TSTP Solution File: SET980+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET980+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n021.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 14:36:31 EDT 2023
% Result : Theorem 0.21s 0.60s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 65 ( 12 unt; 15 typ; 0 def)
% Number of atoms : 127 ( 42 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 132 ( 55 ~; 60 |; 10 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 8 >; 5 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 92 ( 18 sgn; 32 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_24,type,
empty_set: $i ).
tff(decl_25,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_26,type,
singleton: $i > $i ).
tff(decl_27,type,
empty: $i > $o ).
tff(decl_28,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk1_1: $i > $i ).
tff(decl_30,type,
esk2_0: $i ).
tff(decl_31,type,
esk3_0: $i ).
tff(decl_32,type,
esk4_0: $i ).
tff(decl_33,type,
esk5_0: $i ).
tff(decl_34,type,
esk6_0: $i ).
tff(decl_35,type,
esk7_0: $i ).
tff(decl_36,type,
esk8_2: ( $i * $i ) > $i ).
fof(l55_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t134_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
=> ( X1 = empty_set
| X2 = empty_set
| ( X1 = X3
& X2 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(c_0_5,plain,
! [X17,X18,X19,X20] :
( ( in(X17,X19)
| ~ in(ordered_pair(X17,X18),cartesian_product2(X19,X20)) )
& ( in(X18,X20)
| ~ in(ordered_pair(X17,X18),cartesian_product2(X19,X20)) )
& ( ~ in(X17,X19)
| ~ in(X18,X20)
| in(ordered_pair(X17,X18),cartesian_product2(X19,X20)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(c_0_6,plain,
! [X13,X14] : ordered_pair(X13,X14) = unordered_pair(unordered_pair(X13,X14),singleton(X13)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
=> ( X1 = empty_set
| X2 = empty_set
| ( X1 = X3
& X2 = X4 ) ) ),
inference(assume_negation,[status(cth)],[t134_zfmisc_1]) ).
fof(c_0_8,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_9,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
( cartesian_product2(esk4_0,esk5_0) = cartesian_product2(esk6_0,esk7_0)
& esk4_0 != empty_set
& esk5_0 != empty_set
& ( esk4_0 != esk6_0
| esk5_0 != esk7_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_12,plain,
! [X9,X10,X11] :
( ( X9 != empty_set
| ~ in(X10,X9) )
& ( in(esk1_1(X11),X11)
| X11 = empty_set ) ),
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_8])])])])]) ).
cnf(c_0_13,plain,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
cartesian_product2(esk4_0,esk5_0) = cartesian_product2(esk6_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X29,X30] :
( ( ~ in(esk8_2(X29,X30),X29)
| ~ in(esk8_2(X29,X30),X30)
| X29 = X30 )
& ( in(esk8_2(X29,X30),X29)
| in(esk8_2(X29,X30),X30)
| X29 = X30 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(c_0_18,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_19,plain,
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_20,negated_conjecture,
( in(X1,esk7_0)
| ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),cartesian_product2(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( in(esk8_2(X1,X2),X1)
| in(esk8_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[c_0_18,c_0_10]) ).
cnf(c_0_24,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk4_0,esk5_0))
| ~ in(X2,esk7_0)
| ~ in(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_25,negated_conjecture,
( in(X1,esk7_0)
| ~ in(X1,esk5_0)
| ~ in(X2,esk4_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_26,plain,
( empty_set = X1
| in(esk8_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
esk4_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X2,esk7_0)
| ~ in(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( in(X1,esk7_0)
| ~ in(X1,esk5_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X1,esk6_0)
| ~ in(X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
( esk6_0 = X1
| in(esk8_2(esk6_0,X1),esk4_0)
| in(esk8_2(esk6_0,X1),X1)
| ~ in(X2,esk5_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_32,negated_conjecture,
esk5_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_33,negated_conjecture,
( esk6_0 = X1
| in(esk8_2(esk6_0,X1),esk4_0)
| in(esk8_2(esk6_0,X1),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_26]),c_0_32]) ).
cnf(c_0_34,negated_conjecture,
( in(X1,esk6_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_35,plain,
( X1 = X2
| ~ in(esk8_2(X1,X2),X1)
| ~ in(esk8_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_36,negated_conjecture,
( esk6_0 = esk4_0
| in(esk8_2(esk6_0,esk4_0),esk4_0) ),
inference(ef,[status(thm)],[c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( in(X1,esk6_0)
| ~ in(X2,esk5_0)
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_19]) ).
cnf(c_0_38,negated_conjecture,
( esk6_0 = esk4_0
| ~ in(esk8_2(esk6_0,esk4_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( in(X1,esk6_0)
| ~ in(X1,esk4_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_26]),c_0_32]) ).
cnf(c_0_40,negated_conjecture,
( in(X1,esk5_0)
| ~ in(X1,esk7_0)
| ~ in(X2,esk6_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_24]) ).
cnf(c_0_41,negated_conjecture,
esk6_0 = esk4_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_36]) ).
cnf(c_0_42,negated_conjecture,
( in(X1,esk5_0)
| ~ in(X1,esk7_0)
| ~ in(X2,esk4_0) ),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,negated_conjecture,
( esk7_0 = X1
| in(esk8_2(esk7_0,X1),esk5_0)
| in(esk8_2(esk7_0,X1),X1)
| ~ in(X2,esk4_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_22]) ).
cnf(c_0_44,negated_conjecture,
( esk4_0 != esk6_0
| esk5_0 != esk7_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_45,negated_conjecture,
( esk7_0 = X1
| in(esk8_2(esk7_0,X1),esk5_0)
| in(esk8_2(esk7_0,X1),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_26]),c_0_27]) ).
cnf(c_0_46,negated_conjecture,
esk7_0 != esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_41])]) ).
cnf(c_0_47,negated_conjecture,
in(esk8_2(esk7_0,esk5_0),esk5_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_45]),c_0_46]) ).
cnf(c_0_48,negated_conjecture,
~ in(esk8_2(esk7_0,esk5_0),esk7_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_47]),c_0_46]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_29]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET980+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n021.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
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 13:45:26 EDT 2023
% 0.21/0.35 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.21/0.60 % Version : CSE_E---1.5
% 0.21/0.60 % Problem : theBenchmark.p
% 0.21/0.60 % Proof found
% 0.21/0.60 % SZS status Theorem for theBenchmark.p
% 0.21/0.60 % SZS output start Proof
% See solution above
% 0.21/0.61 % Total time : 0.020000 s
% 0.21/0.61 % SZS output end Proof
% 0.21/0.61 % Total time : 0.023000 s
%------------------------------------------------------------------------------