TSTP Solution File: SET014+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET014+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 : n027.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 14:32:04 EDT 2023
% Result : Theorem 0.20s 0.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 53 ( 12 unt; 8 typ; 0 def)
% Number of atoms : 112 ( 15 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 99 ( 32 ~; 49 |; 11 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 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 : 85 ( 7 sgn; 33 !; 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_union_subset,conjecture,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(union(X1,X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_subset) ).
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(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(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(union(X1,X3),X2) ),
inference(assume_negation,[status(cth)],[prove_union_subset]) ).
fof(c_0_6,plain,
! [X7,X8,X9,X10,X11] :
( ( ~ subset(X7,X8)
| ~ member(X9,X7)
| member(X9,X8) )
& ( member(esk1_2(X10,X11),X10)
| subset(X10,X11) )
& ( ~ member(esk1_2(X10,X11),X11)
| subset(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)],[subset_defn])])])])])]) ).
fof(c_0_7,negated_conjecture,
( subset(esk3_0,esk4_0)
& subset(esk5_0,esk4_0)
& ~ subset(union(esk3_0,esk5_0),esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[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,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
subset(esk5_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X16,X17,X18,X19,X20,X21] :
( ( ~ member(X18,X16)
| member(X18,X17)
| X16 != X17 )
& ( ~ member(X19,X17)
| member(X19,X16)
| X16 != X17 )
& ( ~ member(esk2_2(X20,X21),X20)
| ~ member(esk2_2(X20,X21),X21)
| X20 = X21 )
& ( member(esk2_2(X20,X21),X20)
| member(esk2_2(X20,X21),X21)
| X20 = X21 ) ),
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_12,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
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,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_20,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,negated_conjecture,
( subset(esk5_0,X1)
| member(esk1_2(esk5_0,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_22,plain,
! [X13,X14] : union(X13,X14) = union(X14,X13),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_23,plain,
( union(X1,X2) = X3
| member(esk2_2(union(X1,X2),X3),X3)
| member(esk2_2(union(X1,X2),X3),X1)
| member(esk2_2(union(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( subset(esk3_0,X1)
| member(esk1_2(esk3_0,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_25,negated_conjecture,
subset(esk5_0,union(X1,esk4_0)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( union(X1,X1) = X2
| member(esk2_2(union(X1,X1),X2),X1)
| member(esk2_2(union(X1,X1),X2),X2) ),
inference(ef,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
subset(esk3_0,union(X1,esk4_0)),
inference(spm,[status(thm)],[c_0_20,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
subset(esk5_0,union(esk4_0,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ member(esk2_2(X1,X2),X1)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_31,plain,
( union(X1,X1) = X1
| member(esk2_2(union(X1,X1),X1),X1) ),
inference(ef,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
subset(esk3_0,union(esk4_0,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
( member(X1,union(esk4_0,X2))
| ~ member(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_29]) ).
cnf(c_0_34,plain,
( union(X1,X1) = X1
| ~ member(esk2_2(union(X1,X1),X1),union(X1,X1)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( member(X1,union(esk4_0,X2))
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( subset(X1,union(esk4_0,X2))
| ~ member(esk1_2(X1,union(esk4_0,X2)),esk5_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_33]) ).
cnf(c_0_37,plain,
union(X1,X1) = X1,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_14]),c_0_31]) ).
cnf(c_0_38,negated_conjecture,
( subset(X1,union(esk4_0,X2))
| ~ member(esk1_2(X1,union(esk4_0,X2)),esk3_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( subset(X1,esk4_0)
| ~ member(esk1_2(X1,esk4_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,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_17,c_0_16]) ).
cnf(c_0_41,negated_conjecture,
( subset(X1,esk4_0)
| ~ member(esk1_2(X1,esk4_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( subset(union(esk5_0,X1),esk4_0)
| member(esk1_2(union(esk5_0,X1),esk4_0),X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
~ subset(union(esk3_0,esk5_0),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_26]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET014+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
% 0.12/0.35 % Computer : n027.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sat Aug 26 12:47:49 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.20/0.60 start to proof: theBenchmark
% 0.20/0.63 % Version : CSE_E---1.5
% 0.20/0.63 % Problem : theBenchmark.p
% 0.20/0.63 % Proof found
% 0.20/0.63 % SZS status Theorem for theBenchmark.p
% 0.20/0.63 % SZS output start Proof
% See solution above
% 0.20/0.64 % Total time : 0.019000 s
% 0.20/0.64 % SZS output end Proof
% 0.20/0.64 % Total time : 0.021000 s
%------------------------------------------------------------------------------