TSTP Solution File: SET633+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET633+3 : TPTP v8.1.2. Released v2.2.0.
% 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 14:34:58 EDT 2023
% Result : Theorem 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 13
% Syntax : Number of formulae : 24 ( 8 unt; 10 typ; 0 def)
% Number of atoms : 26 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 8 ~; 4 |; 5 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 7 >; 7 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn; 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
symmetric_difference: ( $i * $i ) > $i ).
tff(decl_23,type,
difference: ( $i * $i ) > $i ).
tff(decl_24,type,
union: ( $i * $i ) > $i ).
tff(decl_25,type,
subset: ( $i * $i ) > $o ).
tff(decl_26,type,
member: ( $i * $i ) > $o ).
tff(decl_27,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk3_0: $i ).
tff(decl_30,type,
esk4_0: $i ).
tff(decl_31,type,
esk5_0: $i ).
fof(prove_th115,conjecture,
! [X1,X2,X3] :
( ( subset(difference(X1,X2),X3)
& subset(difference(X2,X1),X3) )
=> subset(symmetric_difference(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th115) ).
fof(symmetric_difference_defn,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(union_subset,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(union(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_subset) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(difference(X1,X2),X3)
& subset(difference(X2,X1),X3) )
=> subset(symmetric_difference(X1,X2),X3) ),
inference(assume_negation,[status(cth)],[prove_th115]) ).
fof(c_0_4,negated_conjecture,
( subset(difference(esk3_0,esk4_0),esk5_0)
& subset(difference(esk4_0,esk3_0),esk5_0)
& ~ subset(symmetric_difference(esk3_0,esk4_0),esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_5,plain,
! [X4,X5] : symmetric_difference(X4,X5) = union(difference(X4,X5),difference(X5,X4)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
cnf(c_0_6,negated_conjecture,
~ subset(symmetric_difference(esk3_0,esk4_0),esk5_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X6,X7,X8] :
( ~ subset(X6,X7)
| ~ subset(X8,X7)
| subset(union(X6,X8),X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_subset])]) ).
cnf(c_0_9,negated_conjecture,
~ subset(union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)),esk5_0),
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
( subset(union(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
subset(difference(esk4_0,esk3_0),esk5_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_12,negated_conjecture,
subset(difference(esk3_0,esk4_0),esk5_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET633+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 09:25:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.59 start to proof: theBenchmark
% 0.20/0.61 % Version : CSE_E---1.5
% 0.20/0.61 % Problem : theBenchmark.p
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark.p
% 0.20/0.61 % SZS output start Proof
% See solution above
% 0.20/0.61 % Total time : 0.008000 s
% 0.20/0.61 % SZS output end Proof
% 0.20/0.61 % Total time : 0.011000 s
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