TSTP Solution File: SWV376+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV376+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 : n025.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 21:38:19 EDT 2023
% Result : Theorem 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 45
% Syntax : Number of formulae : 69 ( 11 unt; 40 typ; 0 def)
% Number of atoms : 74 ( 6 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 87 ( 42 ~; 22 |; 4 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 25 >; 18 *; 0 +; 0 <<)
% Number of predicates : 12 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 15 con; 0-3 aty)
% Number of variables : 92 ( 4 sgn; 66 !; 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_slb: $i ).
tff(decl_26,type,
isnonempty_slb: $i > $o ).
tff(decl_27,type,
pair: ( $i * $i ) > $i ).
tff(decl_28,type,
insert_slb: ( $i * $i ) > $i ).
tff(decl_29,type,
contains_slb: ( $i * $i ) > $o ).
tff(decl_30,type,
pair_in_list: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
remove_slb: ( $i * $i ) > $i ).
tff(decl_32,type,
lookup_slb: ( $i * $i ) > $i ).
tff(decl_33,type,
update_slb: ( $i * $i ) > $i ).
tff(decl_34,type,
succ_cpq: ( $i * $i ) > $o ).
tff(decl_35,type,
insert_cpq: ( $i * $i ) > $i ).
tff(decl_36,type,
remove_cpq: ( $i * $i ) > $i ).
tff(decl_37,type,
findmin_cpq_eff: $i > $i ).
tff(decl_38,type,
removemin_cpq_eff: $i > $i ).
tff(decl_39,type,
triple: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
check_cpq: $i > $o ).
tff(decl_41,type,
contains_cpq: ( $i * $i ) > $o ).
tff(decl_42,type,
bad: $i ).
tff(decl_43,type,
ok: $i > $o ).
tff(decl_44,type,
insert_pqp: ( $i * $i ) > $i ).
tff(decl_45,type,
remove_pqp: ( $i * $i ) > $i ).
tff(decl_46,type,
findmin_pqp_res: $i > $i ).
tff(decl_47,type,
findmin_cpq_res: $i > $i ).
tff(decl_48,type,
removemin_cpq_res: $i > $i ).
tff(decl_49,type,
im_succ_cpq: $i > $i ).
tff(decl_50,type,
esk1_0: $i ).
tff(decl_51,type,
esk2_0: $i ).
tff(decl_52,type,
esk3_0: $i ).
tff(decl_53,type,
esk4_0: $i ).
tff(decl_54,type,
esk5_0: $i ).
tff(decl_55,type,
esk6_0: $i ).
tff(decl_56,type,
esk7_0: $i ).
tff(decl_57,type,
esk8_0: $i ).
tff(decl_58,type,
esk9_0: $i ).
tff(decl_59,type,
esk10_0: $i ).
tff(decl_60,type,
esk11_0: $i ).
tff(decl_61,type,
esk12_0: $i ).
fof(l12_co,conjecture,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> ! [X4,X5,X6] :
( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
=> ~ ok(triple(X4,X5,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_co) ).
fof(ax41,axiom,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> X3 = bad ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax41) ).
fof(l12_induction,axiom,
( ! [X1,X2,X3,X4,X5,X6] :
( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
=> ( ~ ok(triple(X4,X5,X6))
=> ~ ok(im_succ_cpq(triple(X4,X5,X6))) ) )
=> ! [X7,X8,X9] :
( ~ ok(triple(X7,X8,X9))
=> ! [X10,X11,X12] :
( succ_cpq(triple(X7,X8,X9),triple(X10,X11,X12))
=> ~ ok(triple(X10,X11,X12)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_induction) ).
fof(ax40,axiom,
! [X1,X2] :
( ok(triple(X1,X2,bad))
<=> ~ $true ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax40) ).
fof(l12_l13,lemma,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> ~ ok(im_succ_cpq(triple(X1,X2,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_l13) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> ! [X4,X5,X6] :
( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
=> ~ ok(triple(X4,X5,X6)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l12_co])]) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> X3 = bad ),
inference(fof_simplification,[status(thm)],[ax41]) ).
fof(c_0_7,plain,
( ! [X1,X2,X3,X4,X5,X6] :
( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
=> ( ~ ok(triple(X4,X5,X6))
=> ~ ok(im_succ_cpq(triple(X4,X5,X6))) ) )
=> ! [X7,X8,X9] :
( ~ ok(triple(X7,X8,X9))
=> ! [X10,X11,X12] :
( succ_cpq(triple(X7,X8,X9),triple(X10,X11,X12))
=> ~ ok(triple(X10,X11,X12)) ) ) ),
inference(fof_simplification,[status(thm)],[l12_induction]) ).
fof(c_0_8,negated_conjecture,
( ~ ok(triple(esk7_0,esk8_0,esk9_0))
& succ_cpq(triple(esk7_0,esk8_0,esk9_0),triple(esk10_0,esk11_0,esk12_0))
& ok(triple(esk10_0,esk11_0,esk12_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_9,plain,
! [X89,X90,X91] :
( ok(triple(X89,X90,X91))
| X91 = bad ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
fof(c_0_10,plain,
! [X1,X2] : ~ ok(triple(X1,X2,bad)),
inference(fof_simplification,[status(thm)],[ax40]) ).
fof(c_0_11,plain,
! [X132,X133,X134,X135,X136,X137] :
( ( succ_cpq(triple(esk1_0,esk2_0,esk3_0),triple(esk4_0,esk5_0,esk6_0))
| ok(triple(X132,X133,X134))
| ~ succ_cpq(triple(X132,X133,X134),triple(X135,X136,X137))
| ~ ok(triple(X135,X136,X137)) )
& ( ~ ok(triple(esk4_0,esk5_0,esk6_0))
| ok(triple(X132,X133,X134))
| ~ succ_cpq(triple(X132,X133,X134),triple(X135,X136,X137))
| ~ ok(triple(X135,X136,X137)) )
& ( ok(im_succ_cpq(triple(esk4_0,esk5_0,esk6_0)))
| ok(triple(X132,X133,X134))
| ~ succ_cpq(triple(X132,X133,X134),triple(X135,X136,X137))
| ~ ok(triple(X135,X136,X137)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
cnf(c_0_12,negated_conjecture,
~ ok(triple(esk7_0,esk8_0,esk9_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ok(triple(X1,X2,X3))
| X3 = bad ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X87,X88] : ~ ok(triple(X87,X88,bad)),
inference(variable_rename,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( ok(triple(X1,X2,X3))
| ~ ok(triple(esk4_0,esk5_0,esk6_0))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
| ~ ok(triple(X4,X5,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
succ_cpq(triple(esk7_0,esk8_0,esk9_0),triple(esk10_0,esk11_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
esk9_0 = bad,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
ok(triple(esk10_0,esk11_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,plain,
~ ok(triple(X1,X2,bad)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
~ ok(triple(esk4_0,esk5_0,esk6_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]),c_0_19]) ).
fof(c_0_21,lemma,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> ~ ok(im_succ_cpq(triple(X1,X2,X3))) ),
inference(fof_simplification,[status(thm)],[l12_l13]) ).
cnf(c_0_22,plain,
( ok(im_succ_cpq(triple(esk4_0,esk5_0,esk6_0)))
| ok(triple(X1,X2,X3))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
| ~ ok(triple(X4,X5,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,negated_conjecture,
esk6_0 = bad,
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
fof(c_0_24,lemma,
! [X138,X139,X140] :
( ok(triple(X138,X139,X140))
| ~ ok(im_succ_cpq(triple(X138,X139,X140))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])]) ).
cnf(c_0_25,plain,
( ok(im_succ_cpq(triple(esk4_0,esk5_0,bad)))
| ok(triple(X1,X2,X3))
| ~ ok(triple(X4,X5,X6))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6)) ),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,lemma,
( ok(triple(X1,X2,X3))
| ~ ok(im_succ_cpq(triple(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,negated_conjecture,
ok(im_succ_cpq(triple(esk4_0,esk5_0,bad))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_16]),c_0_17]),c_0_18])]),c_0_19]) ).
cnf(c_0_28,lemma,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV376+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n025.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 : Tue Aug 29 09:03:10 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.57 % Version : CSE_E---1.5
% 0.19/0.57 % Problem : theBenchmark.p
% 0.19/0.57 % Proof found
% 0.19/0.57 % SZS status Theorem for theBenchmark.p
% 0.19/0.57 % SZS output start Proof
% See solution above
% 0.19/0.57 % Total time : 0.014000 s
% 0.19/0.57 % SZS output end Proof
% 0.19/0.57 % Total time : 0.018000 s
%------------------------------------------------------------------------------