TSTP Solution File: SWV415+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV415+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 : n005.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 21:38:29 EDT 2023
% Result : Theorem 1.03s 1.11s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 71
% Syntax : Number of formulae : 105 ( 34 unt; 64 typ; 0 def)
% Number of atoms : 56 ( 55 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 28 ( 13 ~; 11 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 6 ( 2 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 : 45 ( 45 usr; 19 con; 0-3 aty)
% Number of variables : 182 ( 57 sgn; 69 !; 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 ).
tff(decl_74,type,
esk8_0: $i ).
tff(decl_75,type,
esk9_0: $i ).
tff(decl_76,type,
esk10_0: $i ).
tff(decl_77,type,
esk11_0: $i ).
tff(decl_78,type,
esk12_0: $i ).
tff(decl_79,type,
esk13_0: $i ).
tff(decl_80,type,
esk14_0: $i ).
tff(decl_81,type,
esk15_0: $i ).
tff(decl_82,type,
esk16_0: $i ).
tff(decl_83,type,
esk17_0: $i ).
tff(decl_84,type,
esk18_0: $i ).
tff(decl_85,type,
esk19_0: $i ).
fof(big2_induction,axiom,
( ( ! [X1,X2,X3,X4] : i(triple(X1,create_slb,X3)) = i(triple(X2,create_slb,X4))
& ! [X5] :
( ! [X6,X7,X8,X9] : i(triple(X6,X5,X8)) = i(triple(X7,X5,X9))
=> ! [X10,X11,X12,X13,X14,X15] : i(triple(X10,insert_slb(X5,pair(X14,X15)),X12)) = i(triple(X11,insert_slb(X5,pair(X14,X15)),X13)) ) )
=> ! [X16,X17,X18,X19,X20] : i(triple(X16,X18,X19)) = i(triple(X17,X18,X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big2_induction) ).
fof(ax54,axiom,
! [X1,X2] : i(triple(X1,create_slb,X2)) = create_pq,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax',ax54) ).
fof(ax17,axiom,
! [X1,X2,X3] : insert_pq(insert_pq(X1,X2),X3) = insert_pq(insert_pq(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax',ax17) ).
fof(ax55,axiom,
! [X1,X2,X3,X4,X5] : i(triple(X1,insert_slb(X2,pair(X4,X5)),X3)) = insert_pq(i(triple(X1,X2,X3)),X4),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax',ax55) ).
fof(ax42,axiom,
! [X1,X2,X3,X4] : insert_cpq(triple(X1,X2,X3),X4) = triple(insert_pqp(X1,X4),insert_slb(X2,pair(X4,bottom)),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax42) ).
fof(co2,conjecture,
! [X1,X2,X3,X4] : i(insert_cpq(triple(X1,X2,X3),X4)) = insert_pq(i(triple(X1,X2,X3)),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co2) ).
fof(ax11,axiom,
! [X1,X2] : remove_pq(insert_pq(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax',ax11) ).
fof(c_0_7,plain,
! [X194,X195,X196,X197,X204,X205,X206,X207,X208] :
( ( i(triple(X194,esk9_0,X196)) = i(triple(X195,esk9_0,X197))
| i(triple(esk5_0,create_slb,esk7_0)) != i(triple(esk6_0,create_slb,esk8_0))
| i(triple(X204,X206,X207)) = i(triple(X205,X206,X208)) )
& ( i(triple(esk10_0,insert_slb(esk9_0,pair(esk14_0,esk15_0)),esk12_0)) != i(triple(esk11_0,insert_slb(esk9_0,pair(esk14_0,esk15_0)),esk13_0))
| i(triple(esk5_0,create_slb,esk7_0)) != i(triple(esk6_0,create_slb,esk8_0))
| i(triple(X204,X206,X207)) = i(triple(X205,X206,X208)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[big2_induction])])])])]) ).
fof(c_0_8,plain,
! [X162,X163] : i(triple(X162,create_slb,X163)) = create_pq,
inference(variable_rename,[status(thm)],[ax54]) ).
fof(c_0_9,plain,
! [X55,X56,X57] : insert_pq(insert_pq(X55,X56),X57) = insert_pq(insert_pq(X55,X57),X56),
inference(variable_rename,[status(thm)],[ax17]) ).
fof(c_0_10,plain,
! [X164,X165,X166,X167,X168] : i(triple(X164,insert_slb(X165,pair(X167,X168)),X166)) = insert_pq(i(triple(X164,X165,X166)),X167),
inference(variable_rename,[status(thm)],[ax55]) ).
fof(c_0_11,plain,
! [X128,X129,X130,X131] : insert_cpq(triple(X128,X129,X130),X131) = triple(insert_pqp(X128,X131),insert_slb(X129,pair(X131,bottom)),X130),
inference(variable_rename,[status(thm)],[ax42]) ).
cnf(c_0_12,plain,
( i(triple(X1,esk9_0,X2)) = i(triple(X3,esk9_0,X4))
| i(triple(X5,X6,X7)) = i(triple(X8,X6,X9))
| i(triple(esk5_0,create_slb,esk7_0)) != i(triple(esk6_0,create_slb,esk8_0)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
i(triple(X1,create_slb,X2)) = create_pq,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
insert_pq(insert_pq(X1,X2),X3) = insert_pq(insert_pq(X1,X3),X2),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
i(triple(X1,insert_slb(X2,pair(X3,X4)),X5)) = insert_pq(i(triple(X1,X2,X5)),X3),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
insert_cpq(triple(X1,X2,X3),X4) = triple(insert_pqp(X1,X4),insert_slb(X2,pair(X4,bottom)),X3),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( i(triple(X1,X2,X3)) = i(triple(X4,X2,X5))
| i(triple(esk10_0,insert_slb(esk9_0,pair(esk14_0,esk15_0)),esk12_0)) != i(triple(esk11_0,insert_slb(esk9_0,pair(esk14_0,esk15_0)),esk13_0))
| i(triple(esk5_0,create_slb,esk7_0)) != i(triple(esk6_0,create_slb,esk8_0)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,plain,
( i(triple(X1,esk9_0,X2)) = i(triple(X3,esk9_0,X4))
| i(triple(X5,X6,X7)) = i(triple(X8,X6,X9)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13])]) ).
cnf(c_0_19,plain,
i(triple(X1,insert_slb(insert_slb(X2,pair(X3,X4)),pair(X5,bottom)),X6)) = i(triple(X1,insert_slb(insert_slb(X2,pair(X5,bottom)),pair(X3,bottom)),X6)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_15]),c_0_15]),c_0_15]) ).
cnf(c_0_20,plain,
i(triple(insert_pqp(X1,X2),insert_slb(insert_slb(X3,pair(X2,bottom)),pair(X4,X5)),X6)) = insert_pq(i(insert_cpq(triple(X1,X3,X6),X2)),X4),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( i(triple(X1,X2,X3)) = i(triple(X4,X2,X5))
| i(triple(esk10_0,insert_slb(esk9_0,pair(esk14_0,esk15_0)),esk12_0)) != i(triple(esk11_0,insert_slb(esk9_0,pair(esk14_0,esk15_0)),esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_13]),c_0_13])]) ).
cnf(c_0_22,plain,
i(triple(X1,insert_slb(X2,pair(X3,X4)),X5)) = i(triple(X1,insert_slb(X2,pair(X3,X6)),X5)),
inference(spm,[status(thm)],[c_0_15,c_0_15]) ).
cnf(c_0_23,plain,
i(triple(X1,esk9_0,X2)) = i(triple(X3,esk9_0,X4)),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_18]),c_0_18]) ).
fof(c_0_24,negated_conjecture,
~ ! [X1,X2,X3,X4] : i(insert_cpq(triple(X1,X2,X3),X4)) = insert_pq(i(triple(X1,X2,X3)),X4),
inference(assume_negation,[status(cth)],[co2]) ).
cnf(c_0_25,plain,
insert_pq(i(insert_cpq(triple(X1,X2,X3),X4)),X5) = i(insert_cpq(triple(X1,insert_slb(X2,pair(X5,bottom)),X3),X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16]) ).
cnf(c_0_26,plain,
( i(triple(X1,X2,X3)) = i(triple(X4,X2,X5))
| i(triple(esk10_0,insert_slb(esk9_0,pair(esk14_0,bottom)),esk12_0)) != i(triple(esk11_0,insert_slb(esk9_0,pair(esk14_0,bottom)),esk13_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_22]) ).
cnf(c_0_27,plain,
i(triple(X1,insert_slb(esk9_0,pair(X2,X3)),X4)) = i(triple(X5,insert_slb(esk9_0,pair(X2,bottom)),X6)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_23]),c_0_15]) ).
fof(c_0_28,negated_conjecture,
i(insert_cpq(triple(esk16_0,esk17_0,esk18_0),esk19_0)) != insert_pq(i(triple(esk16_0,esk17_0,esk18_0)),esk19_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
cnf(c_0_29,plain,
i(triple(insert_pqp(X1,X2),insert_slb(insert_slb(X3,pair(X2,bottom)),pair(X4,X5)),X6)) = i(insert_cpq(triple(X1,insert_slb(X3,pair(X4,bottom)),X6),X2)),
inference(rw,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_30,plain,
i(triple(X1,X2,X3)) = i(triple(X4,X2,X5)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_27])]) ).
fof(c_0_31,plain,
! [X42,X43] : remove_pq(insert_pq(X42,X43),X43) = X42,
inference(variable_rename,[status(thm)],[ax11]) ).
cnf(c_0_32,negated_conjecture,
i(insert_cpq(triple(esk16_0,esk17_0,esk18_0),esk19_0)) != insert_pq(i(triple(esk16_0,esk17_0,esk18_0)),esk19_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
i(triple(bottom,insert_slb(insert_slb(X1,pair(X2,bottom)),pair(X3,X4)),bottom)) = i(insert_cpq(triple(X5,insert_slb(X1,pair(X3,bottom)),X6),X2)),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
remove_pq(insert_pq(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,negated_conjecture,
i(insert_cpq(triple(esk16_0,esk17_0,esk18_0),esk19_0)) != i(triple(esk16_0,insert_slb(esk17_0,pair(esk19_0,bottom)),esk18_0)),
inference(rw,[status(thm)],[c_0_32,c_0_15]) ).
cnf(c_0_36,plain,
insert_pq(i(insert_cpq(triple(X1,X2,X3),X4)),X5) = i(triple(bottom,insert_slb(insert_slb(X2,pair(X4,bottom)),pair(X5,bottom)),bottom)),
inference(rw,[status(thm)],[c_0_25,c_0_33]) ).
cnf(c_0_37,plain,
remove_pq(i(triple(X1,insert_slb(X2,pair(X3,X4)),X5)),X3) = i(triple(X1,X2,X5)),
inference(spm,[status(thm)],[c_0_34,c_0_15]) ).
cnf(c_0_38,negated_conjecture,
i(insert_cpq(triple(esk16_0,esk17_0,esk18_0),esk19_0)) != i(triple(bottom,insert_slb(esk17_0,pair(esk19_0,bottom)),bottom)),
inference(rw,[status(thm)],[c_0_35,c_0_30]) ).
cnf(c_0_39,plain,
i(insert_cpq(triple(X1,X2,X3),X4)) = i(triple(bottom,insert_slb(X2,pair(X4,bottom)),bottom)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_36]),c_0_37]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV415+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
% 0.12/0.34 % Computer : n005.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 06:10:23 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 1.03/1.11 % Version : CSE_E---1.5
% 1.03/1.11 % Problem : theBenchmark.p
% 1.03/1.11 % Proof found
% 1.03/1.11 % SZS status Theorem for theBenchmark.p
% 1.03/1.11 % SZS output start Proof
% See solution above
% 1.03/1.11 % Total time : 0.526000 s
% 1.03/1.11 % SZS output end Proof
% 1.03/1.11 % Total time : 0.531000 s
%------------------------------------------------------------------------------