0 sgn; 34 !; 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,
relation_rng: $i > $i ).
tff(decl_27,type,
relation_dom: $i > $i ).
tff(decl_28,type,
apply: ( $i * $i ) > $i ).
tff(decl_29,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_30,type,
identity_relation: $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,
subset: ( $i * $i ) > $o ).
tff(decl_36,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk4_1: $i > $i ).
tff(decl_40,type,
esk5_0: $i ).
tff(decl_41,type,
esk6_0: $i ).
tff(decl_42,type,
esk7_1: $i > $i ).
tff(decl_43,type,
esk8_0: $i ).
tff(decl_44,type,
esk9_0: $i ).
tff(decl_45,type,
esk10_1: $i > $i ).
tff(decl_46,type,
esk11_0: $i ).
tff(decl_47,type,
esk12_0: $i ).
tff(decl_48,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk14_0: $i ).
tff(decl_50,type,
esk15_0: $i ).
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(t44_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( relation_rng(X1) = relation_dom(X2)
& relation_composition(X1,X2) = X1 )
=> X2 = identity_relation(relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_1) ).
fof(t23_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(fc1_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(t34_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(c_0_6,plain,
! [X9,X10,X11,X13,X14,X15,X17] :
( ( in(esk1_3(X9,X10,X11),relation_dom(X9))
| ~ in(X11,X10)
| X10 != relation_rng(X9)
| ~ relation(X9)
| ~ function(X9) )
& ( X11 = apply(X9,esk1_3(X9,X10,X11))
| ~ in(X11,X10)
| X10 != relation_rng(X9)
| ~ relation(X9)
| ~ function(X9) )
& ( ~ in(X14,relation_dom(X9))
| X13 != apply(X9,X14)
| in(X13,X10)
| X10 != relation_rng(X9)
| ~ relation(X9)
| ~ function(X9) )
& ( ~ in(esk2_2(X9,X15),X15)
| ~ in(X17,relation_dom(X9))
| esk2_2(X9,X15) != apply(X9,X17)
| X15 = relation_rng(X9)
| ~ relation(X9)
| ~ function(X9) )
& ( in(esk3_2(X9,X15),relation_dom(X9))
| in(esk2_2(X9,X15),X15)
| X15 = relation_rng(X9)
| ~ relation(X9)
| ~ function(X9) )
& ( esk2_2(X9,X15) = apply(X9,esk3_2(X9,X15))
| in(esk2_2(X9,X15),X15)
| X15 = relation_rng(X9)
| ~ relation(X9)
| ~ function(X9) ) ),
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_7,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( relation_rng(X1) = relation_dom(X2)
& relation_composition(X1,X2) = X1 )
=> X2 = identity_relation(relation_dom(X2)) ) ) ),
inference(assume_negation,[status(cth)],[t44_funct_1]) ).
cnf(c_0_8,plain,
( X1 = apply(X2,esk1_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X49,X50,X51] :
( ~ relation(X50)
| ~ function(X50)
| ~ relation(X51)
| ~ function(X51)
| ~ in(X49,relation_dom(X50))
| apply(relation_composition(X50,X51),X49) = apply(X51,apply(X50,X49)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
fof(c_0_10,plain,
! [X26,X27] :
( ( relation(relation_composition(X26,X27))
| ~ relation(X26)
| ~ function(X26)
| ~ relation(X27)
| ~ function(X27) )
& ( function(relation_composition(X26,X27))
| ~ relation(X26)
| ~ function(X26)
| ~ relation(X27)
| ~ function(X27) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).
fof(c_0_11,plain,
! [X19,X20] :
( ~ relation(X19)
| ~ relation(X20)
| relation(relation_composition(X19,X20)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
cnf(c_0_12,plain,
( in(esk1_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_6]) ).
fof(c_0_13,negated_conjecture,
( relation(esk14_0)
& function(esk14_0)
& relation(esk15_0)
& function(esk15_0)
& relation_rng(esk14_0) = relation_dom(esk15_0)
& relation_composition(esk14_0,esk15_0) = esk14_0
& esk15_0 != identity_relation(relation_dom(esk15_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_14,plain,
! [X54,X55,X56] :
( ( relation_dom(X55) = X54
| X55 != identity_relation(X54)
| ~ relation(X55)
| ~ function(X55) )
& ( ~ in(X56,X54)
| apply(X55,X56) = X56
| X55 != identity_relation(X54)
| ~ relation(X55)
| ~ function(X55) )
& ( in(esk13_2(X54,X55),X54)
| relation_dom(X55) != X54
| X55 = identity_relation(X54)
| ~ relation(X55)
| ~ function(X55) )
& ( apply(X55,esk13_2(X54,X55)) != esk13_2(X54,X55)
| relation_dom(X55) != X54
| X55 = identity_relation(X54)
| ~ relation(X55)
| ~ function(X55) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).
cnf(c_0_15,plain,
( apply(X1,esk1_3(X1,relation_rng(X1),X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( function(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( in(esk1_3(X1,relation_rng(X1),X2),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
relation_rng(esk14_0) = relation_dom(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
function(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,plain,
( X1 = identity_relation(X2)
| apply(X1,esk13_2(X2,X1)) != esk13_2(X2,X1)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
( apply(X1,apply(X2,esk1_3(relation_composition(X2,X1),relation_rng(relation_composition(X2,X1)),X3))) = X3
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X1)
| ~ function(X2)
| ~ in(esk1_3(relation_composition(X2,X1),relation_rng(relation_composition(X2,X1)),X3),relation_dom(X2))
| ~ in(X3,relation_rng(relation_composition(X2,X1))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]) ).
cnf(c_0_25,negated_conjecture,
relation_composition(esk14_0,esk15_0) = esk14_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_26,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_27,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_28,negated_conjecture,
( in(esk1_3(esk14_0,relation_dom(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(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_29,plain,
( in(esk13_2(X1,X2),X1)
| X2 = identity_relation(X1)
| relation_dom(X2) != X1
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_30,negated_conjecture,
esk15_0 != identity_relation(relation_dom(esk15_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_31,plain,
( identity_relation(relation_dom(X1)) = X1
| apply(X1,esk13_2(relation_dom(X1),X1)) != esk13_2(relation_dom(X1),X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_32,negated_conjecture,
( apply(esk15_0,apply(esk14_0,esk1_3(esk14_0,relation_dom(esk15_0),X1))) = X1
| ~ in(X1,relation_dom(esk15_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_20]),c_0_26]),c_0_21]),c_0_27]),c_0_22]),c_0_20]),c_0_20])]),c_0_28]) ).
cnf(c_0_33,negated_conjecture,
( apply(esk14_0,esk1_3(esk14_0,relation_dom(esk15_0),X1)) = X1
| ~ in(X1,relation_dom(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_34,plain,
( identity_relation(relation_dom(X1)) = X1
| in(esk13_2(relation_dom(X1),X1),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_35,negated_conjecture,
apply(esk15_0,esk13_2(relation_dom(esk15_0),esk15_0)) != esk13_2(relation_dom(esk15_0),esk15_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_26]),c_0_27])]) ).
cnf(c_0_36,negated_conjecture,
( apply(esk15_0,X1) = X1
| ~ in(X1,relation_dom(esk15_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
in(esk13_2(relation_dom(esk15_0),esk15_0),relation_dom(esk15_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_26]),c_0_27])]),c_0_30]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU012+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n025.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 18:35:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 6.62/6.69 % Version : CSE_E---1.5
% 6.62/6.69 % Problem : theBenchmark.p
% 6.62/6.69 % Proof found
% 6.62/6.69 % SZS status Theorem for theBenchmark.p
% 6.62/6.69 % SZS output start Proof
% See solution above
% 6.62/6.70 % Total time : 6.104000 s
% 6.62/6.70 % SZS output end Proof
% 6.62/6.70 % Total time : 6.107000 s
%------------------------------------------------------------------------------