TSTP Solution File: SWV381+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV381+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 : n016.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 21:38:20 EDT 2023
% Result : Theorem 0.54s 0.61s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 62
% Syntax : Number of formulae : 97 ( 14 unt; 52 typ; 0 def)
% Number of atoms : 102 ( 19 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 91 ( 34 ~; 37 |; 10 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 76 ( 45 >; 31 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 7 con; 0-3 aty)
% Number of variables : 96 ( 8 sgn; 59 !; 2 ?; 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_pq: $i ).
tff(decl_26,type,
isnonempty_pq: $i > $o ).
tff(decl_27,type,
insert_pq: ( $i * $i ) > $i ).
tff(decl_28,type,
contains_pq: ( $i * $i ) > $o ).
tff(decl_29,type,
issmallestelement_pq: ( $i * $i ) > $o ).
tff(decl_30,type,
remove_pq: ( $i * $i ) > $i ).
tff(decl_31,type,
findmin_pq_eff: ( $i * $i ) > $i ).
tff(decl_32,type,
findmin_pq_res: ( $i * $i ) > $i ).
tff(decl_33,type,
removemin_pq_eff: ( $i * $i ) > $i ).
tff(decl_34,type,
removemin_pq_res: ( $i * $i ) > $i ).
tff(decl_35,type,
create_slb: $i ).
tff(decl_36,type,
isnonempty_slb: $i > $o ).
tff(decl_37,type,
pair: ( $i * $i ) > $i ).
tff(decl_38,type,
insert_slb: ( $i * $i ) > $i ).
tff(decl_39,type,
contains_slb: ( $i * $i ) > $o ).
tff(decl_40,type,
pair_in_list: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
remove_slb: ( $i * $i ) > $i ).
tff(decl_42,type,
lookup_slb: ( $i * $i ) > $i ).
tff(decl_43,type,
update_slb: ( $i * $i ) > $i ).
tff(decl_44,type,
succ_cpq: ( $i * $i ) > $o ).
tff(decl_45,type,
insert_cpq: ( $i * $i ) > $i ).
tff(decl_46,type,
remove_cpq: ( $i * $i ) > $i ).
tff(decl_47,type,
findmin_cpq_eff: $i > $i ).
tff(decl_48,type,
removemin_cpq_eff: $i > $i ).
tff(decl_49,type,
triple: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
check_cpq: $i > $o ).
tff(decl_51,type,
contains_cpq: ( $i * $i ) > $o ).
tff(decl_52,type,
bad: $i ).
tff(decl_53,type,
ok: $i > $o ).
tff(decl_54,type,
insert_pqp: ( $i * $i ) > $i ).
tff(decl_55,type,
remove_pqp: ( $i * $i ) > $i ).
tff(decl_56,type,
findmin_pqp_res: $i > $i ).
tff(decl_57,type,
findmin_cpq_res: $i > $i ).
tff(decl_58,type,
removemin_cpq_res: $i > $i ).
tff(decl_59,type,
i: $i > $i ).
tff(decl_60,type,
pi_sharp_remove: ( $i * $i ) > $o ).
tff(decl_61,type,
pi_remove: ( $i * $i ) > $o ).
tff(decl_62,type,
pi_sharp_find_min: ( $i * $i ) > $o ).
tff(decl_63,type,
pi_find_min: $i > $o ).
tff(decl_64,type,
pi_sharp_removemin: ( $i * $i ) > $o ).
tff(decl_65,type,
pi_removemin: $i > $o ).
tff(decl_66,type,
phi: $i > $o ).
tff(decl_67,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_68,type,
esk2_1: $i > $i ).
tff(decl_69,type,
esk3_1: $i > $i ).
tff(decl_70,type,
esk4_1: $i > $i ).
tff(decl_71,type,
esk5_0: $i ).
tff(decl_72,type,
esk6_0: $i ).
tff(decl_73,type,
esk7_0: $i ).
fof(l17_l18,lemma,
! [X1,X2,X3] :
( ? [X4] :
( contains_cpq(triple(X1,X2,X3),X4)
& strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
=> ~ phi(findmin_cpq_eff(triple(X1,X2,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l17_l18) ).
fof(ax51,axiom,
! [X1,X2,X3,X4] :
( X2 != create_slb
=> findmin_cpq_res(triple(X1,X2,X3)) = findmin_pqp_res(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax51) ).
fof(l17_co,conjecture,
! [X1,X2,X3] :
( phi(findmin_cpq_eff(triple(X1,X2,X3)))
=> issmallestelement_pq(i(triple(X1,X2,X3)),findmin_cpq_res(triple(X1,X2,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l17_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(l17_li56,lemma,
! [X1,X2,X3,X4] :
( contains_cpq(triple(X1,X2,X3),X4)
<=> contains_pq(i(triple(X1,X2,X3)),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l17_li56) ).
fof(ax10,axiom,
! [X1,X2] :
( issmallestelement_pq(X1,X2)
<=> ! [X3] :
( contains_pq(X1,X3)
=> less_than(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax',ax10) ).
fof(bottom_smallest,axiom,
! [X1] : less_than(bottom,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',bottom_smallest) ).
fof(ax54,axiom,
! [X1,X2] : i(triple(X1,create_slb,X2)) = create_pq,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax',ax54) ).
fof(ax50,axiom,
! [X1,X2] : findmin_cpq_res(triple(X1,create_slb,X2)) = bottom,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax50) ).
fof(c_0_10,lemma,
! [X1,X2,X3] :
( ? [X4] :
( contains_cpq(triple(X1,X2,X3),X4)
& strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
=> ~ phi(findmin_cpq_eff(triple(X1,X2,X3))) ),
inference(fof_simplification,[status(thm)],[l17_l18]) ).
fof(c_0_11,lemma,
! [X178,X179,X180,X181] :
( ~ contains_cpq(triple(X178,X179,X180),X181)
| ~ strictly_less_than(X181,findmin_cpq_res(triple(X178,X179,X180)))
| ~ phi(findmin_cpq_eff(triple(X178,X179,X180))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_12,plain,
! [X142,X143,X144] :
( X143 = create_slb
| findmin_cpq_res(triple(X142,X143,X144)) = findmin_pqp_res(X142) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax51])])]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2,X3] :
( phi(findmin_cpq_eff(triple(X1,X2,X3)))
=> issmallestelement_pq(i(triple(X1,X2,X3)),findmin_cpq_res(triple(X1,X2,X3))) ),
inference(assume_negation,[status(cth)],[l17_co]) ).
fof(c_0_14,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_15,lemma,
( ~ contains_cpq(triple(X1,X2,X3),X4)
| ~ strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3)))
| ~ phi(findmin_cpq_eff(triple(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( X1 = create_slb
| findmin_cpq_res(triple(X2,X1,X3)) = findmin_pqp_res(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,negated_conjecture,
( phi(findmin_cpq_eff(triple(esk5_0,esk6_0,esk7_0)))
& ~ issmallestelement_pq(i(triple(esk5_0,esk6_0,esk7_0)),findmin_cpq_res(triple(esk5_0,esk6_0,esk7_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_18,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_14])])]) ).
fof(c_0_19,plain,
! [X9,X10] :
( less_than(X9,X10)
| less_than(X10,X9) ),
inference(variable_rename,[status(thm)],[totality]) ).
cnf(c_0_20,lemma,
( X1 = create_slb
| ~ phi(findmin_cpq_eff(triple(X2,X1,X3)))
| ~ contains_cpq(triple(X2,X1,X3),X4)
| ~ strictly_less_than(X4,findmin_pqp_res(X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
phi(findmin_cpq_eff(triple(esk5_0,esk6_0,esk7_0))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( esk6_0 = create_slb
| ~ contains_cpq(triple(esk5_0,esk6_0,esk7_0),X1)
| ~ strictly_less_than(X1,findmin_pqp_res(esk5_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_26,lemma,
! [X174,X175,X176,X177] :
( ( ~ contains_cpq(triple(X174,X175,X176),X177)
| contains_pq(i(triple(X174,X175,X176)),X177) )
& ( ~ contains_pq(i(triple(X174,X175,X176)),X177)
| contains_cpq(triple(X174,X175,X176),X177) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l17_li56])]) ).
cnf(c_0_27,negated_conjecture,
( esk6_0 = create_slb
| less_than(findmin_pqp_res(esk5_0),X1)
| ~ contains_cpq(triple(esk5_0,esk6_0,esk7_0),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,lemma,
( contains_cpq(triple(X1,X2,X3),X4)
| ~ contains_pq(i(triple(X1,X2,X3)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_29,plain,
! [X21,X22,X23,X24,X25] :
( ( ~ issmallestelement_pq(X21,X22)
| ~ contains_pq(X21,X23)
| less_than(X22,X23) )
& ( contains_pq(X24,esk1_2(X24,X25))
| issmallestelement_pq(X24,X25) )
& ( ~ less_than(X25,esk1_2(X24,X25))
| issmallestelement_pq(X24,X25) ) ),
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)],[ax10])])])])])]) ).
cnf(c_0_30,lemma,
( esk6_0 = create_slb
| less_than(findmin_pqp_res(esk5_0),X1)
| ~ contains_pq(i(triple(esk5_0,esk6_0,esk7_0)),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
( contains_pq(X1,esk1_2(X1,X2))
| issmallestelement_pq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,negated_conjecture,
~ issmallestelement_pq(i(triple(esk5_0,esk6_0,esk7_0)),findmin_cpq_res(triple(esk5_0,esk6_0,esk7_0))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_33,plain,
! [X14] : less_than(bottom,X14),
inference(variable_rename,[status(thm)],[bottom_smallest]) ).
cnf(c_0_34,plain,
( issmallestelement_pq(X2,X1)
| ~ less_than(X1,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,lemma,
( esk6_0 = create_slb
| issmallestelement_pq(i(triple(esk5_0,esk6_0,esk7_0)),X1)
| less_than(findmin_pqp_res(esk5_0),esk1_2(i(triple(esk5_0,esk6_0,esk7_0)),X1)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( esk6_0 = create_slb
| ~ issmallestelement_pq(i(triple(esk5_0,esk6_0,esk7_0)),findmin_pqp_res(esk5_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_16]) ).
fof(c_0_37,plain,
! [X147,X148] : i(triple(X147,create_slb,X148)) = create_pq,
inference(variable_rename,[status(thm)],[ax54]) ).
fof(c_0_38,plain,
! [X140,X141] : findmin_cpq_res(triple(X140,create_slb,X141)) = bottom,
inference(variable_rename,[status(thm)],[ax50]) ).
cnf(c_0_39,plain,
less_than(bottom,X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,lemma,
esk6_0 = create_slb,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_41,plain,
i(triple(X1,create_slb,X2)) = create_pq,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
findmin_cpq_res(triple(X1,create_slb,X2)) = bottom,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,plain,
issmallestelement_pq(X1,bottom),
inference(spm,[status(thm)],[c_0_34,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_40]),c_0_41]),c_0_42]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 04:11:30 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.54/0.61 % Version : CSE_E---1.5
% 0.54/0.61 % Problem : theBenchmark.p
% 0.54/0.61 % Proof found
% 0.54/0.61 % SZS status Theorem for theBenchmark.p
% 0.54/0.61 % SZS output start Proof
% See solution above
% 0.54/0.62 % Total time : 0.026000 s
% 0.54/0.62 % SZS output end Proof
% 0.54/0.62 % Total time : 0.030000 s
%------------------------------------------------------------------------------