TSTP Solution File: SEU422+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU422+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 : n010.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 16:26:07 EDT 2023
% Result : Theorem 119.09s 119.20s
% Output : CNFRefutation 119.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 28
% Syntax : Number of formulae : 59 ( 14 unt; 21 typ; 0 def)
% Number of atoms : 106 ( 6 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 112 ( 44 ~; 40 |; 15 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 15 >; 8 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 61 ( 1 sgn; 37 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v1_xboole_0: $i > $o ).
tff(decl_23,type,
k1_zfmisc_1: $i > $i ).
tff(decl_24,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(decl_25,type,
a_2_0_relset_2: ( $i * $i ) > $i ).
tff(decl_26,type,
r2_hidden: ( $i * $i ) > $o ).
tff(decl_27,type,
v1_relat_1: $i > $o ).
tff(decl_28,type,
r1_tarski: ( $i * $i ) > $o ).
tff(decl_29,type,
k1_xboole_0: $i ).
tff(decl_30,type,
v3_relat_1: $i > $o ).
tff(decl_31,type,
k1_tarski: $i > $i ).
tff(decl_32,type,
esk1_0: $i ).
tff(decl_33,type,
esk2_0: $i ).
tff(decl_34,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk4_1: $i > $i ).
tff(decl_36,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
esk6_0: $i ).
tff(decl_38,type,
esk7_1: $i > $i ).
tff(decl_39,type,
esk8_0: $i ).
tff(decl_40,type,
esk9_1: $i > $i ).
tff(decl_41,type,
esk10_0: $i ).
tff(decl_42,type,
esk11_2: ( $i * $i ) > $i ).
fof(t16_relset_2,conjecture,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> m1_subset_1(a_2_0_relset_2(X1,X2),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_2) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ v1_xboole_0(k1_zfmisc_1(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(fraenkel_a_2_0_relset_2,axiom,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_subset_1(X3,k1_zfmisc_1(X2)) )
=> ( r2_hidden(X1,a_2_0_relset_2(X2,X3))
<=> ? [X4] :
( m1_subset_1(X4,X2)
& X1 = k1_tarski(X4)
& r2_hidden(X4,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_relset_2) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( r1_tarski(X1,X2)
<=> ! [X3] :
( r2_hidden(X3,X1)
=> r2_hidden(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t37_zfmisc_1,axiom,
! [X1,X2] :
( r1_tarski(k1_tarski(X1),X2)
<=> r2_hidden(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> m1_subset_1(a_2_0_relset_2(X1,X2),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t16_relset_2])]) ).
fof(c_0_8,plain,
! [X1] : ~ v1_xboole_0(k1_zfmisc_1(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(c_0_9,negated_conjecture,
( ~ v1_xboole_0(esk1_0)
& m1_subset_1(esk2_0,k1_zfmisc_1(esk1_0))
& ~ m1_subset_1(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(k1_zfmisc_1(esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,plain,
! [X42,X43] :
( ( ~ m1_subset_1(X42,k1_zfmisc_1(X43))
| r1_tarski(X42,X43) )
& ( ~ r1_tarski(X42,X43)
| m1_subset_1(X42,k1_zfmisc_1(X43)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_11,plain,
! [X35,X36] :
( ~ m1_subset_1(X35,X36)
| v1_xboole_0(X36)
| r2_hidden(X35,X36) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_12,plain,
! [X18] : ~ v1_xboole_0(k1_zfmisc_1(X18)),
inference(variable_rename,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_subset_1(X3,k1_zfmisc_1(X2)) )
=> ( r2_hidden(X1,a_2_0_relset_2(X2,X3))
<=> ? [X4] :
( m1_subset_1(X4,X2)
& X1 = k1_tarski(X4)
& r2_hidden(X4,X3) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_0_relset_2]) ).
cnf(c_0_14,negated_conjecture,
~ m1_subset_1(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(k1_zfmisc_1(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X10,X11,X12,X13,X14] :
( ( ~ r1_tarski(X10,X11)
| ~ r2_hidden(X12,X10)
| r2_hidden(X12,X11) )
& ( r2_hidden(esk3_2(X13,X14),X13)
| r1_tarski(X13,X14) )
& ( ~ r2_hidden(esk3_2(X13,X14),X14)
| r1_tarski(X13,X14) ) ),
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_17,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
~ v1_xboole_0(k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_19,plain,
! [X40,X41] :
( ( ~ r1_tarski(k1_tarski(X40),X41)
| r2_hidden(X40,X41) )
& ( ~ r2_hidden(X40,X41)
| r1_tarski(k1_tarski(X40),X41) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_zfmisc_1])]) ).
fof(c_0_20,plain,
! [X20,X21,X22,X24] :
( ( m1_subset_1(esk5_3(X20,X21,X22),X21)
| ~ r2_hidden(X20,a_2_0_relset_2(X21,X22))
| v1_xboole_0(X21)
| ~ m1_subset_1(X22,k1_zfmisc_1(X21)) )
& ( X20 = k1_tarski(esk5_3(X20,X21,X22))
| ~ r2_hidden(X20,a_2_0_relset_2(X21,X22))
| v1_xboole_0(X21)
| ~ m1_subset_1(X22,k1_zfmisc_1(X21)) )
& ( r2_hidden(esk5_3(X20,X21,X22),X22)
| ~ r2_hidden(X20,a_2_0_relset_2(X21,X22))
| v1_xboole_0(X21)
| ~ m1_subset_1(X22,k1_zfmisc_1(X21)) )
& ( ~ m1_subset_1(X24,X21)
| X20 != k1_tarski(X24)
| ~ r2_hidden(X24,X22)
| r2_hidden(X20,a_2_0_relset_2(X21,X22))
| v1_xboole_0(X21)
| ~ m1_subset_1(X22,k1_zfmisc_1(X21)) ) ),
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_13])])])])]) ).
cnf(c_0_21,negated_conjecture,
~ r1_tarski(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( r2_hidden(esk3_2(X1,X2),X1)
| r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( r2_hidden(X1,k1_zfmisc_1(X2))
| ~ r1_tarski(X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_18]) ).
cnf(c_0_24,plain,
( r1_tarski(k1_tarski(X1),X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( X1 = k1_tarski(esk5_3(X1,X2,X3))
| v1_xboole_0(X2)
| ~ r2_hidden(X1,a_2_0_relset_2(X2,X3))
| ~ m1_subset_1(X3,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
r2_hidden(esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),a_2_0_relset_2(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,negated_conjecture,
~ v1_xboole_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_29,plain,
( m1_subset_1(esk5_3(X1,X2,X3),X2)
| v1_xboole_0(X2)
| ~ r2_hidden(X1,a_2_0_relset_2(X2,X3))
| ~ m1_subset_1(X3,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
( r2_hidden(k1_tarski(X1),k1_zfmisc_1(X2))
| ~ r2_hidden(X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
k1_tarski(esk5_3(esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),esk1_0,esk2_0)) = esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),c_0_28]) ).
cnf(c_0_32,negated_conjecture,
m1_subset_1(esk5_3(esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),esk1_0,esk2_0),esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_26]),c_0_27])]),c_0_28]) ).
cnf(c_0_33,plain,
( r1_tarski(X1,X2)
| ~ r2_hidden(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_34,negated_conjecture,
( r2_hidden(esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),k1_zfmisc_1(X1))
| ~ r2_hidden(esk5_3(esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
r2_hidden(esk5_3(esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),esk1_0,esk2_0),esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_32]),c_0_28]) ).
cnf(c_0_36,negated_conjecture,
~ r2_hidden(esk3_2(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk1_0)),k1_zfmisc_1(esk1_0)),
inference(spm,[status(thm)],[c_0_21,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU422+1 : TPTP v8.1.2. Released v3.4.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Aug 23 19:52:36 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.57 start to proof: theBenchmark
% 119.09/119.20 % Version : CSE_E---1.5
% 119.09/119.20 % Problem : theBenchmark.p
% 119.09/119.20 % Proof found
% 119.09/119.20 % SZS status Theorem for theBenchmark.p
% 119.09/119.20 % SZS output start Proof
% See solution above
% 119.18/119.21 % Total time : 118.578000 s
% 119.18/119.21 % SZS output end Proof
% 119.18/119.21 % Total time : 118.586000 s
%------------------------------------------------------------------------------