TSTP Solution File: ALG227+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG227+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/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 : Wed Aug 30 16:06:56 EDT 2023
% Result : Theorem 0.22s 0.59s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 33
% Syntax : Number of formulae : 63 ( 15 unt; 27 typ; 0 def)
% Number of atoms : 116 ( 36 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 127 ( 47 ~; 43 |; 18 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 16 >; 9 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 11 con; 0-3 aty)
% Number of variables : 49 ( 0 sgn; 27 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v1_xboole_0: $i > $o ).
tff(decl_23,type,
m1_pboole: ( $i * $i ) > $o ).
tff(decl_24,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_25,type,
k1_closure3: ( $i * $i ) > $i ).
tff(decl_26,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_27,type,
k1_funct_1: ( $i * $i ) > $i ).
tff(decl_28,type,
k1_xboole_0: $i ).
tff(decl_29,type,
v1_fraenkel: $i > $o ).
tff(decl_30,type,
v1_finset_1: $i > $o ).
tff(decl_31,type,
v1_funct_1: $i > $o ).
tff(decl_32,type,
v1_relat_1: $i > $o ).
tff(decl_33,type,
v2_funct_1: $i > $o ).
tff(decl_34,type,
a_2_0_closure3: ( $i * $i ) > $i ).
tff(decl_35,type,
esk1_0: $i ).
tff(decl_36,type,
esk2_0: $i ).
tff(decl_37,type,
esk3_0: $i ).
tff(decl_38,type,
esk4_1: $i > $i ).
tff(decl_39,type,
esk5_1: $i > $i ).
tff(decl_40,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
esk7_0: $i ).
tff(decl_42,type,
esk8_0: $i ).
tff(decl_43,type,
esk9_0: $i ).
tff(decl_44,type,
esk10_0: $i ).
tff(decl_45,type,
esk11_0: $i ).
tff(decl_46,type,
esk12_0: $i ).
tff(decl_47,type,
esk13_0: $i ).
tff(decl_48,type,
esk14_2: ( $i * $i ) > $i ).
fof(t6_boole,axiom,
! [X1] :
( v1_xboole_0(X1)
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_funct_1,axiom,
? [X1] :
( v1_relat_1(X1)
& v1_xboole_0(X1)
& v1_funct_1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(fraenkel_a_2_0_closure3,axiom,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_pboole(X3,X2) )
=> ( r2_hidden(X1,a_2_0_closure3(X2,X3))
<=> ? [X4] :
( m1_subset_1(X4,X2)
& X1 = X4
& k1_funct_1(X3,X4) != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
fof(d3_closure3,axiom,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( X3 = k1_closure3(X1,X2)
<=> X3 = a_2_0_closure3(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_closure3) ).
fof(rc1_xboole_0,axiom,
? [X1] : v1_xboole_0(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(t8_closure3,conjecture,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,X1)
=> ( ~ r2_hidden(X3,k1_closure3(X1,X2))
=> k1_funct_1(X2,X3) = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_closure3) ).
fof(c_0_6,plain,
! [X42] :
( ~ v1_xboole_0(X42)
| X42 = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_7,plain,
( v1_relat_1(esk11_0)
& v1_xboole_0(esk11_0)
& v1_funct_1(esk11_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(c_0_8,plain,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_pboole(X3,X2) )
=> ( r2_hidden(X1,a_2_0_closure3(X2,X3))
<=> ? [X4] :
( m1_subset_1(X4,X2)
& X1 = X4
& k1_funct_1(X3,X4) != k1_xboole_0 ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_0_closure3]) ).
cnf(c_0_9,plain,
( X1 = k1_xboole_0
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
v1_xboole_0(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( X3 = k1_closure3(X1,X2)
<=> X3 = a_2_0_closure3(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d3_closure3]) ).
fof(c_0_12,plain,
! [X23,X24,X25,X27] :
( ( m1_subset_1(esk6_3(X23,X24,X25),X24)
| ~ r2_hidden(X23,a_2_0_closure3(X24,X25))
| v1_xboole_0(X24)
| ~ m1_pboole(X25,X24) )
& ( X23 = esk6_3(X23,X24,X25)
| ~ r2_hidden(X23,a_2_0_closure3(X24,X25))
| v1_xboole_0(X24)
| ~ m1_pboole(X25,X24) )
& ( k1_funct_1(X25,esk6_3(X23,X24,X25)) != k1_xboole_0
| ~ r2_hidden(X23,a_2_0_closure3(X24,X25))
| v1_xboole_0(X24)
| ~ m1_pboole(X25,X24) )
& ( ~ m1_subset_1(X27,X24)
| X23 != X27
| k1_funct_1(X25,X27) = k1_xboole_0
| r2_hidden(X23,a_2_0_closure3(X24,X25))
| v1_xboole_0(X24)
| ~ m1_pboole(X25,X24) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
cnf(c_0_13,plain,
k1_xboole_0 = esk11_0,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_14,plain,
v1_xboole_0(esk10_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
fof(c_0_15,plain,
! [X14,X15,X16] :
( ( X16 != k1_closure3(X14,X15)
| X16 = a_2_0_closure3(X14,X15)
| ~ m1_pboole(X15,X14)
| v1_xboole_0(X14) )
& ( X16 != a_2_0_closure3(X14,X15)
| X16 = k1_closure3(X14,X15)
| ~ m1_pboole(X15,X14)
| v1_xboole_0(X14) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,X1)
=> ( ~ r2_hidden(X3,k1_closure3(X1,X2))
=> k1_funct_1(X2,X3) = k1_xboole_0 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t8_closure3])]) ).
cnf(c_0_17,plain,
( k1_funct_1(X4,X1) = k1_xboole_0
| r2_hidden(X3,a_2_0_closure3(X2,X4))
| v1_xboole_0(X2)
| ~ m1_subset_1(X1,X2)
| X3 != X1
| ~ m1_pboole(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( X1 = esk11_0
| ~ v1_xboole_0(X1) ),
inference(rw,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_19,plain,
v1_xboole_0(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( X1 = k1_closure3(X2,X3)
| v1_xboole_0(X2)
| X1 != a_2_0_closure3(X2,X3)
| ~ m1_pboole(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,negated_conjecture,
( ~ v1_xboole_0(esk1_0)
& m1_pboole(esk2_0,esk1_0)
& m1_subset_1(esk3_0,esk1_0)
& ~ r2_hidden(esk3_0,k1_closure3(esk1_0,esk2_0))
& k1_funct_1(esk2_0,esk3_0) != k1_xboole_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
cnf(c_0_22,plain,
( k1_funct_1(X1,X2) = k1_xboole_0
| r2_hidden(X2,a_2_0_closure3(X3,X1))
| v1_xboole_0(X3)
| ~ m1_subset_1(X2,X3)
| ~ m1_pboole(X1,X3) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
esk11_0 = esk10_0,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( k1_closure3(X1,X2) = a_2_0_closure3(X1,X2)
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
m1_pboole(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
~ v1_xboole_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( k1_funct_1(X1,X2) = esk10_0
| r2_hidden(X2,a_2_0_closure3(X3,X1))
| v1_xboole_0(X3)
| ~ m1_subset_1(X2,X3)
| ~ m1_pboole(X1,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_13]),c_0_23]) ).
cnf(c_0_28,negated_conjecture,
m1_subset_1(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,negated_conjecture,
k1_funct_1(esk2_0,esk3_0) != k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
~ r2_hidden(esk3_0,k1_closure3(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,negated_conjecture,
k1_closure3(esk1_0,esk2_0) = a_2_0_closure3(esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( k1_funct_1(X1,esk3_0) = esk10_0
| r2_hidden(esk3_0,a_2_0_closure3(esk1_0,X1))
| ~ m1_pboole(X1,esk1_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_26]) ).
cnf(c_0_33,negated_conjecture,
k1_funct_1(esk2_0,esk3_0) != esk10_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_13]),c_0_23]) ).
cnf(c_0_34,negated_conjecture,
~ r2_hidden(esk3_0,a_2_0_closure3(esk1_0,esk2_0)),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_25]),c_0_33]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG227+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 04:00:24 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.57 start to proof: theBenchmark
% 0.22/0.59 % Version : CSE_E---1.5
% 0.22/0.59 % Problem : theBenchmark.p
% 0.22/0.59 % Proof found
% 0.22/0.59 % SZS status Theorem for theBenchmark.p
% 0.22/0.59 % SZS output start Proof
% See solution above
% 0.22/0.59 % Total time : 0.011000 s
% 0.22/0.59 % SZS output end Proof
% 0.22/0.59 % Total time : 0.014000 s
%------------------------------------------------------------------------------