TSTP Solution File: SEU014+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU014+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 : n005.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 16:22:08 EDT 2023
% Result : Theorem 0.22s 0.75s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 33
% Syntax : Number of formulae : 72 ( 17 unt; 27 typ; 0 def)
% Number of atoms : 169 ( 27 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 202 ( 78 ~; 80 |; 27 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 18 >; 5 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn; 28 !; 0 ?; 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_dom: $i > $i ).
tff(decl_28,type,
apply: ( $i * $i ) > $i ).
tff(decl_29,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_30,type,
element: ( $i * $i ) > $o ).
tff(decl_31,type,
empty_set: $i ).
tff(decl_32,type,
relation_empty_yielding: $i > $o ).
tff(decl_33,type,
powerset: $i > $i ).
tff(decl_34,type,
relation_rng: $i > $i ).
tff(decl_35,type,
subset: ( $i * $i ) > $o ).
tff(decl_36,type,
esk1_1: $i > $i ).
tff(decl_37,type,
esk2_1: $i > $i ).
tff(decl_38,type,
esk3_1: $i > $i ).
tff(decl_39,type,
esk4_0: $i ).
tff(decl_40,type,
esk5_0: $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_0: $i ).
fof(t47_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(relation_composition(X2,X1))
& subset(relation_rng(X2),relation_dom(X1)) )
=> one_to_one(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_1) ).
fof(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_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/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(d8_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(t46_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_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/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(relation_composition(X2,X1))
& subset(relation_rng(X2),relation_dom(X1)) )
=> one_to_one(X2) ) ) ),
inference(assume_negation,[status(cth)],[t47_funct_1]) ).
fof(c_0_7,plain,
! [X13,X14] :
( ~ relation(X13)
| ~ relation(X14)
| relation(relation_composition(X13,X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
fof(c_0_8,negated_conjecture,
( relation(esk12_0)
& function(esk12_0)
& relation(esk13_0)
& function(esk13_0)
& one_to_one(relation_composition(esk13_0,esk12_0))
& subset(relation_rng(esk13_0),relation_dom(esk12_0))
& ~ one_to_one(esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,plain,
! [X19,X20] :
( ( relation(relation_composition(X19,X20))
| ~ relation(X19)
| ~ function(X19)
| ~ relation(X20)
| ~ function(X20) )
& ( function(relation_composition(X19,X20))
| ~ relation(X19)
| ~ function(X19)
| ~ relation(X20)
| ~ function(X20) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).
fof(c_0_10,plain,
! [X8,X9,X10] :
( ( ~ one_to_one(X8)
| ~ in(X9,relation_dom(X8))
| ~ in(X10,relation_dom(X8))
| apply(X8,X9) != apply(X8,X10)
| X9 = X10
| ~ relation(X8)
| ~ function(X8) )
& ( in(esk1_1(X8),relation_dom(X8))
| one_to_one(X8)
| ~ relation(X8)
| ~ function(X8) )
& ( in(esk2_1(X8),relation_dom(X8))
| one_to_one(X8)
| ~ relation(X8)
| ~ function(X8) )
& ( apply(X8,esk1_1(X8)) = apply(X8,esk2_1(X8))
| one_to_one(X8)
| ~ relation(X8)
| ~ function(X8) )
& ( esk1_1(X8) != esk2_1(X8)
| one_to_one(X8)
| ~ relation(X8)
| ~ function(X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])]) ).
fof(c_0_11,plain,
! [X48,X49] :
( ~ relation(X48)
| ~ relation(X49)
| ~ subset(relation_rng(X48),relation_dom(X49))
| relation_dom(relation_composition(X48,X49)) = relation_dom(X48) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_relat_1])])]) ).
cnf(c_0_12,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( function(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
function(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_16,plain,
! [X41,X42,X43] :
( ~ relation(X42)
| ~ function(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ in(X41,relation_dom(X42))
| apply(relation_composition(X42,X43),X41) = apply(X43,apply(X42,X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
cnf(c_0_17,plain,
( in(esk2_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
function(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
~ one_to_one(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,plain,
( apply(X1,esk1_1(X1)) = apply(X1,esk2_1(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,plain,
( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ subset(relation_rng(X1),relation_dom(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,negated_conjecture,
subset(relation_rng(esk13_0),relation_dom(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,negated_conjecture,
( relation(relation_composition(X1,esk12_0))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_25,negated_conjecture,
( function(relation_composition(X1,esk12_0))
| ~ relation(X1)
| ~ function(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_15])]) ).
cnf(c_0_26,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_16]) ).
cnf(c_0_27,negated_conjecture,
in(esk2_1(esk13_0),relation_dom(esk13_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_28,negated_conjecture,
apply(esk13_0,esk2_1(esk13_0)) = apply(esk13_0,esk1_1(esk13_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_29,plain,
( in(esk1_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_30,plain,
( X2 = X3
| ~ one_to_one(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X3,relation_dom(X1))
| apply(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_31,negated_conjecture,
relation_dom(relation_composition(esk13_0,esk12_0)) = relation_dom(esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_13]),c_0_18])]) ).
cnf(c_0_32,negated_conjecture,
one_to_one(relation_composition(esk13_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_33,negated_conjecture,
relation(relation_composition(esk13_0,esk12_0)),
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
cnf(c_0_34,negated_conjecture,
function(relation_composition(esk13_0,esk12_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_18]),c_0_19])]) ).
cnf(c_0_35,negated_conjecture,
( apply(relation_composition(esk13_0,X1),esk2_1(esk13_0)) = apply(X1,apply(esk13_0,esk1_1(esk13_0)))
| ~ relation(X1)
| ~ function(X1) ),
inference(rw,[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_18]),c_0_19])]),c_0_28]) ).
cnf(c_0_36,negated_conjecture,
in(esk1_1(esk13_0),relation_dom(esk13_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_37,negated_conjecture,
( X1 = X2
| apply(relation_composition(esk13_0,esk12_0),X1) != apply(relation_composition(esk13_0,esk12_0),X2)
| ~ in(X2,relation_dom(esk13_0))
| ~ in(X1,relation_dom(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),c_0_33]),c_0_34])]) ).
cnf(c_0_38,negated_conjecture,
apply(relation_composition(esk13_0,esk12_0),esk2_1(esk13_0)) = apply(esk12_0,apply(esk13_0,esk1_1(esk13_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_13]),c_0_15])]) ).
cnf(c_0_39,negated_conjecture,
( apply(relation_composition(esk13_0,X1),esk1_1(esk13_0)) = apply(X1,apply(esk13_0,esk1_1(esk13_0)))
| ~ relation(X1)
| ~ function(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_36]),c_0_18]),c_0_19])]) ).
cnf(c_0_40,plain,
( one_to_one(X1)
| esk1_1(X1) != esk2_1(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_41,negated_conjecture,
( X1 = esk2_1(esk13_0)
| apply(relation_composition(esk13_0,esk12_0),X1) != apply(esk12_0,apply(esk13_0,esk1_1(esk13_0)))
| ~ in(X1,relation_dom(esk13_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_27]),c_0_38]) ).
cnf(c_0_42,negated_conjecture,
apply(relation_composition(esk13_0,esk12_0),esk1_1(esk13_0)) = apply(esk12_0,apply(esk13_0,esk1_1(esk13_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_13]),c_0_15])]) ).
cnf(c_0_43,negated_conjecture,
esk2_1(esk13_0) != esk1_1(esk13_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_36]),c_0_42])]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU014+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.37 % Computer : n005.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Wed Aug 23 13:26:54 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.22/0.64 start to proof: theBenchmark
% 0.22/0.75 % Version : CSE_E---1.5
% 0.22/0.75 % Problem : theBenchmark.p
% 0.22/0.75 % Proof found
% 0.22/0.75 % SZS status Theorem for theBenchmark.p
% 0.22/0.75 % SZS output start Proof
% See solution above
% 0.22/0.75 % Total time : 0.100000 s
% 0.22/0.75 % SZS output end Proof
% 0.22/0.75 % Total time : 0.103000 s
%------------------------------------------------------------------------------