TSTP Solution File: SET577+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET577+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 : n004.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 14:34:35 EDT 2023
% Result : Theorem 0.20s 0.62s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 54 ( 12 unt; 8 typ; 0 def)
% Number of atoms : 132 ( 22 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 126 ( 40 ~; 63 |; 13 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 87 ( 3 sgn; 40 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
union: ( $i * $i ) > $i ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
subset: ( $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(prove_th18,conjecture,
! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
| member(X4,X3) ) )
=> X1 = union(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th18) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X2)
| member(X4,X3) ) )
=> X1 = union(X2,X3) ),
inference(assume_negation,[status(cth)],[prove_th18]) ).
fof(c_0_7,plain,
! [X12,X13,X14,X15,X16] :
( ( ~ subset(X12,X13)
| ~ member(X14,X12)
| member(X14,X13) )
& ( member(esk1_2(X15,X16),X15)
| subset(X15,X16) )
& ( ~ member(esk1_2(X15,X16),X16)
| subset(X15,X16) ) ),
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)],[subset_defn])])])])])]) ).
fof(c_0_8,plain,
! [X5,X6,X7] :
( ( ~ member(X7,union(X5,X6))
| member(X7,X5)
| member(X7,X6) )
& ( ~ member(X7,X5)
| member(X7,union(X5,X6)) )
& ( ~ member(X7,X6)
| member(X7,union(X5,X6)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
fof(c_0_9,negated_conjecture,
! [X29] :
( ( ~ member(X29,esk3_0)
| member(X29,esk4_0)
| member(X29,esk5_0) )
& ( ~ member(X29,esk4_0)
| member(X29,esk3_0) )
& ( ~ member(X29,esk5_0)
| member(X29,esk3_0) )
& esk3_0 != union(esk4_0,esk5_0) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( member(X1,esk4_0)
| member(X1,esk5_0)
| ~ member(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( subset(esk3_0,X1)
| member(esk1_2(esk3_0,X1),esk5_0)
| member(esk1_2(esk3_0,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_17,plain,
! [X10,X11] : union(X10,X11) = union(X11,X10),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_18,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( subset(esk3_0,union(esk5_0,X1))
| member(esk1_2(esk3_0,union(esk5_0,X1)),esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
subset(esk3_0,union(esk4_0,esk5_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_23,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_24,plain,
! [X19,X20,X21,X22,X23,X24] :
( ( ~ member(X21,X19)
| member(X21,X20)
| X19 != X20 )
& ( ~ member(X22,X20)
| member(X22,X19)
| X19 != X20 )
& ( ~ member(esk2_2(X23,X24),X23)
| ~ member(esk2_2(X23,X24),X24)
| X23 = X24 )
& ( member(esk2_2(X23,X24),X23)
| member(esk2_2(X23,X24),X24)
| X23 = X24 ) ),
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)],[equal_member_defn])])])])])]) ).
cnf(c_0_25,negated_conjecture,
( member(X1,union(esk4_0,esk5_0))
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( subset(union(X1,X2),X3)
| member(esk1_2(union(X1,X2),X3),X1)
| member(esk1_2(union(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_27,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_28,plain,
! [X8,X9] :
( ( subset(X8,X9)
| X8 != X9 )
& ( subset(X9,X8)
| X8 != X9 )
& ( ~ subset(X8,X9)
| ~ subset(X9,X8)
| X8 = X9 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_29,negated_conjecture,
( subset(X1,union(esk4_0,esk5_0))
| ~ member(esk1_2(X1,union(esk4_0,esk5_0)),esk3_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_25]) ).
cnf(c_0_30,plain,
( subset(union(X1,X2),X2)
| member(esk1_2(union(X1,X2),X2),X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( esk3_0 = X1
| member(esk2_2(esk3_0,X1),esk5_0)
| member(esk2_2(esk3_0,X1),esk4_0)
| member(esk2_2(esk3_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_27]) ).
cnf(c_0_32,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,negated_conjecture,
subset(union(esk3_0,union(esk4_0,esk5_0)),union(esk4_0,esk5_0)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_35,negated_conjecture,
( union(X1,X2) = esk3_0
| member(esk2_2(esk3_0,union(X1,X2)),esk4_0)
| member(esk2_2(esk3_0,union(X1,X2)),esk5_0)
| member(esk2_2(esk3_0,union(X1,X2)),X1)
| member(esk2_2(esk3_0,union(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
union(esk3_0,union(esk4_0,esk5_0)) = union(esk4_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_37,negated_conjecture,
esk3_0 != union(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_38,negated_conjecture,
member(esk2_2(esk3_0,union(esk4_0,esk5_0)),union(esk4_0,esk5_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_12]),c_0_14]),c_0_11]) ).
cnf(c_0_39,plain,
( X1 = X2
| ~ member(esk2_2(X1,X2),X1)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_40,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_41,negated_conjecture,
( member(esk2_2(esk3_0,union(esk4_0,esk5_0)),esk4_0)
| member(esk2_2(esk3_0,union(esk4_0,esk5_0)),esk5_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
~ member(esk2_2(esk3_0,union(esk4_0,esk5_0)),esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_38]),c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_44,negated_conjecture,
member(esk2_2(esk3_0,union(esk4_0,esk5_0)),esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET577+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 10:06:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.62 % Version : CSE_E---1.5
% 0.20/0.62 % Problem : theBenchmark.p
% 0.20/0.62 % Proof found
% 0.20/0.62 % SZS status Theorem for theBenchmark.p
% 0.20/0.62 % SZS output start Proof
% See solution above
% 0.20/0.62 % Total time : 0.037000 s
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time : 0.040000 s
%------------------------------------------------------------------------------