TSTP Solution File: SET618+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET618+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 : 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 14:34:52 EDT 2023
% Result : Theorem 0.21s 0.59s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 27 ( 16 unt; 11 typ; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn; 10 !; 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,
empty_set: $i ).
tff(decl_26,type,
member: ( $i * $i ) > $o ).
tff(decl_27,type,
subset: ( $i * $i ) > $o ).
tff(decl_28,type,
empty: $i > $o ).
tff(decl_29,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_31,type,
esk3_1: $i > $i ).
tff(decl_32,type,
esk4_0: $i ).
fof(prove_th93,conjecture,
! [X1] : symmetric_difference(X1,X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th93) ).
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(self_difference_is_empty_set,axiom,
! [X1] : difference(X1,X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_difference_is_empty_set) ).
fof(idempotency_of_union,axiom,
! [X1] : union(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotency_of_union) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] : symmetric_difference(X1,X1) = empty_set,
inference(assume_negation,[status(cth)],[prove_th93]) ).
fof(c_0_5,negated_conjecture,
symmetric_difference(esk4_0,esk4_0) != empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_6,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_7,negated_conjecture,
symmetric_difference(esk4_0,esk4_0) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X7] : difference(X7,X7) = empty_set,
inference(variable_rename,[status(thm)],[self_difference_is_empty_set]) ).
cnf(c_0_10,negated_conjecture,
union(difference(esk4_0,esk4_0),difference(esk4_0,esk4_0)) != empty_set,
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
difference(X1,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X6] : union(X6,X6) = X6,
inference(variable_rename,[status(thm)],[idempotency_of_union]) ).
cnf(c_0_13,negated_conjecture,
union(empty_set,empty_set) != empty_set,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).
cnf(c_0_14,plain,
union(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET618+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n008.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 11:10:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.59 % Version : CSE_E---1.5
% 0.21/0.59 % Problem : theBenchmark.p
% 0.21/0.59 % Proof found
% 0.21/0.59 % SZS status Theorem for theBenchmark.p
% 0.21/0.60 % SZS output start Proof
% See solution above
% 0.21/0.60 % Total time : 0.005000 s
% 0.21/0.60 % SZS output end Proof
% 0.21/0.60 % Total time : 0.008000 s
%------------------------------------------------------------------------------