TSTP Solution File: SET628+3 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET628+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 14:34:56 EDT 2023
% Result : Theorem 0.20s 0.58s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 45 ( 9 unt; 9 typ; 0 def)
% Number of atoms : 89 ( 16 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 92 ( 39 ~; 36 |; 9 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 7 >; 5 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 4 sgn; 32 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
intersect: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
empty_set: $i ).
tff(decl_25,type,
not_equal: ( $i * $i ) > $o ).
tff(decl_26,type,
empty: $i > $o ).
tff(decl_27,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk3_1: $i > $i ).
tff(decl_30,type,
esk4_0: $i ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
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(prove_th110,conjecture,
! [X1] :
( intersect(X1,X1)
<=> not_equal(X1,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th110) ).
fof(not_equal_defn,axiom,
! [X1,X2] :
( not_equal(X1,X2)
<=> X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
fof(c_0_6,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_7,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(c_0_8,plain,
! [X10] : ~ member(X10,empty_set),
inference(variable_rename,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( ~ member(X13,X11)
| member(X13,X12)
| X11 != X12 )
& ( ~ member(X14,X12)
| member(X14,X11)
| X11 != X12 )
& ( ~ member(esk2_2(X15,X16),X15)
| ~ member(esk2_2(X15,X16),X16)
| X15 = X16 )
& ( member(esk2_2(X15,X16),X15)
| member(esk2_2(X15,X16),X16)
| 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)],[equal_member_defn])])])])])]) ).
fof(c_0_10,plain,
! [X4,X5,X7,X8,X9] :
( ( member(esk1_2(X4,X5),X4)
| ~ intersect(X4,X5) )
& ( member(esk1_2(X4,X5),X5)
| ~ intersect(X4,X5) )
& ( ~ member(X9,X7)
| ~ member(X9,X8)
| intersect(X7,X8) ) ),
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])])])])])]) ).
fof(c_0_11,plain,
! [X22,X23,X24] :
( ( ~ empty(X22)
| ~ member(X23,X22) )
& ( member(esk3_1(X24),X24)
| empty(X24) ) ),
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_7])])])])]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( intersect(X1,X1)
<=> not_equal(X1,empty_set) ),
inference(assume_negation,[status(cth)],[prove_th110]) ).
cnf(c_0_13,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( intersect(X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( member(esk3_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,negated_conjecture,
( ( ~ intersect(esk4_0,esk4_0)
| ~ not_equal(esk4_0,empty_set) )
& ( intersect(esk4_0,esk4_0)
| not_equal(esk4_0,empty_set) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_18,plain,
! [X18,X19] :
( ( ~ not_equal(X18,X19)
| X18 != X19 )
& ( X18 = X19
| not_equal(X18,X19) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[not_equal_defn])]) ).
cnf(c_0_19,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
( empty_set = X1
| member(esk2_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,plain,
( empty(X1)
| intersect(X2,X1)
| ~ member(esk3_1(X1),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( ~ intersect(esk4_0,esk4_0)
| ~ not_equal(esk4_0,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( X1 = X2
| not_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( empty_set = X1
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( empty(X1)
| intersect(X1,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_26,plain,
( member(esk1_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,negated_conjecture,
( empty_set = esk4_0
| ~ intersect(esk4_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( empty_set = X1
| intersect(X1,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
( ~ not_equal(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_30,plain,
~ intersect(X1,empty_set),
inference(spm,[status(thm)],[c_0_13,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
empty_set = esk4_0,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( intersect(esk4_0,esk4_0)
| not_equal(esk4_0,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,plain,
~ not_equal(X1,X1),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_34,plain,
~ intersect(X1,esk4_0),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_31]),c_0_33]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET628+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n031.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 : Sat Aug 26 15:24:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.58 % Version : CSE_E---1.5
% 0.20/0.58 % Problem : theBenchmark.p
% 0.20/0.58 % Proof found
% 0.20/0.58 % SZS status Theorem for theBenchmark.p
% 0.20/0.58 % SZS output start Proof
% See solution above
% 0.20/0.59 % Total time : 0.008000 s
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59 % Total time : 0.010000 s
%------------------------------------------------------------------------------