TSTP Solution File: SET624+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET624+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 : n031.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 14:34:54 EDT 2023
% Result : Theorem 0.21s 0.60s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 45 ( 8 unt; 8 typ; 0 def)
% Number of atoms : 94 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 93 ( 36 ~; 45 |; 7 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 5 sgn; 27 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
union: ( $i * $i ) > $i ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
intersect: ( $i * $i ) > $o ).
tff(decl_25,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_26,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_27,type,
esk3_0: $i ).
tff(decl_28,type,
esk4_0: $i ).
tff(decl_29,type,
esk5_0: $i ).
fof(intersect_defn,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(prove_intersect_with_union,conjecture,
! [X1,X2,X3] :
( intersect(X1,union(X2,X3))
<=> ( intersect(X1,X2)
| intersect(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersect_with_union) ).
fof(symmetry_of_intersect,axiom,
! [X1,X2] :
( intersect(X1,X2)
=> intersect(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(c_0_5,plain,
! [X7,X8,X10,X11,X12] :
( ( member(esk1_2(X7,X8),X7)
| ~ intersect(X7,X8) )
& ( member(esk1_2(X7,X8),X8)
| ~ intersect(X7,X8) )
& ( ~ member(X12,X10)
| ~ member(X12,X11)
| intersect(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[intersect_defn])])])])])]) ).
cnf(c_0_6,plain,
( intersect(X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_7,plain,
( member(esk1_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
cnf(c_0_9,plain,
( intersect(X1,X2)
| ~ intersect(X3,X2)
| ~ member(esk1_2(X3,X2),X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X2,X3] :
( intersect(X1,union(X2,X3))
<=> ( intersect(X1,X2)
| intersect(X1,X3) ) ),
inference(assume_negation,[status(cth)],[prove_intersect_with_union]) ).
fof(c_0_12,plain,
! [X15,X16] :
( ~ intersect(X15,X16)
| intersect(X16,X15) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_of_intersect])]) ).
cnf(c_0_13,plain,
( intersect(union(X1,X2),X3)
| ~ intersect(X4,X3)
| ~ member(esk1_2(X4,X3),X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( member(esk1_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_15,negated_conjecture,
( ( ~ intersect(esk3_0,esk4_0)
| ~ intersect(esk3_0,union(esk4_0,esk5_0)) )
& ( ~ intersect(esk3_0,esk5_0)
| ~ intersect(esk3_0,union(esk4_0,esk5_0)) )
& ( intersect(esk3_0,union(esk4_0,esk5_0))
| intersect(esk3_0,esk4_0)
| intersect(esk3_0,esk5_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_16,plain,
( intersect(X2,X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( intersect(union(X1,X2),X3)
| ~ intersect(X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( ~ intersect(esk3_0,esk5_0)
| ~ intersect(esk3_0,union(esk4_0,esk5_0)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( intersect(X1,union(X2,X3))
| ~ intersect(X3,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( intersect(esk3_0,union(esk4_0,esk5_0))
| intersect(esk3_0,esk4_0)
| intersect(esk3_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
~ intersect(esk3_0,esk5_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_16]) ).
cnf(c_0_23,plain,
( member(esk1_2(X1,union(X2,X3)),X2)
| member(esk1_2(X1,union(X2,X3)),X3)
| ~ intersect(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_20,c_0_7]) ).
cnf(c_0_24,negated_conjecture,
( intersect(esk3_0,union(esk4_0,esk5_0))
| intersect(esk3_0,esk4_0) ),
inference(sr,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
( intersect(X1,X2)
| ~ intersect(X2,X3)
| ~ member(esk1_2(X2,X3),X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_14]) ).
cnf(c_0_26,negated_conjecture,
( intersect(esk3_0,esk4_0)
| member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk5_0)
| member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk4_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
( intersect(esk3_0,esk4_0)
| intersect(esk5_0,esk3_0)
| member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( intersect(esk5_0,esk3_0)
| intersect(esk4_0,esk3_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_27]),c_0_24]),c_0_16]) ).
cnf(c_0_29,negated_conjecture,
intersect(esk4_0,esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_28]),c_0_22]) ).
fof(c_0_30,plain,
! [X13,X14] : union(X13,X14) = union(X14,X13),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_31,negated_conjecture,
( ~ intersect(esk3_0,esk4_0)
| ~ intersect(esk3_0,union(esk4_0,esk5_0)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,negated_conjecture,
intersect(esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_16,c_0_29]) ).
cnf(c_0_33,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,negated_conjecture,
~ intersect(esk3_0,union(esk4_0,esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
cnf(c_0_35,plain,
( intersect(X1,union(X2,X3))
| ~ intersect(X2,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET624+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n031.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 14:22:38 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.21/0.60 % Version : CSE_E---1.5
% 0.21/0.60 % Problem : theBenchmark.p
% 0.21/0.60 % Proof found
% 0.21/0.60 % SZS status Theorem for theBenchmark.p
% 0.21/0.60 % SZS output start Proof
% See solution above
% 0.21/0.60 % Total time : 0.019000 s
% 0.21/0.60 % SZS output end Proof
% 0.21/0.60 % Total time : 0.022000 s
%------------------------------------------------------------------------------