TSTP Solution File: SEU132+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU132+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 16:22:38 EDT 2023
% Result : Theorem 0.19s 0.70s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 26
% Syntax : Number of formulae : 55 ( 9 unt; 21 typ; 0 def)
% Number of atoms : 113 ( 23 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 126 ( 47 ~; 52 |; 16 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 15 >; 16 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 83 ( 7 sgn; 46 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_24,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_25,type,
subset: ( $i * $i ) > $o ).
tff(decl_26,type,
empty_set: $i ).
tff(decl_27,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_28,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_29,type,
empty: $i > $o ).
tff(decl_30,type,
esk1_1: $i > $i ).
tff(decl_31,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_33,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
esk6_0: $i ).
tff(decl_36,type,
esk7_0: $i ).
tff(decl_37,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk9_0: $i ).
tff(decl_39,type,
esk10_0: $i ).
tff(decl_40,type,
esk11_0: $i ).
tff(decl_41,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk13_2: ( $i * $i ) > $i ).
fof(t33_xboole_1,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t28_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
inference(assume_negation,[status(cth)],[t33_xboole_1]) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_7,plain,
! [X32,X33,X34,X35,X36,X37,X38,X39] :
( ( in(X35,X32)
| ~ in(X35,X34)
| X34 != set_intersection2(X32,X33) )
& ( in(X35,X33)
| ~ in(X35,X34)
| X34 != set_intersection2(X32,X33) )
& ( ~ in(X36,X32)
| ~ in(X36,X33)
| in(X36,X34)
| X34 != set_intersection2(X32,X33) )
& ( ~ in(esk4_3(X37,X38,X39),X39)
| ~ in(esk4_3(X37,X38,X39),X37)
| ~ in(esk4_3(X37,X38,X39),X38)
| X39 = set_intersection2(X37,X38) )
& ( in(esk4_3(X37,X38,X39),X37)
| in(esk4_3(X37,X38,X39),X39)
| X39 = set_intersection2(X37,X38) )
& ( in(esk4_3(X37,X38,X39),X38)
| in(esk4_3(X37,X38,X39),X39)
| X39 = set_intersection2(X37,X38) ) ),
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)],[d3_xboole_0])])])])])]) ).
fof(c_0_8,lemma,
! [X79,X80] :
( ~ subset(X79,X80)
| set_intersection2(X79,X80) = X79 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(c_0_9,negated_conjecture,
( subset(esk9_0,esk10_0)
& ~ subset(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_10,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48] :
( ( in(X44,X41)
| ~ in(X44,X43)
| X43 != set_difference(X41,X42) )
& ( ~ in(X44,X42)
| ~ in(X44,X43)
| X43 != set_difference(X41,X42) )
& ( ~ in(X45,X41)
| in(X45,X42)
| in(X45,X43)
| X43 != set_difference(X41,X42) )
& ( ~ in(esk5_3(X46,X47,X48),X48)
| ~ in(esk5_3(X46,X47,X48),X46)
| in(esk5_3(X46,X47,X48),X47)
| X48 = set_difference(X46,X47) )
& ( in(esk5_3(X46,X47,X48),X46)
| in(esk5_3(X46,X47,X48),X48)
| X48 = set_difference(X46,X47) )
& ( ~ in(esk5_3(X46,X47,X48),X47)
| in(esk5_3(X46,X47,X48),X48)
| X48 = set_difference(X46,X47) ) ),
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)],[c_0_6])])])])])]) ).
fof(c_0_11,plain,
! [X26,X27,X28,X29,X30] :
( ( ~ subset(X26,X27)
| ~ in(X28,X26)
| in(X28,X27) )
& ( in(esk3_2(X29,X30),X29)
| subset(X29,X30) )
& ( ~ in(esk3_2(X29,X30),X30)
| subset(X29,X30) ) ),
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)],[d3_tarski])])])])])]) ).
cnf(c_0_12,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
subset(esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
~ subset(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
set_intersection2(esk9_0,esk10_0) = esk9_0,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
in(esk3_2(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),set_difference(esk9_0,esk11_0)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,negated_conjecture,
( in(X1,esk10_0)
| ~ in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
in(esk3_2(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),esk9_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
in(esk3_2(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),esk10_0),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,plain,
( subset(X1,X2)
| ~ in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
( in(esk3_2(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),set_difference(esk10_0,X1))
| in(esk3_2(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( ~ in(X1,set_difference(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_31,negated_conjecture,
in(esk3_2(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),esk11_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_16]) ).
cnf(c_0_32,negated_conjecture,
~ in(esk3_2(set_difference(esk9_0,esk11_0),set_difference(esk10_0,esk11_0)),set_difference(X1,esk11_0)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_21,c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU132+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 12:34:41 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 0.19/0.70 % Version : CSE_E---1.5
% 0.19/0.70 % Problem : theBenchmark.p
% 0.19/0.70 % Proof found
% 0.19/0.70 % SZS status Theorem for theBenchmark.p
% 0.19/0.70 % SZS output start Proof
% See solution above
% 0.19/0.70 % Total time : 0.113000 s
% 0.19/0.70 % SZS output end Proof
% 0.19/0.70 % Total time : 0.117000 s
%------------------------------------------------------------------------------