TSTP Solution File: SWV401+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV401+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 : n006.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 21:38:25 EDT 2023
% Result : Theorem 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 24
% Syntax : Number of formulae : 58 ( 8 unt; 18 typ; 0 def)
% Number of atoms : 107 ( 20 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 108 ( 41 ~; 41 |; 15 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 10 >; 10 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 97 ( 6 sgn; 57 !; 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,
esk1_0: $i ).
tff(decl_35,type,
esk2_0: $i ).
tff(decl_36,type,
esk3_0: $i ).
tff(decl_37,type,
esk4_0: $i ).
tff(decl_38,type,
esk5_0: $i ).
tff(decl_39,type,
esk6_0: $i ).
fof(l37_co,conjecture,
! [X1] :
( ! [X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& less_than(X4,X3) )
=> pair_in_list(update_slb(X1,X4),X2,X3) )
=> ! [X5,X6,X7,X8,X9] :
( ( pair_in_list(insert_slb(X1,pair(X8,X9)),X5,X6)
& less_than(X7,X6) )
=> pair_in_list(update_slb(insert_slb(X1,pair(X8,X9)),X7),X5,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l37_co) ).
fof(ax29,axiom,
! [X1,X2,X3,X4] :
( strictly_less_than(X4,X3)
=> update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax29) ).
fof(ax30,axiom,
! [X1,X2,X3,X4] :
( less_than(X3,X4)
=> update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax30) ).
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(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ! [X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& less_than(X4,X3) )
=> pair_in_list(update_slb(X1,X4),X2,X3) )
=> ! [X5,X6,X7,X8,X9] :
( ( pair_in_list(insert_slb(X1,pair(X8,X9)),X5,X6)
& less_than(X7,X6) )
=> pair_in_list(update_slb(insert_slb(X1,pair(X8,X9)),X7),X5,X6) ) ),
inference(assume_negation,[status(cth)],[l37_co]) ).
fof(c_0_7,negated_conjecture,
! [X58,X59,X60] :
( ( ~ pair_in_list(esk1_0,X58,X59)
| ~ less_than(X60,X59)
| pair_in_list(update_slb(esk1_0,X60),X58,X59) )
& pair_in_list(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk2_0,esk3_0)
& less_than(esk4_0,esk3_0)
& ~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk4_0),esk2_0,esk3_0) ),
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_8,plain,
! [X49,X50,X51,X52] :
( ~ strictly_less_than(X52,X51)
| update_slb(insert_slb(X49,pair(X50,X52)),X51) = insert_slb(update_slb(X49,X51),pair(X50,X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax29])]) ).
fof(c_0_9,plain,
! [X53,X54,X55,X56] :
( ~ less_than(X55,X56)
| update_slb(insert_slb(X53,pair(X54,X56)),X55) = insert_slb(update_slb(X53,X55),pair(X54,X56)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax30])]) ).
cnf(c_0_10,negated_conjecture,
~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk4_0),esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( update_slb(insert_slb(X3,pair(X4,X1)),X2) = insert_slb(update_slb(X3,X2),pair(X4,X2))
| ~ strictly_less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X29,X30,X31,X32,X33] :
( ( X30 = X31
| pair_in_list(X29,X31,X33)
| ~ pair_in_list(insert_slb(X29,pair(X30,X32)),X31,X33) )
& ( X32 = X33
| pair_in_list(X29,X31,X33)
| ~ pair_in_list(insert_slb(X29,pair(X30,X32)),X31,X33) )
& ( ~ pair_in_list(X29,X31,X33)
| pair_in_list(insert_slb(X29,pair(X30,X32)),X31,X33) )
& ( X30 != X31
| X32 != X33
| pair_in_list(insert_slb(X29,pair(X30,X32)),X31,X33) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
fof(c_0_13,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_14,plain,
( update_slb(insert_slb(X3,pair(X4,X2)),X1) = insert_slb(update_slb(X3,X1),pair(X4,X2))
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( ~ pair_in_list(insert_slb(update_slb(esk1_0,esk4_0),pair(esk5_0,esk4_0)),esk2_0,esk3_0)
| ~ strictly_less_than(esk6_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,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_12]) ).
fof(c_0_17,plain,
! [X16,X17] :
( ( less_than(X16,X17)
| ~ strictly_less_than(X16,X17) )
& ( ~ less_than(X17,X16)
| ~ strictly_less_than(X16,X17) )
& ( ~ less_than(X16,X17)
| less_than(X17,X16)
| strictly_less_than(X16,X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_18,plain,
! [X13,X14] :
( less_than(X13,X14)
| less_than(X14,X13) ),
inference(variable_rename,[status(thm)],[totality]) ).
cnf(c_0_19,negated_conjecture,
( ~ pair_in_list(insert_slb(update_slb(esk1_0,esk4_0),pair(esk5_0,esk6_0)),esk2_0,esk3_0)
| ~ less_than(esk4_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( ~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk3_0)
| ~ strictly_less_than(esk6_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( pair_in_list(update_slb(esk1_0,X3),X1,X2)
| ~ pair_in_list(esk1_0,X1,X2)
| ~ less_than(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
less_than(esk4_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
( ~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk3_0)
| ~ less_than(esk4_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_26,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_12]) ).
cnf(c_0_27,negated_conjecture,
pair_in_list(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_28,negated_conjecture,
( ~ pair_in_list(esk1_0,esk2_0,esk3_0)
| ~ strictly_less_than(esk6_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_29,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( ~ pair_in_list(esk1_0,esk2_0,esk3_0)
| ~ less_than(esk4_0,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_21]),c_0_22])]) ).
cnf(c_0_31,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_12]) ).
cnf(c_0_32,negated_conjecture,
( esk6_0 = esk3_0
| pair_in_list(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
~ pair_in_list(esk1_0,esk2_0,esk3_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( esk2_0 = esk5_0
| pair_in_list(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_27]) ).
cnf(c_0_35,plain,
( pair_in_list(insert_slb(X5,pair(X1,X3)),X2,X4)
| X1 != X2
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_36,negated_conjecture,
esk6_0 = esk3_0,
inference(sr,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
esk2_0 = esk5_0,
inference(sr,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_38,plain,
pair_in_list(insert_slb(X1,pair(X2,X3)),X2,X3),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_35])]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_36]),c_0_36]),c_0_22])]),c_0_37]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV401+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n006.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 03:24:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 0.19/0.59 % Version : CSE_E---1.5
% 0.19/0.59 % Problem : theBenchmark.p
% 0.19/0.59 % Proof found
% 0.19/0.59 % SZS status Theorem for theBenchmark.p
% 0.19/0.59 % SZS output start Proof
% See solution above
% 0.19/0.60 % Total time : 0.008000 s
% 0.19/0.60 % SZS output end Proof
% 0.19/0.60 % Total time : 0.011000 s
%------------------------------------------------------------------------------