TSTP Solution File: SWV370+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV370+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n021.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 21:38:17 EDT 2023
% Result : Theorem 0.21s 0.66s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 60
% Syntax : Number of formulae : 94 ( 9 unt; 55 typ; 0 def)
% Number of atoms : 97 ( 17 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 92 ( 34 ~; 41 |; 8 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 76 ( 45 >; 31 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 36 ( 36 usr; 10 con; 0-3 aty)
% Number of variables : 121 ( 26 sgn; 53 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
less_than: ( $i * $i ) > $o ).
tff(decl_23,type,
strictly_less_than: ( $i * $i ) > $o ).
tff(decl_24,type,
bottom: $i ).
tff(decl_25,type,
create_pq: $i ).
tff(decl_26,type,
isnonempty_pq: $i > $o ).
tff(decl_27,type,
insert_pq: ( $i * $i ) > $i ).
tff(decl_28,type,
contains_pq: ( $i * $i ) > $o ).
tff(decl_29,type,
issmallestelement_pq: ( $i * $i ) > $o ).
tff(decl_30,type,
remove_pq: ( $i * $i ) > $i ).
tff(decl_31,type,
findmin_pq_eff: ( $i * $i ) > $i ).
tff(decl_32,type,
findmin_pq_res: ( $i * $i ) > $i ).
tff(decl_33,type,
removemin_pq_eff: ( $i * $i ) > $i ).
tff(decl_34,type,
removemin_pq_res: ( $i * $i ) > $i ).
tff(decl_35,type,
create_slb: $i ).
tff(decl_36,type,
isnonempty_slb: $i > $o ).
tff(decl_37,type,
pair: ( $i * $i ) > $i ).
tff(decl_38,type,
insert_slb: ( $i * $i ) > $i ).
tff(decl_39,type,
contains_slb: ( $i * $i ) > $o ).
tff(decl_40,type,
pair_in_list: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
remove_slb: ( $i * $i ) > $i ).
tff(decl_42,type,
lookup_slb: ( $i * $i ) > $i ).
tff(decl_43,type,
update_slb: ( $i * $i ) > $i ).
tff(decl_44,type,
succ_cpq: ( $i * $i ) > $o ).
tff(decl_45,type,
insert_cpq: ( $i * $i ) > $i ).
tff(decl_46,type,
remove_cpq: ( $i * $i ) > $i ).
tff(decl_47,type,
findmin_cpq_eff: $i > $i ).
tff(decl_48,type,
removemin_cpq_eff: $i > $i ).
tff(decl_49,type,
triple: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
check_cpq: $i > $o ).
tff(decl_51,type,
contains_cpq: ( $i * $i ) > $o ).
tff(decl_52,type,
bad: $i ).
tff(decl_53,type,
ok: $i > $o ).
tff(decl_54,type,
insert_pqp: ( $i * $i ) > $i ).
tff(decl_55,type,
remove_pqp: ( $i * $i ) > $i ).
tff(decl_56,type,
findmin_pqp_res: $i > $i ).
tff(decl_57,type,
findmin_cpq_res: $i > $i ).
tff(decl_58,type,
removemin_cpq_res: $i > $i ).
tff(decl_59,type,
i: $i > $i ).
tff(decl_60,type,
pi_sharp_remove: ( $i * $i ) > $o ).
tff(decl_61,type,
pi_remove: ( $i * $i ) > $o ).
tff(decl_62,type,
pi_sharp_find_min: ( $i * $i ) > $o ).
tff(decl_63,type,
pi_find_min: $i > $o ).
tff(decl_64,type,
pi_sharp_removemin: ( $i * $i ) > $o ).
tff(decl_65,type,
pi_removemin: $i > $o ).
tff(decl_66,type,
phi: $i > $o ).
tff(decl_67,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_68,type,
esk2_1: $i > $i ).
tff(decl_69,type,
esk3_1: $i > $i ).
tff(decl_70,type,
esk4_1: $i > $i ).
tff(decl_71,type,
esk5_0: $i ).
tff(decl_72,type,
esk6_0: $i ).
tff(decl_73,type,
esk7_0: $i ).
tff(decl_74,type,
esk8_0: $i ).
tff(decl_75,type,
esk9_0: $i ).
tff(decl_76,type,
esk10_0: $i ).
fof(l6_co,conjecture,
! [X1] :
( ! [X2,X3,X4] :
( contains_cpq(triple(X2,X1,X3),X4)
<=> contains_pq(i(triple(X2,X1,X3)),X4) )
=> ! [X5,X6,X7,X8,X9] :
( contains_cpq(triple(X5,insert_slb(X1,pair(X7,X8)),X6),X9)
<=> contains_pq(i(triple(X5,insert_slb(X1,pair(X7,X8)),X6)),X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l6_co) ).
fof(ax39,axiom,
! [X1,X2,X3,X4] :
( contains_cpq(triple(X1,X2,X3),X4)
<=> contains_slb(X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax39) ).
fof(ax9,axiom,
! [X1,X2,X3] :
( contains_pq(insert_pq(X1,X2),X3)
<=> ( contains_pq(X1,X3)
| X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+1.ax',ax9) ).
fof(ax55,axiom,
! [X1,X2,X3,X4,X5] : i(triple(X1,insert_slb(X2,pair(X4,X5)),X3)) = insert_pq(i(triple(X1,X2,X3)),X4),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+4.ax',ax55) ).
fof(ax21,axiom,
! [X1,X2,X3,X4] :
( contains_slb(insert_slb(X1,pair(X2,X4)),X3)
<=> ( contains_slb(X1,X3)
| X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax21) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ! [X2,X3,X4] :
( contains_cpq(triple(X2,X1,X3),X4)
<=> contains_pq(i(triple(X2,X1,X3)),X4) )
=> ! [X5,X6,X7,X8,X9] :
( contains_cpq(triple(X5,insert_slb(X1,pair(X7,X8)),X6),X9)
<=> contains_pq(i(triple(X5,insert_slb(X1,pair(X7,X8)),X6)),X9) ) ),
inference(assume_negation,[status(cth)],[l6_co]) ).
fof(c_0_6,negated_conjecture,
! [X179,X180,X181] :
( ( ~ contains_cpq(triple(X179,esk5_0,X180),X181)
| contains_pq(i(triple(X179,esk5_0,X180)),X181) )
& ( ~ contains_pq(i(triple(X179,esk5_0,X180)),X181)
| contains_cpq(triple(X179,esk5_0,X180),X181) )
& ( ~ contains_cpq(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0),esk10_0)
| ~ contains_pq(i(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0)),esk10_0) )
& ( contains_cpq(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0),esk10_0)
| contains_pq(i(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0)),esk10_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_7,plain,
! [X108,X109,X110,X111] :
( ( ~ contains_cpq(triple(X108,X109,X110),X111)
| contains_slb(X109,X111) )
& ( ~ contains_slb(X109,X111)
| contains_cpq(triple(X108,X109,X110),X111) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax39])]) ).
fof(c_0_8,plain,
! [X22,X23,X24] :
( ( ~ contains_pq(insert_pq(X22,X23),X24)
| contains_pq(X22,X24)
| X23 = X24 )
& ( ~ contains_pq(X22,X24)
| contains_pq(insert_pq(X22,X23),X24) )
& ( X23 != X24
| contains_pq(insert_pq(X22,X23),X24) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax9])])]) ).
fof(c_0_9,plain,
! [X153,X154,X155,X156,X157] : i(triple(X153,insert_slb(X154,pair(X156,X157)),X155)) = insert_pq(i(triple(X153,X154,X155)),X156),
inference(variable_rename,[status(thm)],[ax55]) ).
cnf(c_0_10,negated_conjecture,
( ~ contains_cpq(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0),esk10_0)
| ~ contains_pq(i(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0)),esk10_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( contains_cpq(triple(X3,X1,X4),X2)
| ~ contains_slb(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( contains_pq(insert_pq(X1,X3),X2)
| ~ contains_pq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
i(triple(X1,insert_slb(X2,pair(X3,X4)),X5)) = insert_pq(i(triple(X1,X2,X5)),X3),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( contains_pq(X1,X3)
| X2 = X3
| ~ contains_pq(insert_pq(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( contains_slb(X2,X4)
| ~ contains_cpq(triple(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
( contains_cpq(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0),esk10_0)
| contains_pq(i(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0)),esk10_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
( ~ contains_slb(insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk10_0)
| ~ contains_pq(i(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0)),esk10_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_18,plain,
( contains_pq(i(triple(X1,insert_slb(X2,pair(X3,X4)),X5)),X6)
| ~ contains_pq(i(triple(X1,X2,X5)),X6) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( contains_pq(i(triple(X1,esk5_0,X2)),X3)
| ~ contains_cpq(triple(X1,esk5_0,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_20,plain,
! [X51,X52,X53,X54] :
( ( ~ contains_slb(insert_slb(X51,pair(X52,X54)),X53)
| contains_slb(X51,X53)
| X52 = X53 )
& ( ~ contains_slb(X51,X53)
| contains_slb(insert_slb(X51,pair(X52,X54)),X53) )
& ( X52 != X53
| contains_slb(insert_slb(X51,pair(X52,X54)),X53) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
cnf(c_0_21,negated_conjecture,
( contains_cpq(triple(X1,esk5_0,X2),X3)
| ~ contains_pq(i(triple(X1,esk5_0,X2)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,plain,
( X1 = X2
| contains_pq(i(triple(X3,X4,X5)),X2)
| ~ contains_pq(i(triple(X3,insert_slb(X4,pair(X1,X6)),X5)),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_23,negated_conjecture,
( contains_slb(insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk10_0)
| contains_pq(i(triple(esk6_0,insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk7_0)),esk10_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( ~ contains_slb(insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk10_0)
| ~ contains_pq(i(triple(esk6_0,esk5_0,esk7_0)),esk10_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,negated_conjecture,
( contains_pq(i(triple(X1,esk5_0,X2)),X3)
| ~ contains_slb(esk5_0,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_26,plain,
( contains_slb(insert_slb(X1,pair(X3,X4)),X2)
| ~ contains_slb(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( contains_slb(esk5_0,X1)
| ~ contains_pq(i(triple(X2,esk5_0,X3)),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( esk10_0 = esk8_0
| contains_slb(insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk10_0)
| contains_pq(i(triple(esk6_0,esk5_0,esk7_0)),esk10_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
~ contains_slb(esk5_0,esk10_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,plain,
( contains_pq(insert_pq(X3,X1),X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_31,plain,
( contains_slb(X1,X4)
| X2 = X4
| ~ contains_slb(insert_slb(X1,pair(X2,X3)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,negated_conjecture,
( esk10_0 = esk8_0
| contains_slb(insert_slb(esk5_0,pair(esk8_0,esk9_0)),esk10_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_33,plain,
( contains_slb(insert_slb(X3,pair(X1,X4)),X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_34,plain,
contains_pq(insert_pq(X1,X2),X2),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
esk10_0 = esk8_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_29]) ).
cnf(c_0_36,plain,
contains_slb(insert_slb(X1,pair(X2,X3)),X2),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
contains_pq(i(triple(X1,insert_slb(X2,pair(X3,X4)),X5)),X3),
inference(spm,[status(thm)],[c_0_34,c_0_13]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_35]),c_0_36]),c_0_35]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV370+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n021.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 : Tue Aug 29 04:52:14 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.59 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
% 0.21/0.67 % Total time : 0.067000 s
% 0.21/0.67 % SZS output end Proof
% 0.21/0.67 % Total time : 0.072000 s
%------------------------------------------------------------------------------