TSTP Solution File: SET015+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET015+4 : 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 : n015.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 14:32:07 EDT 2023
% Result : Theorem 0.21s 0.66s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 55 ( 11 unt; 17 typ; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 94 ( 47 ~; 36 |; 7 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 14 >; 10 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 2 sgn; 22 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
equal_set: ( $i * $i ) > $o ).
tff(decl_25,type,
power_set: $i > $i ).
tff(decl_26,type,
intersection: ( $i * $i ) > $i ).
tff(decl_27,type,
union: ( $i * $i ) > $i ).
tff(decl_28,type,
empty_set: $i ).
tff(decl_29,type,
difference: ( $i * $i ) > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_32,type,
sum: $i > $i ).
tff(decl_33,type,
product: $i > $i ).
tff(decl_34,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk4_0: $i ).
tff(decl_38,type,
esk5_0: $i ).
fof(thI07,conjecture,
! [X1,X2] : equal_set(union(X1,X2),union(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI07) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(union,axiom,
! [X3,X1,X2] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',union) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] : equal_set(union(X1,X2),union(X2,X1)),
inference(assume_negation,[status(cth)],[thI07]) ).
fof(c_0_5,negated_conjecture,
~ equal_set(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_6,plain,
! [X12,X13] :
( ( subset(X12,X13)
| ~ equal_set(X12,X13) )
& ( subset(X13,X12)
| ~ equal_set(X12,X13) )
& ( ~ subset(X12,X13)
| ~ subset(X13,X12)
| equal_set(X12,X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
cnf(c_0_7,negated_conjecture,
~ equal_set(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X6,X7,X8,X9,X10] :
( ( ~ subset(X6,X7)
| ~ member(X8,X6)
| member(X8,X7) )
& ( member(esk1_2(X9,X10),X9)
| subset(X9,X10) )
& ( ~ member(esk1_2(X9,X10),X10)
| subset(X9,X10) ) ),
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])])])])])]) ).
cnf(c_0_10,negated_conjecture,
( ~ subset(union(esk5_0,esk4_0),union(esk4_0,esk5_0))
| ~ subset(union(esk4_0,esk5_0),union(esk5_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,negated_conjecture,
( ~ member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),union(esk4_0,esk5_0))
| ~ subset(union(esk4_0,esk5_0),union(esk5_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_13,plain,
! [X19,X20,X21] :
( ( ~ member(X19,union(X20,X21))
| member(X19,X20)
| member(X19,X21) )
& ( ~ member(X19,X20)
| member(X19,union(X20,X21)) )
& ( ~ member(X19,X21)
| member(X19,union(X20,X21)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union])])]) ).
cnf(c_0_14,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( ~ member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),union(esk4_0,esk5_0))
| ~ member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),union(esk5_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_16,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),union(esk4_0,esk5_0))
| ~ member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),union(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( ~ member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),union(esk5_0,esk4_0))
| ~ member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( ~ member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),union(esk5_0,esk4_0))
| ~ member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),esk5_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),union(esk5_0,esk4_0))
| ~ subset(union(esk4_0,esk5_0),union(esk5_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_22,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,negated_conjecture,
( member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),union(esk4_0,esk5_0))
| ~ member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),esk4_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( ~ member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),esk4_0)
| ~ member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),esk4_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_25,negated_conjecture,
( ~ member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),esk4_0)
| ~ member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),esk5_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),union(esk4_0,esk5_0))
| ~ member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),esk5_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_27,negated_conjecture,
( ~ member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),esk5_0)
| ~ member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),esk4_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_28,negated_conjecture,
( ~ member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),esk5_0)
| ~ member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),esk5_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_29,negated_conjecture,
( member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),union(esk5_0,esk4_0))
| ~ member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),union(esk5_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_11]) ).
cnf(c_0_30,negated_conjecture,
~ member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),esk4_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]) ).
cnf(c_0_31,negated_conjecture,
~ member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),esk5_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_26]),c_0_27]),c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),union(esk4_0,esk5_0))
| member(esk1_2(union(esk5_0,esk4_0),union(esk4_0,esk5_0)),union(esk5_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_14]) ).
cnf(c_0_33,negated_conjecture,
~ member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),union(esk5_0,esk4_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_29]),c_0_30]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),union(esk4_0,esk5_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_32]),c_0_30]),c_0_31]) ).
cnf(c_0_35,negated_conjecture,
~ member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),esk5_0),
inference(spm,[status(thm)],[c_0_33,c_0_16]) ).
cnf(c_0_36,negated_conjecture,
~ member(esk1_2(union(esk4_0,esk5_0),union(esk5_0,esk4_0)),esk4_0),
inference(spm,[status(thm)],[c_0_33,c_0_17]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_34]),c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET015+4 : 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
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 11:32:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.63 start to proof: theBenchmark
% 0.21/0.66 % Version : CSE_E---1.5
% 0.21/0.66 % Problem : theBenchmark.p
% 0.21/0.66 % Proof found
% 0.21/0.66 % SZS status Theorem for theBenchmark.p
% 0.21/0.66 % SZS output start Proof
% See solution above
% 0.21/0.66 % Total time : 0.019000 s
% 0.21/0.66 % SZS output end Proof
% 0.21/0.66 % Total time : 0.022000 s
%------------------------------------------------------------------------------