TSTP Solution File: SET620+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET620+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 : n008.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 14:34:53 EDT 2023
% Result : Theorem 0.19s 0.55s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of formulae : 35 ( 25 unt; 10 typ; 0 def)
% Number of atoms : 25 ( 24 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 : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 8 >; 8 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn; 26 !; 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,
intersection: ( $i * $i ) > $i ).
tff(decl_26,type,
member: ( $i * $i ) > $o ).
tff(decl_27,type,
subset: ( $i * $i ) > $o ).
tff(decl_28,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk3_0: $i ).
tff(decl_31,type,
esk4_0: $i ).
fof(difference_distributes_over_union,axiom,
! [X1,X2,X3] : difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_distributes_over_union) ).
fof(difference_into_intersection,axiom,
! [X1,X2] : difference(X1,intersection(X1,X2)) = difference(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_into_intersection) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(prove_th96,conjecture,
! [X1,X2] : symmetric_difference(X1,X2) = difference(union(X1,X2),intersection(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th96) ).
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(c_0_6,plain,
! [X8,X9,X10] : difference(union(X8,X9),X10) = union(difference(X8,X10),difference(X9,X10)),
inference(variable_rename,[status(thm)],[difference_distributes_over_union]) ).
fof(c_0_7,plain,
! [X6,X7] : difference(X6,intersection(X6,X7)) = difference(X6,X7),
inference(variable_rename,[status(thm)],[difference_into_intersection]) ).
fof(c_0_8,plain,
! [X22,X23] : union(X22,X23) = union(X23,X22),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_9,plain,
! [X24,X25] : intersection(X24,X25) = intersection(X25,X24),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X2] : symmetric_difference(X1,X2) = difference(union(X1,X2),intersection(X1,X2)),
inference(assume_negation,[status(cth)],[prove_th96]) ).
cnf(c_0_11,plain,
difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
difference(X1,intersection(X1,X2)) = difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,negated_conjecture,
symmetric_difference(esk3_0,esk4_0) != difference(union(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_16,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_17,plain,
union(difference(X1,X2),difference(X3,intersection(X1,X2))) = difference(union(X3,X1),intersection(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_18,plain,
difference(X1,intersection(X2,X1)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
symmetric_difference(esk3_0,esk4_0) != difference(union(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
difference(union(X1,X2),intersection(X2,X1)) = union(difference(X2,X1),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)) != difference(union(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
difference(union(X1,X2),intersection(X1,X2)) = union(difference(X2,X1),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_14]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET620+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 15:40:17 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.53 start to proof: theBenchmark
% 0.19/0.55 % Version : CSE_E---1.5
% 0.19/0.55 % Problem : theBenchmark.p
% 0.19/0.55 % Proof found
% 0.19/0.55 % SZS status Theorem for theBenchmark.p
% 0.19/0.55 % SZS output start Proof
% See solution above
% 0.19/0.56 % Total time : 0.014000 s
% 0.19/0.56 % SZS output end Proof
% 0.19/0.56 % Total time : 0.016000 s
%------------------------------------------------------------------------------