TSTP Solution File: SWV409+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV409+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 : n029.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 21:38:28 EDT 2023
% Result : Theorem 0.56s 0.62s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 23
% Syntax : Number of formulae : 51 ( 8 unt; 17 typ; 0 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 107 ( 41 ~; 42 |; 17 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 12 >; 14 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 66 ( 0 sgn; 37 !; 4 ?; 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_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk2_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_36,type,
esk3_0: $i ).
tff(decl_37,type,
esk4_0: $i ).
tff(decl_38,type,
esk5_0: $i ).
fof(l45_co,conjecture,
! [X1,X2,X3] :
( ( contains_slb(X1,X2)
& strictly_less_than(X2,X3) )
=> ( pair_in_list(update_slb(X1,X3),X2,X3)
| ? [X4] :
( pair_in_list(update_slb(X1,X3),X2,X4)
& less_than(X3,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_co) ).
fof(l45_li4647,lemma,
! [X1,X2] :
( contains_slb(X1,X2)
=> ? [X3] : pair_in_list(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_li4647) ).
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(l45_l48,lemma,
! [X1,X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& strictly_less_than(X2,X4)
& strictly_less_than(X3,X4) )
=> pair_in_list(update_slb(X1,X4),X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l48) ).
fof(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(l45_l49,lemma,
! [X1,X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& strictly_less_than(X2,X4)
& less_than(X4,X3) )
=> ? [X5] :
( pair_in_list(update_slb(X1,X4),X2,X5)
& less_than(X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l49) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( ( contains_slb(X1,X2)
& strictly_less_than(X2,X3) )
=> ( pair_in_list(update_slb(X1,X3),X2,X3)
| ? [X4] :
( pair_in_list(update_slb(X1,X3),X2,X4)
& less_than(X3,X4) ) ) ),
inference(assume_negation,[status(cth)],[l45_co]) ).
fof(c_0_7,lemma,
! [X53,X54] :
( ~ contains_slb(X53,X54)
| pair_in_list(X53,X54,esk1_2(X53,X54)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_li4647])])]) ).
fof(c_0_8,negated_conjecture,
! [X68] :
( contains_slb(esk3_0,esk4_0)
& strictly_less_than(esk4_0,esk5_0)
& ~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,esk5_0)
& ( ~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,X68)
| ~ less_than(esk5_0,X68) ) ),
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_9,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_10,lemma,
! [X56,X57,X58,X59] :
( ~ pair_in_list(X56,X57,X58)
| ~ strictly_less_than(X57,X59)
| ~ strictly_less_than(X58,X59)
| pair_in_list(update_slb(X56,X59),X57,X59) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_l48])]) ).
cnf(c_0_11,lemma,
( pair_in_list(X1,X2,esk1_2(X1,X2))
| ~ contains_slb(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
contains_slb(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,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_9])])]) ).
fof(c_0_14,plain,
! [X9,X10] :
( less_than(X9,X10)
| less_than(X10,X9) ),
inference(variable_rename,[status(thm)],[totality]) ).
cnf(c_0_15,lemma,
( pair_in_list(update_slb(X1,X4),X2,X4)
| ~ pair_in_list(X1,X2,X3)
| ~ strictly_less_than(X2,X4)
| ~ strictly_less_than(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
pair_in_list(esk3_0,esk4_0,esk1_2(esk3_0,esk4_0)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,lemma,
! [X60,X61,X62,X63] :
( ( pair_in_list(update_slb(X60,X63),X61,esk2_4(X60,X61,X62,X63))
| ~ pair_in_list(X60,X61,X62)
| ~ strictly_less_than(X61,X63)
| ~ less_than(X63,X62) )
& ( less_than(X63,esk2_4(X60,X61,X62,X63))
| ~ pair_in_list(X60,X61,X62)
| ~ strictly_less_than(X61,X63)
| ~ less_than(X63,X62) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_l49])])])]) ).
cnf(c_0_20,negated_conjecture,
( pair_in_list(update_slb(esk3_0,X1),esk4_0,X1)
| ~ strictly_less_than(esk1_2(esk3_0,esk4_0),X1)
| ~ strictly_less_than(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,lemma,
( pair_in_list(update_slb(X1,X2),X3,esk2_4(X1,X3,X4,X2))
| ~ pair_in_list(X1,X3,X4)
| ~ strictly_less_than(X3,X2)
| ~ less_than(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( pair_in_list(update_slb(esk3_0,X1),esk4_0,X1)
| less_than(X1,esk1_2(esk3_0,esk4_0))
| ~ strictly_less_than(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
strictly_less_than(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,lemma,
( less_than(X1,esk2_4(X2,X3,X4,X1))
| ~ pair_in_list(X2,X3,X4)
| ~ strictly_less_than(X3,X1)
| ~ less_than(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,negated_conjecture,
( pair_in_list(update_slb(esk3_0,X1),esk4_0,esk2_4(esk3_0,esk4_0,esk1_2(esk3_0,esk4_0),X1))
| ~ strictly_less_than(esk4_0,X1)
| ~ less_than(X1,esk1_2(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_28,negated_conjecture,
less_than(esk5_0,esk1_2(esk3_0,esk4_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( less_than(X1,esk2_4(esk3_0,esk4_0,esk1_2(esk3_0,esk4_0),X1))
| ~ strictly_less_than(esk4_0,X1)
| ~ less_than(X1,esk1_2(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_30,negated_conjecture,
( ~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,X1)
| ~ less_than(esk5_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_31,negated_conjecture,
pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,esk2_4(esk3_0,esk4_0,esk1_2(esk3_0,esk4_0),esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_24])]) ).
cnf(c_0_32,negated_conjecture,
less_than(esk5_0,esk2_4(esk3_0,esk4_0,esk1_2(esk3_0,esk4_0),esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_28]),c_0_24])]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV409+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 03:37:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.56/0.62 % Version : CSE_E---1.5
% 0.56/0.62 % Problem : theBenchmark.p
% 0.56/0.62 % Proof found
% 0.56/0.62 % SZS status Theorem for theBenchmark.p
% 0.56/0.62 % SZS output start Proof
% See solution above
% 0.56/0.63 % Total time : 0.037000 s
% 0.56/0.63 % SZS output end Proof
% 0.56/0.63 % Total time : 0.040000 s
%------------------------------------------------------------------------------