TSTP Solution File: SWV391+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV391+1 : 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 : 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 21:38:23 EDT 2023
% Result : Theorem 0.56s 0.74s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 43
% Syntax : Number of formulae : 87 ( 11 unt; 33 typ; 0 def)
% Number of atoms : 141 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 139 ( 52 ~; 60 |; 13 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 26 >; 20 *; 0 +; 0 <<)
% Number of predicates : 12 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 7 con; 0-3 aty)
% Number of variables : 152 ( 24 sgn; 79 !; 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,
esk1_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk3_0: $i ).
tff(decl_52,type,
esk4_0: $i ).
tff(decl_53,type,
esk5_0: $i ).
tff(decl_54,type,
esk6_0: $i ).
fof(ax40,axiom,
! [X1,X2] :
( ok(triple(X1,X2,bad))
<=> ~ $true ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax40) ).
fof(ax45,axiom,
! [X1,X2,X3,X4] :
( ( contains_slb(X2,X4)
& strictly_less_than(X4,lookup_slb(X2,X4)) )
=> remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),bad) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax45) ).
fof(l27_l33,lemma,
! [X1,X2,X3,X4] :
( ok(remove_cpq(triple(X1,X2,X3),X4))
=> contains_slb(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l27_l33) ).
fof(l27_co,conjecture,
! [X1,X2,X3,X4] :
( ( check_cpq(remove_cpq(triple(X1,X2,X3),X4))
& ok(remove_cpq(triple(X1,X2,X3),X4)) )
=> check_cpq(triple(X1,X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l27_co) ).
fof(stricly_smaller_definition,axiom,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
fof(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(l27_li4142,lemma,
! [X1,X2,X3] :
( check_cpq(triple(X1,X2,X3))
<=> ! [X4,X5] :
( pair_in_list(X2,X4,X5)
=> less_than(X5,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l27_li4142) ).
fof(ax44,axiom,
! [X1,X2,X3,X4] :
( ( contains_slb(X2,X4)
& less_than(lookup_slb(X2,X4),X4) )
=> remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax44) ).
fof(l27_li2829,lemma,
! [X1,X2,X3] :
( pair_in_list(X1,X2,X3)
=> ! [X4] :
( contains_slb(X1,X4)
=> ( pair_in_list(remove_slb(X1,X4),X2,X3)
| X2 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l27_li2829) ).
fof(l27_l30,lemma,
! [X1,X2,X3,X4] :
( ( check_cpq(remove_cpq(triple(X1,X2,X3),X4))
& ok(remove_cpq(triple(X1,X2,X3),X4)) )
=> ! [X5] :
( pair_in_list(X2,X4,X5)
=> less_than(X5,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l27_l30) ).
fof(c_0_10,plain,
! [X1,X2] : ~ ok(triple(X1,X2,bad)),
inference(fof_simplification,[status(thm)],[ax40]) ).
fof(c_0_11,plain,
! [X80,X81] : ~ ok(triple(X80,X81,bad)),
inference(variable_rename,[status(thm)],[c_0_10]) ).
fof(c_0_12,plain,
! [X97,X98,X99,X100] :
( ~ contains_slb(X98,X100)
| ~ strictly_less_than(X100,lookup_slb(X98,X100))
| remove_cpq(triple(X97,X98,X99),X100) = triple(remove_pqp(X97,X100),remove_slb(X98,X100),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
fof(c_0_13,lemma,
! [X138,X139,X140,X141] :
( ~ ok(remove_cpq(triple(X138,X139,X140),X141))
| contains_slb(X139,X141) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l27_l33])]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( check_cpq(remove_cpq(triple(X1,X2,X3),X4))
& ok(remove_cpq(triple(X1,X2,X3),X4)) )
=> check_cpq(triple(X1,X2,X3)) ),
inference(assume_negation,[status(cth)],[l27_co]) ).
fof(c_0_15,plain,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_0_16,plain,
~ ok(triple(X1,X2,bad)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( remove_cpq(triple(X3,X1,X4),X2) = triple(remove_pqp(X3,X2),remove_slb(X1,X2),bad)
| ~ contains_slb(X1,X2)
| ~ strictly_less_than(X2,lookup_slb(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,lemma,
( contains_slb(X2,X4)
| ~ ok(remove_cpq(triple(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,negated_conjecture,
( check_cpq(remove_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0))
& ok(remove_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0))
& ~ check_cpq(triple(esk3_0,esk4_0,esk5_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_20,plain,
! [X12,X13] :
( ( less_than(X12,X13)
| ~ strictly_less_than(X12,X13) )
& ( ~ less_than(X13,X12)
| ~ strictly_less_than(X12,X13) )
& ( ~ less_than(X12,X13)
| less_than(X13,X12)
| strictly_less_than(X12,X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_21,plain,
! [X9,X10] :
( less_than(X9,X10)
| less_than(X10,X9) ),
inference(variable_rename,[status(thm)],[totality]) ).
fof(c_0_22,lemma,
! [X119,X120,X121,X122,X123,X124,X125,X128] :
( ( ~ check_cpq(triple(X119,X120,X121))
| ~ pair_in_list(X120,X122,X123)
| less_than(X123,X122) )
& ( pair_in_list(X125,esk1_2(X124,X125),esk2_2(X124,X125))
| check_cpq(triple(X124,X125,X128)) )
& ( ~ less_than(esk2_2(X124,X125),esk1_2(X124,X125))
| check_cpq(triple(X124,X125,X128)) ) ),
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)],[l27_li4142])])])])])]) ).
fof(c_0_23,plain,
! [X93,X94,X95,X96] :
( ~ contains_slb(X94,X96)
| ~ less_than(lookup_slb(X94,X96),X96)
| remove_cpq(triple(X93,X94,X95),X96) = triple(remove_pqp(X93,X96),remove_slb(X94,X96),X95) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])]) ).
cnf(c_0_24,plain,
( ~ ok(remove_cpq(triple(X1,X2,X3),X4))
| ~ strictly_less_than(X4,lookup_slb(X2,X4)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_25,negated_conjecture,
ok(remove_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_28,lemma,
! [X129,X130,X131,X132] :
( ~ pair_in_list(X129,X130,X131)
| ~ contains_slb(X129,X132)
| pair_in_list(remove_slb(X129,X132),X130,X131)
| X130 = X132 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l27_li2829])])]) ).
cnf(c_0_29,lemma,
( less_than(X5,X4)
| ~ check_cpq(triple(X1,X2,X3))
| ~ pair_in_list(X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( remove_cpq(triple(X3,X1,X4),X2) = triple(remove_pqp(X3,X2),remove_slb(X1,X2),X4)
| ~ contains_slb(X1,X2)
| ~ less_than(lookup_slb(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
~ strictly_less_than(esk6_0,lookup_slb(esk4_0,esk6_0)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,lemma,
( pair_in_list(remove_slb(X1,X4),X2,X3)
| X2 = X4
| ~ pair_in_list(X1,X2,X3)
| ~ contains_slb(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,lemma,
( pair_in_list(X1,esk1_2(X2,X1),esk2_2(X2,X1))
| check_cpq(triple(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35,lemma,
( less_than(X1,X2)
| ~ check_cpq(remove_cpq(triple(X3,X4,X5),X6))
| ~ pair_in_list(remove_slb(X4,X6),X2,X1)
| ~ contains_slb(X4,X6)
| ~ less_than(lookup_slb(X4,X6),X6) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
check_cpq(remove_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_37,negated_conjecture,
contains_slb(esk4_0,esk6_0),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_38,negated_conjecture,
less_than(lookup_slb(esk4_0,esk6_0),esk6_0),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,lemma,
( esk1_2(X1,X2) = X3
| check_cpq(triple(X1,X2,X4))
| pair_in_list(remove_slb(X2,X3),esk1_2(X1,X2),esk2_2(X1,X2))
| ~ contains_slb(X2,X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( less_than(X1,X2)
| ~ pair_in_list(remove_slb(esk4_0,esk6_0),X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38])]) ).
cnf(c_0_41,negated_conjecture,
( esk1_2(X1,esk4_0) = esk6_0
| check_cpq(triple(X1,esk4_0,X2))
| pair_in_list(remove_slb(esk4_0,esk6_0),esk1_2(X1,esk4_0),esk2_2(X1,esk4_0)) ),
inference(spm,[status(thm)],[c_0_39,c_0_37]) ).
cnf(c_0_42,lemma,
( check_cpq(triple(X1,X2,X3))
| ~ less_than(esk2_2(X1,X2),esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_43,lemma,
! [X133,X134,X135,X136,X137] :
( ~ check_cpq(remove_cpq(triple(X133,X134,X135),X136))
| ~ ok(remove_cpq(triple(X133,X134,X135),X136))
| ~ pair_in_list(X134,X136,X137)
| less_than(X137,X136) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l27_l30])])]) ).
cnf(c_0_44,negated_conjecture,
( esk1_2(X1,esk4_0) = esk6_0
| check_cpq(triple(X1,esk4_0,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_45,lemma,
( less_than(X5,X4)
| ~ check_cpq(remove_cpq(triple(X1,X2,X3),X4))
| ~ ok(remove_cpq(triple(X1,X2,X3),X4))
| ~ pair_in_list(X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_46,lemma,
( check_cpq(triple(X1,esk4_0,X2))
| check_cpq(triple(X1,esk4_0,X3))
| pair_in_list(esk4_0,esk6_0,esk2_2(X1,esk4_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_44]) ).
cnf(c_0_47,lemma,
( check_cpq(triple(X1,esk4_0,X2))
| check_cpq(triple(X1,esk4_0,X3))
| ~ less_than(esk2_2(X1,esk4_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( less_than(X1,esk6_0)
| ~ pair_in_list(esk4_0,esk6_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_25]),c_0_36])]) ).
cnf(c_0_49,lemma,
( check_cpq(triple(X1,esk4_0,X2))
| pair_in_list(esk4_0,esk6_0,esk2_2(X1,esk4_0)) ),
inference(ef,[status(thm)],[c_0_46]) ).
cnf(c_0_50,lemma,
( check_cpq(triple(X1,esk4_0,X2))
| ~ less_than(esk2_2(X1,esk4_0),esk6_0) ),
inference(ef,[status(thm)],[c_0_47]) ).
cnf(c_0_51,negated_conjecture,
~ check_cpq(triple(esk3_0,esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_52,negated_conjecture,
check_cpq(triple(X1,esk4_0,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV391+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/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 08:15:29 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.56/0.74 % Version : CSE_E---1.5
% 0.56/0.74 % Problem : theBenchmark.p
% 0.56/0.74 % Proof found
% 0.56/0.74 % SZS status Theorem for theBenchmark.p
% 0.56/0.74 % SZS output start Proof
% See solution above
% 0.56/0.74 % Total time : 0.160000 s
% 0.56/0.74 % SZS output end Proof
% 0.56/0.74 % Total time : 0.164000 s
%------------------------------------------------------------------------------