TSTP Solution File: SET930+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET930+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 : n024.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 14:36:20 EDT 2023
% Result : Theorem 0.16s 0.56s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 48 ( 12 unt; 11 typ; 0 def)
% Number of atoms : 99 ( 51 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 116 ( 54 ~; 34 |; 21 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 68 ( 2 sgn; 40 !; 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,
empty: $i > $o ).
tff(decl_26,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_27,type,
singleton: $i > $i ).
tff(decl_28,type,
esk1_0: $i ).
tff(decl_29,type,
esk2_0: $i ).
tff(decl_30,type,
esk3_0: $i ).
tff(decl_31,type,
esk4_0: $i ).
tff(decl_32,type,
esk5_0: $i ).
fof(l39_zfmisc_1,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(t72_zfmisc_1,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
<=> ( ~ in(X1,X3)
& ~ in(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t74_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( set_difference(unordered_pair(X1,X2),X3) != empty_set
& set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
& set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_zfmisc_1) ).
fof(t73_zfmisc_1,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = empty_set
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
inference(fof_simplification,[status(thm)],[l39_zfmisc_1]) ).
fof(c_0_7,plain,
! [X8,X9,X10] :
( ( ~ in(X8,X10)
| set_difference(unordered_pair(X8,X9),X10) != singleton(X8) )
& ( in(X9,X10)
| X8 = X9
| set_difference(unordered_pair(X8,X9),X10) != singleton(X8) )
& ( ~ in(X9,X10)
| in(X8,X10)
| set_difference(unordered_pair(X8,X9),X10) = singleton(X8) )
& ( X8 != X9
| in(X8,X10)
| set_difference(unordered_pair(X8,X9),X10) = singleton(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
<=> ( ~ in(X1,X3)
& ~ in(X2,X3) ) ),
inference(fof_simplification,[status(thm)],[t72_zfmisc_1]) ).
fof(c_0_9,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_0_10,plain,
( in(X1,X3)
| set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X13,X14,X15] :
( ( ~ in(X13,X15)
| set_difference(unordered_pair(X13,X14),X15) != unordered_pair(X13,X14) )
& ( ~ in(X14,X15)
| set_difference(unordered_pair(X13,X14),X15) != unordered_pair(X13,X14) )
& ( in(X13,X15)
| in(X14,X15)
| set_difference(unordered_pair(X13,X14),X15) = unordered_pair(X13,X14) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X4,X5] :
( ~ in(X4,X5)
| ~ in(X5,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
cnf(c_0_13,plain,
( set_difference(unordered_pair(X1,X1),X2) = singleton(X1)
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( in(X1,X2)
| in(X3,X2)
| set_difference(unordered_pair(X1,X3),X2) = unordered_pair(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( set_difference(unordered_pair(X1,X2),X3) != empty_set
& set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
& set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2) ),
inference(assume_negation,[status(cth)],[t74_zfmisc_1]) ).
cnf(c_0_16,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( unordered_pair(X1,X1) = singleton(X1)
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_18,negated_conjecture,
( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != empty_set
& set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0)
& set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk4_0)
& set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != unordered_pair(esk3_0,esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_19,plain,
! [X16,X17,X18] :
( ( in(X16,X18)
| set_difference(unordered_pair(X16,X17),X18) != empty_set )
& ( in(X17,X18)
| set_difference(unordered_pair(X16,X17),X18) != empty_set )
& ( ~ in(X16,X18)
| ~ in(X17,X18)
| set_difference(unordered_pair(X16,X17),X18) = empty_set ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t73_zfmisc_1])])]) ).
cnf(c_0_20,plain,
( unordered_pair(X1,X1) = singleton(X1)
| ~ in(X2,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( set_difference(unordered_pair(X1,X3),X2) = empty_set
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
( unordered_pair(X1,X1) = singleton(X1)
| unordered_pair(X2,X2) = singleton(X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
fof(c_0_24,plain,
! [X6,X7] : unordered_pair(X6,X7) = unordered_pair(X7,X6),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_25,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( in(X3,X2)
| set_difference(unordered_pair(X3,X1),X2) = singleton(X3)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,negated_conjecture,
( ~ in(esk4_0,esk5_0)
| ~ in(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(ef,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != unordered_pair(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_32,negated_conjecture,
~ in(esk4_0,esk5_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_33,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != unordered_pair(esk4_0,esk4_0),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( set_difference(unordered_pair(X1,X2),X3) = singleton(X2)
| in(X2,X3)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
in(esk3_0,esk5_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_14]),c_0_32]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]),c_0_35])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.31 % Computer : n024.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sat Aug 26 09:17:24 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.54 start to proof: theBenchmark
% 0.16/0.56 % Version : CSE_E---1.5
% 0.16/0.56 % Problem : theBenchmark.p
% 0.16/0.56 % Proof found
% 0.16/0.56 % SZS status Theorem for theBenchmark.p
% 0.16/0.56 % SZS output start Proof
% See solution above
% 0.16/0.57 % Total time : 0.012000 s
% 0.16/0.57 % SZS output end Proof
% 0.16/0.57 % Total time : 0.015000 s
%------------------------------------------------------------------------------