TSTP Solution File: SWV406+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV406+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 : n004.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 21:38:26 EDT 2023
% Result : Theorem 0.19s 0.61s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 42
% Syntax : Number of formulae : 88 ( 8 unt; 36 typ; 0 def)
% Number of atoms : 151 ( 17 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 155 ( 56 ~; 67 |; 14 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 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 : 27 ( 27 usr; 10 con; 0-3 aty)
% Number of variables : 137 ( 17 sgn; 73 !; 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_0: $i ).
tff(decl_50,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk4_0: $i ).
tff(decl_53,type,
esk5_0: $i ).
tff(decl_54,type,
esk6_0: $i ).
tff(decl_55,type,
esk7_0: $i ).
tff(decl_56,type,
esk8_0: $i ).
tff(decl_57,type,
esk9_0: $i ).
fof(l42_co,conjecture,
! [X1] :
( ! [X2,X3] :
( check_cpq(triple(X2,X1,X3))
<=> ! [X4,X5] :
( pair_in_list(X1,X4,X5)
=> less_than(X5,X4) ) )
=> ! [X6,X7,X8,X9] :
( check_cpq(triple(X6,insert_slb(X1,pair(X8,X9)),X7))
<=> ! [X10,X11] :
( pair_in_list(insert_slb(X1,pair(X8,X9)),X10,X11)
=> less_than(X11,X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l42_co) ).
fof(ax23,axiom,
! [X1,X2,X3,X4,X5] :
( pair_in_list(insert_slb(X1,pair(X2,X4)),X3,X5)
<=> ( pair_in_list(X1,X3,X5)
| ( X2 = X3
& X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax23) ).
fof(stricly_smaller_definition,axiom,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
fof(ax38,axiom,
! [X1,X2,X3,X4,X5] :
( strictly_less_than(X4,X5)
=> ( check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3))
<=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax38) ).
fof(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(ax37,axiom,
! [X1,X2,X3,X4,X5] :
( less_than(X5,X4)
=> ( check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3))
<=> check_cpq(triple(X1,X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax37) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ! [X2,X3] :
( check_cpq(triple(X2,X1,X3))
<=> ! [X4,X5] :
( pair_in_list(X1,X4,X5)
=> less_than(X5,X4) ) )
=> ! [X6,X7,X8,X9] :
( check_cpq(triple(X6,insert_slb(X1,pair(X8,X9)),X7))
<=> ! [X10,X11] :
( pair_in_list(insert_slb(X1,pair(X8,X9)),X10,X11)
=> less_than(X11,X10) ) ) ),
inference(assume_negation,[status(cth)],[l42_co]) ).
fof(c_0_7,plain,
! [X31,X32,X33,X34,X35] :
( ( X32 = X33
| pair_in_list(X31,X33,X35)
| ~ pair_in_list(insert_slb(X31,pair(X32,X34)),X33,X35) )
& ( X34 = X35
| pair_in_list(X31,X33,X35)
| ~ pair_in_list(insert_slb(X31,pair(X32,X34)),X33,X35) )
& ( ~ pair_in_list(X31,X33,X35)
| pair_in_list(insert_slb(X31,pair(X32,X34)),X33,X35) )
& ( X32 != X33
| X34 != X35
| pair_in_list(insert_slb(X31,pair(X32,X34)),X33,X35) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
fof(c_0_8,plain,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[stricly_smaller_definition]) ).
fof(c_0_9,negated_conjecture,
! [X126,X127,X128,X129,X138,X139] :
( ( ~ check_cpq(triple(X126,esk1_0,X127))
| ~ pair_in_list(esk1_0,X128,X129)
| less_than(X129,X128) )
& ( pair_in_list(esk1_0,esk2_2(X126,X127),esk3_2(X126,X127))
| check_cpq(triple(X126,esk1_0,X127)) )
& ( ~ less_than(esk3_2(X126,X127),esk2_2(X126,X127))
| check_cpq(triple(X126,esk1_0,X127)) )
& ( pair_in_list(insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk8_0,esk9_0)
| ~ check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0)) )
& ( ~ less_than(esk9_0,esk8_0)
| ~ check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0)) )
& ( check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0))
| ~ pair_in_list(insert_slb(esk1_0,pair(esk6_0,esk7_0)),X138,X139)
| less_than(X139,X138) ) ),
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_6])])])])]) ).
fof(c_0_10,plain,
! [X1,X2,X3,X4,X5] :
( strictly_less_than(X4,X5)
=> ~ check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3)) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_11,plain,
( pair_in_list(insert_slb(X5,pair(X1,X3)),X2,X4)
| X1 != X2
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X18,X19] :
( ( less_than(X18,X19)
| ~ strictly_less_than(X18,X19) )
& ( ~ less_than(X19,X18)
| ~ strictly_less_than(X18,X19) )
& ( ~ less_than(X18,X19)
| less_than(X19,X18)
| strictly_less_than(X18,X19) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_13,plain,
! [X15,X16] :
( less_than(X15,X16)
| less_than(X16,X15) ),
inference(variable_rename,[status(thm)],[totality]) ).
cnf(c_0_14,negated_conjecture,
( check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0))
| less_than(X2,X1)
| ~ pair_in_list(insert_slb(esk1_0,pair(esk6_0,esk7_0)),X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( pair_in_list(insert_slb(X1,pair(X4,X5)),X2,X3)
| ~ pair_in_list(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_16,plain,
! [X77,X78,X79,X80,X81] :
( ~ strictly_less_than(X80,X81)
| ~ check_cpq(triple(X77,insert_slb(X78,pair(X80,X81)),X79)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
cnf(c_0_17,plain,
pair_in_list(insert_slb(X1,pair(X2,X3)),X2,X3),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_11])]) ).
cnf(c_0_18,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X72,X73,X74,X75,X76] :
( ( ~ check_cpq(triple(X72,insert_slb(X73,pair(X75,X76)),X74))
| check_cpq(triple(X72,X73,X74))
| ~ less_than(X76,X75) )
& ( ~ check_cpq(triple(X72,X73,X74))
| check_cpq(triple(X72,insert_slb(X73,pair(X75,X76)),X74))
| ~ less_than(X76,X75) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])]) ).
cnf(c_0_21,negated_conjecture,
( check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0))
| less_than(X1,X2)
| ~ pair_in_list(esk1_0,X2,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,negated_conjecture,
( pair_in_list(esk1_0,esk2_2(X1,X2),esk3_2(X1,X2))
| check_cpq(triple(X1,esk1_0,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,negated_conjecture,
( check_cpq(triple(X1,esk1_0,X2))
| ~ less_than(esk3_2(X1,X2),esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,plain,
( ~ strictly_less_than(X1,X2)
| ~ check_cpq(triple(X3,insert_slb(X4,pair(X1,X2)),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,negated_conjecture,
( check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0))
| less_than(esk7_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_26,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
( check_cpq(triple(X1,X2,X5))
| ~ check_cpq(triple(X1,insert_slb(X2,pair(X3,X4)),X5))
| ~ less_than(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0))
| check_cpq(triple(X1,esk1_0,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_29,negated_conjecture,
less_than(esk7_0,esk6_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( pair_in_list(insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk8_0,esk9_0)
| ~ check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_31,plain,
( check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3))
| ~ check_cpq(triple(X1,X2,X3))
| ~ less_than(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,negated_conjecture,
( check_cpq(triple(esk4_0,esk1_0,esk5_0))
| check_cpq(triple(X1,esk1_0,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_33,plain,
( X1 = X2
| pair_in_list(X3,X4,X2)
| ~ pair_in_list(insert_slb(X3,pair(X5,X1)),X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_34,negated_conjecture,
( pair_in_list(insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk8_0,esk9_0)
| ~ check_cpq(triple(esk4_0,esk1_0,esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_29])]) ).
cnf(c_0_35,negated_conjecture,
( ~ less_than(esk9_0,esk8_0)
| ~ check_cpq(triple(esk4_0,insert_slb(esk1_0,pair(esk6_0,esk7_0)),esk5_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_36,plain,
( X1 = X2
| pair_in_list(X3,X2,X4)
| ~ pair_in_list(insert_slb(X3,pair(X1,X5)),X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_37,negated_conjecture,
( less_than(X4,X3)
| ~ check_cpq(triple(X1,esk1_0,X2))
| ~ pair_in_list(esk1_0,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_38,negated_conjecture,
check_cpq(triple(esk4_0,esk1_0,esk5_0)),
inference(ef,[status(thm)],[c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( esk9_0 = esk7_0
| pair_in_list(esk1_0,esk8_0,esk9_0)
| ~ check_cpq(triple(esk4_0,esk1_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( ~ check_cpq(triple(esk4_0,esk1_0,esk5_0))
| ~ less_than(esk9_0,esk8_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_31]),c_0_29])]) ).
cnf(c_0_41,negated_conjecture,
( check_cpq(triple(X1,esk1_0,X2))
| ~ less_than(esk9_0,esk8_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_28]) ).
cnf(c_0_42,negated_conjecture,
( esk8_0 = esk6_0
| pair_in_list(esk1_0,esk8_0,esk9_0)
| ~ check_cpq(triple(esk4_0,esk1_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_43,negated_conjecture,
( less_than(X1,X2)
| ~ pair_in_list(esk1_0,X2,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( esk9_0 = esk7_0
| pair_in_list(esk1_0,esk8_0,esk9_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_38])]) ).
cnf(c_0_45,negated_conjecture,
~ less_than(esk9_0,esk8_0),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,negated_conjecture,
( esk8_0 = esk6_0
| pair_in_list(esk1_0,esk8_0,esk9_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_38])]) ).
cnf(c_0_47,negated_conjecture,
esk9_0 = esk7_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_48,negated_conjecture,
( esk8_0 = esk6_0
| pair_in_list(esk1_0,esk8_0,esk7_0) ),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_49,negated_conjecture,
~ less_than(esk7_0,esk8_0),
inference(rw,[status(thm)],[c_0_45,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
esk8_0 = esk6_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_48]),c_0_49]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV406+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 06:29:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.61 % Version : CSE_E---1.5
% 0.19/0.61 % Problem : theBenchmark.p
% 0.19/0.61 % Proof found
% 0.19/0.61 % SZS status Theorem for theBenchmark.p
% 0.19/0.61 % SZS output start Proof
% See solution above
% 0.19/0.61 % Total time : 0.028000 s
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time : 0.032000 s
%------------------------------------------------------------------------------