TSTP Solution File: SWV408+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV408+2 : 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 : n002.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 21:38:27 EDT 2023
% Result : Theorem 0.19s 0.71s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 38
% Syntax : Number of formulae : 61 ( 4 unt; 32 typ; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 80 ( 30 ~; 30 |; 13 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 25 >; 19 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 7 con; 0-3 aty)
% Number of variables : 67 ( 0 sgn; 39 !; 3 ?; 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_0: $i ).
tff(decl_51,type,
esk3_0: $i ).
tff(decl_52,type,
esk4_0: $i ).
tff(decl_53,type,
esk5_0: $i ).
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(l48_li3839,lemma,
! [X1,X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& strictly_less_than(X3,X4) )
=> pair_in_list(update_slb(X1,X4),X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l48_li3839) ).
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(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(l44_co,conjecture,
! [X1,X2,X3,X4] :
( ( contains_slb(X2,X4)
& strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
=> ( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,findmin_pqp_res(X1))
| ? [X5] :
( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,X5)
& less_than(findmin_pqp_res(X1),X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l44_co) ).
fof(l49_li3637,lemma,
! [X1,X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& less_than(X4,X3) )
=> pair_in_list(update_slb(X1,X4),X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l49_li3637) ).
fof(c_0_6,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_7,lemma,
! [X122,X123,X124,X125] :
( ~ pair_in_list(X122,X123,X124)
| ~ strictly_less_than(X124,X125)
| pair_in_list(update_slb(X122,X125),X123,X125) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l48_li3839])]) ).
fof(c_0_8,lemma,
! [X119,X120] :
( ~ contains_slb(X119,X120)
| pair_in_list(X119,X120,esk1_2(X119,X120)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_li4647])])]) ).
fof(c_0_9,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_6])])]) ).
fof(c_0_10,plain,
! [X9,X10] :
( less_than(X9,X10)
| less_than(X10,X9) ),
inference(variable_rename,[status(thm)],[totality]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( contains_slb(X2,X4)
& strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
=> ( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,findmin_pqp_res(X1))
| ? [X5] :
( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,X5)
& less_than(findmin_pqp_res(X1),X5) ) ) ),
inference(assume_negation,[status(cth)],[l44_co]) ).
cnf(c_0_12,lemma,
( pair_in_list(update_slb(X1,X4),X2,X4)
| ~ pair_in_list(X1,X2,X3)
| ~ strictly_less_than(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,lemma,
( pair_in_list(X1,X2,esk1_2(X1,X2))
| ~ contains_slb(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,negated_conjecture,
! [X134] :
( contains_slb(esk3_0,esk5_0)
& strictly_less_than(esk5_0,findmin_cpq_res(triple(esk2_0,esk3_0,esk4_0)))
& ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0))
& ( ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,X134)
| ~ less_than(findmin_pqp_res(esk2_0),X134) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_17,lemma,
! [X126,X127,X128,X129] :
( ~ pair_in_list(X126,X127,X128)
| ~ less_than(X129,X128)
| pair_in_list(update_slb(X126,X129),X127,X128) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l49_li3637])]) ).
cnf(c_0_18,lemma,
( pair_in_list(update_slb(X1,X2),X3,X2)
| ~ contains_slb(X1,X3)
| ~ strictly_less_than(esk1_2(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,X1)
| ~ less_than(findmin_pqp_res(esk2_0),X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,lemma,
( pair_in_list(update_slb(X1,X4),X2,X3)
| ~ pair_in_list(X1,X2,X3)
| ~ less_than(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,lemma,
( pair_in_list(update_slb(X1,X2),X3,X2)
| less_than(X2,esk1_2(X1,X3))
| ~ contains_slb(X1,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
contains_slb(esk3_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( ~ pair_in_list(esk3_0,esk5_0,X1)
| ~ less_than(findmin_pqp_res(esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( pair_in_list(update_slb(esk3_0,X1),esk5_0,X1)
| less_than(X1,esk1_2(esk3_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,negated_conjecture,
~ pair_in_list(esk3_0,esk5_0,esk1_2(esk3_0,esk5_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_28,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_13]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV408+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n002.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 08:15:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.71 % Version : CSE_E---1.5
% 0.19/0.71 % Problem : theBenchmark.p
% 0.19/0.71 % Proof found
% 0.19/0.71 % SZS status Theorem for theBenchmark.p
% 0.19/0.71 % SZS output start Proof
% See solution above
% 0.19/0.71 % Total time : 0.146000 s
% 0.19/0.71 % SZS output end Proof
% 0.19/0.71 % Total time : 0.150000 s
%------------------------------------------------------------------------------