TSTP Solution File: SET599+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET599+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 14:34:43 EDT 2023
% Result : Theorem 0.21s 0.58s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of formulae : 21 ( 12 unt; 9 typ; 0 def)
% Number of atoms : 12 ( 3 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 1 sgn; 12 !; 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 ).
fof(prove_th58,conjecture,
! [X1,X2] : subset(difference(X1,X2),symmetric_difference(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th58) ).
fof(symmetric_difference_defn,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(subset_of_union,axiom,
! [X1,X2] : subset(X1,union(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_of_union) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2] : subset(difference(X1,X2),symmetric_difference(X1,X2)),
inference(assume_negation,[status(cth)],[prove_th58]) ).
fof(c_0_4,negated_conjecture,
~ subset(difference(esk3_0,esk4_0),symmetric_difference(esk3_0,esk4_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(difference(esk3_0,esk4_0),symmetric_difference(esk3_0,esk4_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] : subset(X6,union(X6,X7)),
inference(variable_rename,[status(thm)],[subset_of_union]) ).
cnf(c_0_9,negated_conjecture,
~ subset(difference(esk3_0,esk4_0),union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))),
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
subset(X1,union(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET599+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 14:02:09 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 0.21/0.58 % Version : CSE_E---1.5
% 0.21/0.58 % Problem : theBenchmark.p
% 0.21/0.58 % Proof found
% 0.21/0.58 % SZS status Theorem for theBenchmark.p
% 0.21/0.58 % SZS output start Proof
% See solution above
% 0.21/0.58 % Total time : 0.006000 s
% 0.21/0.58 % SZS output end Proof
% 0.21/0.58 % Total time : 0.009000 s
%------------------------------------------------------------------------------