TSTP Solution File: SWV378+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV378+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 : n007.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 21:38:19 EDT 2023
% Result : Theorem 0.21s 0.59s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 39
% Syntax : Number of formulae : 70 ( 11 unt; 31 typ; 0 def)
% Number of atoms : 83 ( 15 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 82 ( 38 ~; 26 |; 7 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 24 >; 18 *; 0 +; 0 <<)
% Number of predicates : 12 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 7 con; 0-3 aty)
% Number of variables : 91 ( 9 sgn; 61 !; 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,
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_0: $i ).
tff(decl_50,type,
esk2_0: $i ).
tff(decl_51,type,
esk3_0: $i ).
tff(decl_52,type,
esk4_0: $i ).
fof(l14_co,conjecture,
! [X1,X2,X3,X4] :
( ~ ok(triple(X1,X2,X3))
=> ~ ok(remove_cpq(triple(X1,X2,X3),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l14_co) ).
fof(ax41,axiom,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> X3 = bad ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax41) ).
fof(ax40,axiom,
! [X1,X2] :
( ok(triple(X1,X2,bad))
<=> ~ $true ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax40) ).
fof(ax43,axiom,
! [X1,X2,X3,X4] :
( ~ contains_slb(X2,X4)
=> remove_cpq(triple(X1,X2,X3),X4) = triple(X1,X2,bad) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax43) ).
fof(ax45,axiom,
! [X1,X2,X3,X4] :
( ( contains_slb(X2,X4)
& strictly_less_than(X4,lookup_slb(X2,X4)) )
=> remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),bad) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax45) ).
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(ax44,axiom,
! [X1,X2,X3,X4] :
( ( contains_slb(X2,X4)
& less_than(lookup_slb(X2,X4),X4) )
=> remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax44) ).
fof(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ~ ok(triple(X1,X2,X3))
=> ~ ok(remove_cpq(triple(X1,X2,X3),X4)) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l14_co])]) ).
fof(c_0_9,plain,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> X3 = bad ),
inference(fof_simplification,[status(thm)],[ax41]) ).
fof(c_0_10,plain,
! [X1,X2] : ~ ok(triple(X1,X2,bad)),
inference(fof_simplification,[status(thm)],[ax40]) ).
fof(c_0_11,plain,
! [X1,X2,X3,X4] :
( ~ contains_slb(X2,X4)
=> remove_cpq(triple(X1,X2,X3),X4) = triple(X1,X2,bad) ),
inference(fof_simplification,[status(thm)],[ax43]) ).
fof(c_0_12,negated_conjecture,
( ~ ok(triple(esk1_0,esk2_0,esk3_0))
& ok(remove_cpq(triple(esk1_0,esk2_0,esk3_0),esk4_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_13,plain,
! [X82,X83,X84] :
( ok(triple(X82,X83,X84))
| X84 = bad ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
fof(c_0_14,plain,
! [X80,X81] : ~ ok(triple(X80,X81,bad)),
inference(variable_rename,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X97,X98,X99,X100] :
( ~ contains_slb(X98,X100)
| ~ strictly_less_than(X100,lookup_slb(X98,X100))
| remove_cpq(triple(X97,X98,X99),X100) = triple(remove_pqp(X97,X100),remove_slb(X98,X100),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
fof(c_0_16,plain,
! [X89,X90,X91,X92] :
( contains_slb(X90,X92)
| remove_cpq(triple(X89,X90,X91),X92) = triple(X89,X90,bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_17,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_18,plain,
! [X93,X94,X95,X96] :
( ~ contains_slb(X94,X96)
| ~ less_than(lookup_slb(X94,X96),X96)
| remove_cpq(triple(X93,X94,X95),X96) = triple(remove_pqp(X93,X96),remove_slb(X94,X96),X95) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])]) ).
cnf(c_0_19,negated_conjecture,
~ ok(triple(esk1_0,esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( ok(triple(X1,X2,X3))
| X3 = bad ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
~ ok(triple(X1,X2,bad)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( remove_cpq(triple(X3,X1,X4),X2) = triple(remove_pqp(X3,X2),remove_slb(X1,X2),bad)
| ~ contains_slb(X1,X2)
| ~ strictly_less_than(X2,lookup_slb(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
ok(remove_cpq(triple(esk1_0,esk2_0,esk3_0),esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,plain,
( contains_slb(X1,X2)
| remove_cpq(triple(X3,X1,X4),X2) = triple(X3,X1,bad) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_25,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_17])])]) ).
fof(c_0_26,plain,
! [X9,X10] :
( less_than(X9,X10)
| less_than(X10,X9) ),
inference(variable_rename,[status(thm)],[totality]) ).
cnf(c_0_27,plain,
( remove_cpq(triple(X3,X1,X4),X2) = triple(remove_pqp(X3,X2),remove_slb(X1,X2),X4)
| ~ contains_slb(X1,X2)
| ~ less_than(lookup_slb(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,negated_conjecture,
esk3_0 = bad,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_29,plain,
( ~ ok(remove_cpq(triple(X1,X2,X3),X4))
| ~ contains_slb(X2,X4)
| ~ strictly_less_than(X4,lookup_slb(X2,X4)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,negated_conjecture,
contains_slb(esk2_0,esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21]) ).
cnf(c_0_31,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( ~ ok(remove_cpq(triple(X1,X2,bad),X3))
| ~ contains_slb(X2,X3)
| ~ less_than(lookup_slb(X2,X3),X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_27]) ).
cnf(c_0_34,negated_conjecture,
ok(remove_cpq(triple(esk1_0,esk2_0,bad),esk4_0)),
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_35,negated_conjecture,
~ strictly_less_than(esk4_0,lookup_slb(esk2_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_23]),c_0_30])]) ).
cnf(c_0_36,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
~ less_than(lookup_slb(esk2_0,esk4_0),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_30])]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV378+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n007.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 08:11:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 0.21/0.59 % Version : CSE_E---1.5
% 0.21/0.59 % Problem : theBenchmark.p
% 0.21/0.59 % Proof found
% 0.21/0.59 % SZS status Theorem for theBenchmark.p
% 0.21/0.59 % SZS output start Proof
% See solution above
% 0.21/0.60 % Total time : 0.018000 s
% 0.21/0.60 % SZS output end Proof
% 0.21/0.60 % Total time : 0.022000 s
%------------------------------------------------------------------------------