TSTP Solution File: SET929+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET929+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 : n011.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 14:36:19 EDT 2023
% Result : Theorem 0.21s 0.61s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 34 ( 4 unt; 11 typ; 0 def)
% Number of atoms : 60 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 62 ( 25 ~; 25 |; 8 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 29 ( 2 sgn; 16 !; 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,
subset: ( $i * $i ) > $o ).
tff(decl_27,type,
set_difference: ( $i * $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(t73_zfmisc_1,conjecture,
! [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(t37_xboole_1,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(t38_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = empty_set
<=> ( in(X1,X3)
& in(X2,X3) ) ),
inference(assume_negation,[status(cth)],[t73_zfmisc_1]) ).
fof(c_0_4,negated_conjecture,
( ( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != empty_set
| ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk5_0) )
& ( in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = empty_set )
& ( in(esk4_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = empty_set ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
fof(c_0_5,plain,
! [X11,X12] :
( ( set_difference(X11,X12) != empty_set
| subset(X11,X12) )
& ( ~ subset(X11,X12)
| set_difference(X11,X12) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
cnf(c_0_6,negated_conjecture,
( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != empty_set
| ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X13,X14,X15] :
( ( in(X13,X15)
| ~ subset(unordered_pair(X13,X14),X15) )
& ( in(X14,X15)
| ~ subset(unordered_pair(X13,X14),X15) )
& ( ~ in(X13,X15)
| ~ in(X14,X15)
| subset(unordered_pair(X13,X14),X15) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])]) ).
cnf(c_0_9,plain,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
( in(esk4_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,negated_conjecture,
( ~ subset(unordered_pair(esk3_0,esk4_0),esk5_0)
| ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_12,plain,
( subset(unordered_pair(X1,X3),X2)
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( in(X1,X2)
| ~ subset(unordered_pair(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( subset(unordered_pair(esk3_0,esk4_0),esk5_0)
| in(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,negated_conjecture,
( ~ in(esk3_0,esk5_0)
| ~ in(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
in(esk4_0,esk5_0),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( subset(unordered_pair(esk3_0,esk4_0),esk5_0)
| in(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
~ in(esk3_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_20,plain,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
subset(unordered_pair(esk3_0,esk4_0),esk5_0),
inference(sr,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET929+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n011.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 09:22:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.59 start to proof: theBenchmark
% 0.21/0.61 % Version : CSE_E---1.5
% 0.21/0.61 % Problem : theBenchmark.p
% 0.21/0.61 % Proof found
% 0.21/0.61 % SZS status Theorem for theBenchmark.p
% 0.21/0.61 % SZS output start Proof
% See solution above
% 0.21/0.62 % Total time : 0.005000 s
% 0.21/0.62 % SZS output end Proof
% 0.21/0.62 % Total time : 0.008000 s
%------------------------------------------------------------------------------