TSTP Solution File: SWV372+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV372+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 21:38:17 EDT 2023
% Result : Theorem 0.18s 0.58s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 60
% Syntax : Number of formulae : 88 ( 11 unt; 52 typ; 0 def)
% Number of atoms : 70 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 29 ~; 19 |; 5 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 22 ( 19 usr; 2 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 7 con; 0-3 aty)
% Number of variables : 89 ( 15 sgn; 59 !; 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_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(ax40,axiom,
! [X1,X2] :
( ok(triple(X1,X2,bad))
<=> ~ $true ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax40) ).
fof(l8_lX,lemma,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> ~ phi(triple(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l8_lX) ).
fof(l8_co,conjecture,
! [X1,X2,X3] :
( phi(findmin_cpq_eff(triple(X1,X2,X3)))
=> contains_pq(i(triple(X1,X2,X3)),findmin_cpq_res(triple(X1,X2,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l8_co) ).
fof(ax47,axiom,
! [X1,X2,X3,X4] :
( ( X2 != create_slb
& ~ contains_slb(X2,findmin_pqp_res(X1)) )
=> findmin_cpq_eff(triple(X1,X2,X3)) = triple(X1,update_slb(X2,findmin_pqp_res(X1)),bad) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax47) ).
fof(ax51,axiom,
! [X1,X2,X3,X4] :
( X2 != create_slb
=> findmin_cpq_res(triple(X1,X2,X3)) = findmin_pqp_res(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax51) ).
fof(l8_li56,lemma,
! [X1,X2,X3,X4] :
( contains_cpq(triple(X1,X2,X3),X4)
<=> contains_pq(i(triple(X1,X2,X3)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l8_li56) ).
fof(ax39,axiom,
! [X1,X2,X3,X4] :
( contains_cpq(triple(X1,X2,X3),X4)
<=> contains_slb(X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax39) ).
fof(ax46,axiom,
! [X1,X2] : findmin_cpq_eff(triple(X1,create_slb,X2)) = triple(X1,create_slb,bad),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax46) ).
fof(c_0_8,plain,
! [X1,X2] : ~ ok(triple(X1,X2,bad)),
inference(fof_simplification,[status(thm)],[ax40]) ).
fof(c_0_9,lemma,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> ~ phi(triple(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[l8_lX]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X2,X3] :
( phi(findmin_cpq_eff(triple(X1,X2,X3)))
=> contains_pq(i(triple(X1,X2,X3)),findmin_cpq_res(triple(X1,X2,X3))) ),
inference(assume_negation,[status(cth)],[l8_co]) ).
fof(c_0_11,plain,
! [X108,X109] : ~ ok(triple(X108,X109,bad)),
inference(variable_rename,[status(thm)],[c_0_8]) ).
fof(c_0_12,lemma,
! [X181,X182,X183] :
( ok(triple(X181,X182,X183))
| ~ phi(triple(X181,X182,X183)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
fof(c_0_13,plain,
! [X1,X2,X3,X4] :
( ( X2 != create_slb
& ~ contains_slb(X2,findmin_pqp_res(X1)) )
=> findmin_cpq_eff(triple(X1,X2,X3)) = triple(X1,update_slb(X2,findmin_pqp_res(X1)),bad) ),
inference(fof_simplification,[status(thm)],[ax47]) ).
fof(c_0_14,negated_conjecture,
( phi(findmin_cpq_eff(triple(esk5_0,esk6_0,esk7_0)))
& ~ contains_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_10])])]) ).
fof(c_0_15,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_16,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)],[l8_li56])]) ).
fof(c_0_17,plain,
! [X104,X105,X106,X107] :
( ( ~ contains_cpq(triple(X104,X105,X106),X107)
| contains_slb(X105,X107) )
& ( ~ contains_slb(X105,X107)
| contains_cpq(triple(X104,X105,X106),X107) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax39])]) ).
cnf(c_0_18,plain,
~ ok(triple(X1,X2,bad)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,lemma,
( ok(triple(X1,X2,X3))
| ~ phi(triple(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X131,X132,X133] :
( X132 = create_slb
| contains_slb(X132,findmin_pqp_res(X131))
| findmin_cpq_eff(triple(X131,X132,X133)) = triple(X131,update_slb(X132,findmin_pqp_res(X131)),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_13])])]) ).
cnf(c_0_21,negated_conjecture,
~ contains_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_14]) ).
cnf(c_0_22,plain,
( X1 = create_slb
| findmin_cpq_res(triple(X2,X1,X3)) = findmin_pqp_res(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,lemma,
( contains_pq(i(triple(X1,X2,X3)),X4)
| ~ contains_cpq(triple(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( contains_cpq(triple(X3,X1,X4),X2)
| ~ contains_slb(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,lemma,
~ phi(triple(X1,X2,bad)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
( X1 = create_slb
| contains_slb(X1,findmin_pqp_res(X2))
| findmin_cpq_eff(triple(X2,X1,X3)) = triple(X2,update_slb(X1,findmin_pqp_res(X2)),bad) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( esk6_0 = create_slb
| ~ contains_pq(i(triple(esk5_0,esk6_0,esk7_0)),findmin_pqp_res(esk5_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,lemma,
( contains_pq(i(triple(X1,X2,X3)),X4)
| ~ contains_slb(X2,X4) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,lemma,
( X1 = create_slb
| contains_slb(X1,findmin_pqp_res(X2))
| ~ phi(findmin_cpq_eff(triple(X2,X1,X3))) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
phi(findmin_cpq_eff(triple(esk5_0,esk6_0,esk7_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_31,negated_conjecture,
( esk6_0 = create_slb
| ~ contains_slb(esk6_0,findmin_pqp_res(esk5_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_32,plain,
! [X129,X130] : findmin_cpq_eff(triple(X129,create_slb,X130)) = triple(X129,create_slb,bad),
inference(variable_rename,[status(thm)],[ax46]) ).
cnf(c_0_33,negated_conjecture,
esk6_0 = create_slb,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_34,plain,
findmin_cpq_eff(triple(X1,create_slb,X2)) = triple(X1,create_slb,bad),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_33]),c_0_34]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV372+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 02:50:36 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.55 start to proof: theBenchmark
% 0.18/0.58 % Version : CSE_E---1.5
% 0.18/0.58 % Problem : theBenchmark.p
% 0.18/0.58 % Proof found
% 0.18/0.58 % SZS status Theorem for theBenchmark.p
% 0.18/0.58 % SZS output start Proof
% See solution above
% 0.18/0.58 % Total time : 0.020000 s
% 0.18/0.58 % SZS output end Proof
% 0.18/0.58 % Total time : 0.023000 s
%------------------------------------------------------------------------------