TSTP Solution File: SEU430+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU430+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 16:26:35 EDT 2023
% Result : Theorem 0.94s 1.03s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 32
% Syntax : Number of formulae : 85 ( 14 unt; 23 typ; 0 def)
% Number of atoms : 154 ( 60 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 149 ( 57 ~; 66 |; 13 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 16 >; 8 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 76 ( 5 sgn; 41 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
k1_zfmisc_1: $i > $i ).
tff(decl_23,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_24,type,
k5_setfam_1: ( $i * $i ) > $i ).
tff(decl_25,type,
k1_xboole_0: $i ).
tff(decl_26,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_27,type,
v1_xboole_0: $i > $o ).
tff(decl_28,type,
v1_relat_1: $i > $o ).
tff(decl_29,type,
k3_tarski: $i > $i ).
tff(decl_30,type,
v3_relat_1: $i > $o ).
tff(decl_31,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_32,type,
esk1_0: $i ).
tff(decl_33,type,
esk2_0: $i ).
tff(decl_34,type,
esk3_0: $i ).
tff(decl_35,type,
esk4_1: $i > $i ).
tff(decl_36,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk8_1: $i > $i ).
tff(decl_40,type,
esk9_0: $i ).
tff(decl_41,type,
esk10_1: $i > $i ).
tff(decl_42,type,
esk11_0: $i ).
tff(decl_43,type,
esk12_1: $i > $i ).
tff(decl_44,type,
esk13_0: $i ).
fof(t30_relset_2,conjecture,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> ( k5_setfam_1(X1,X2) = k1_xboole_0
<=> ! [X3] :
( r2_hidden(X3,X2)
=> X3 = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relset_2) ).
fof(t6_boole,axiom,
! [X1] :
( v1_xboole_0(X1)
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc1_relat_1,axiom,
? [X1] :
( v1_xboole_0(X1)
& v1_relat_1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(redefinition_k5_setfam_1,axiom,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> k5_setfam_1(X1,X2) = k3_tarski(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(d4_tarski,axiom,
! [X1,X2] :
( X2 = k3_tarski(X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ? [X4] :
( r2_hidden(X3,X4)
& r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( r2_hidden(X1,X2)
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> ( k5_setfam_1(X1,X2) = k1_xboole_0
<=> ! [X3] :
( r2_hidden(X3,X2)
=> X3 = k1_xboole_0 ) ) ),
inference(assume_negation,[status(cth)],[t30_relset_2]) ).
fof(c_0_10,plain,
! [X54] :
( ~ v1_xboole_0(X54)
| X54 = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_11,plain,
( v1_xboole_0(esk9_0)
& v1_relat_1(esk9_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(c_0_12,plain,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_13,negated_conjecture,
! [X8] :
( m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0)))
& ( r2_hidden(esk3_0,esk2_0)
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 )
& ( esk3_0 != k1_xboole_0
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 )
& ( k5_setfam_1(esk1_0,esk2_0) = k1_xboole_0
| ~ r2_hidden(X8,esk2_0)
| X8 = k1_xboole_0 ) ),
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_9])])])])]) ).
cnf(c_0_14,plain,
( X1 = k1_xboole_0
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
v1_xboole_0(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X12,X13,X14] :
( ( X12 != k1_xboole_0
| ~ r2_hidden(X13,X12) )
& ( r2_hidden(esk4_1(X14),X14)
| X14 = k1_xboole_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])]) ).
cnf(c_0_17,negated_conjecture,
( r2_hidden(esk3_0,esk2_0)
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
k1_xboole_0 = esk9_0,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_19,plain,
! [X39,X40] :
( ~ m1_subset_1(X40,k1_zfmisc_1(k1_zfmisc_1(X39)))
| k5_setfam_1(X39,X40) = k3_tarski(X40) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).
cnf(c_0_20,plain,
( X1 != k1_xboole_0
| ~ r2_hidden(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( esk3_0 != k1_xboole_0
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
( r2_hidden(esk3_0,esk2_0)
| k5_setfam_1(esk1_0,esk2_0) != esk9_0 ),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( k5_setfam_1(X2,X1) = k3_tarski(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_25,plain,
! [X16,X17,X18,X20,X21,X22,X23,X25] :
( ( r2_hidden(X18,esk5_3(X16,X17,X18))
| ~ r2_hidden(X18,X17)
| X17 != k3_tarski(X16) )
& ( r2_hidden(esk5_3(X16,X17,X18),X16)
| ~ r2_hidden(X18,X17)
| X17 != k3_tarski(X16) )
& ( ~ r2_hidden(X20,X21)
| ~ r2_hidden(X21,X16)
| r2_hidden(X20,X17)
| X17 != k3_tarski(X16) )
& ( ~ r2_hidden(esk6_2(X22,X23),X23)
| ~ r2_hidden(esk6_2(X22,X23),X25)
| ~ r2_hidden(X25,X22)
| X23 = k3_tarski(X22) )
& ( r2_hidden(esk6_2(X22,X23),esk7_2(X22,X23))
| r2_hidden(esk6_2(X22,X23),X23)
| X23 = k3_tarski(X22) )
& ( r2_hidden(esk7_2(X22,X23),X22)
| r2_hidden(esk6_2(X22,X23),X23)
| X23 = k3_tarski(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)],[d4_tarski])])])])])]) ).
cnf(c_0_26,plain,
~ r2_hidden(X1,k1_xboole_0),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( k5_setfam_1(esk1_0,esk2_0) != esk9_0
| esk3_0 != esk9_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_18]),c_0_18]) ).
cnf(c_0_28,negated_conjecture,
( k5_setfam_1(esk1_0,esk2_0) = k1_xboole_0
| X1 = k1_xboole_0
| ~ r2_hidden(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_29,negated_conjecture,
( r2_hidden(esk3_0,esk2_0)
| k3_tarski(esk2_0) != esk9_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_30,plain,
( r2_hidden(esk7_2(X1,X2),X1)
| r2_hidden(esk6_2(X1,X2),X2)
| X2 = k3_tarski(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
~ r2_hidden(X1,esk9_0),
inference(rw,[status(thm)],[c_0_26,c_0_18]) ).
fof(c_0_32,plain,
! [X44,X45] :
( ~ m1_subset_1(X44,X45)
| v1_xboole_0(X45)
| r2_hidden(X44,X45) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_33,plain,
! [X29] : m1_subset_1(esk8_1(X29),X29),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_34,plain,
! [X55,X56] :
( ~ r2_hidden(X55,X56)
| ~ v1_xboole_0(X56) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_35,negated_conjecture,
( k3_tarski(esk2_0) != esk9_0
| esk3_0 != esk9_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_23]),c_0_24])]) ).
cnf(c_0_36,plain,
( r2_hidden(X1,X4)
| ~ r2_hidden(X1,X2)
| ~ r2_hidden(X2,X3)
| X4 != k3_tarski(X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,negated_conjecture,
( k5_setfam_1(esk1_0,esk2_0) = esk9_0
| X1 = esk9_0
| ~ r2_hidden(X1,esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_18]),c_0_18]) ).
cnf(c_0_38,negated_conjecture,
( r2_hidden(esk7_2(esk2_0,esk9_0),esk2_0)
| r2_hidden(esk3_0,esk2_0) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30])]),c_0_31]) ).
cnf(c_0_39,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
m1_subset_1(esk8_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
( ~ r2_hidden(X1,X2)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
( r2_hidden(esk6_2(X1,X2),esk7_2(X1,X2))
| r2_hidden(esk6_2(X1,X2),X2)
| X2 = k3_tarski(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_43,negated_conjecture,
( r2_hidden(esk7_2(esk2_0,esk9_0),esk2_0)
| esk3_0 != esk9_0 ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30])]),c_0_31]) ).
cnf(c_0_44,plain,
( r2_hidden(X1,k3_tarski(X2))
| ~ r2_hidden(X3,X2)
| ~ r2_hidden(X1,X3) ),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_45,negated_conjecture,
( esk7_2(esk2_0,esk9_0) = esk9_0
| r2_hidden(esk3_0,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_22]) ).
cnf(c_0_46,plain,
( X1 = esk9_0
| ~ v1_xboole_0(X1) ),
inference(rw,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_47,plain,
( v1_xboole_0(X1)
| r2_hidden(esk8_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
( X1 = k3_tarski(X2)
| r2_hidden(esk6_2(X2,X1),X1)
| ~ v1_xboole_0(esk7_2(X2,X1)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( esk7_2(esk2_0,esk9_0) = esk9_0
| esk3_0 != esk9_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_43]),c_0_27]) ).
cnf(c_0_50,negated_conjecture,
( esk7_2(esk2_0,esk9_0) = esk9_0
| r2_hidden(X1,k3_tarski(esk2_0))
| ~ r2_hidden(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,plain,
( X1 = esk9_0
| r2_hidden(esk8_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
esk3_0 != esk9_0,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_15])]),c_0_31]),c_0_35]) ).
cnf(c_0_53,negated_conjecture,
( esk7_2(esk2_0,esk9_0) = esk9_0
| k5_setfam_1(esk1_0,esk2_0) = esk9_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_45]),c_0_49]) ).
cnf(c_0_54,negated_conjecture,
( esk7_2(esk2_0,esk9_0) = esk9_0
| r2_hidden(esk8_1(esk3_0),k3_tarski(esk2_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( esk7_2(esk2_0,esk9_0) = esk9_0
| k3_tarski(esk2_0) = esk9_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_53]),c_0_24])]) ).
cnf(c_0_56,negated_conjecture,
( r2_hidden(esk6_2(esk2_0,esk9_0),esk7_2(esk2_0,esk9_0))
| r2_hidden(esk3_0,esk2_0) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_42])]),c_0_31]) ).
cnf(c_0_57,negated_conjecture,
esk7_2(esk2_0,esk9_0) = esk9_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_31]) ).
cnf(c_0_58,negated_conjecture,
r2_hidden(esk3_0,esk2_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57]),c_0_31]) ).
cnf(c_0_59,negated_conjecture,
k3_tarski(esk2_0) = esk9_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_57]),c_0_15])]),c_0_31]) ).
cnf(c_0_60,negated_conjecture,
~ r2_hidden(X1,esk3_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_58]),c_0_59]),c_0_31]) ).
cnf(c_0_61,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_51]),c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU430+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n002.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 : Thu Aug 24 01:41:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.94/1.03 % Version : CSE_E---1.5
% 0.94/1.03 % Problem : theBenchmark.p
% 0.94/1.03 % Proof found
% 0.94/1.03 % SZS status Theorem for theBenchmark.p
% 0.94/1.03 % SZS output start Proof
% See solution above
% 0.94/1.03 % Total time : 0.445000 s
% 0.94/1.03 % SZS output end Proof
% 0.94/1.03 % Total time : 0.448000 s
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