TSTP Solution File: SWC067+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWC067+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/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 20:19:32 EDT 2023
% Result : Theorem 0.56s 0.67s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 83
% Syntax : Number of formulae : 122 ( 17 unt; 77 typ; 0 def)
% Number of atoms : 230 ( 67 equ)
% Maximal formula atoms : 40 ( 5 avg)
% Number of connectives : 296 ( 111 ~; 107 |; 57 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 85 ( 68 >; 17 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 58 ( 58 usr; 9 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn; 35 !; 20 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ssItem: $i > $o ).
tff(decl_23,type,
neq: ( $i * $i ) > $o ).
tff(decl_24,type,
ssList: $i > $o ).
tff(decl_25,type,
memberP: ( $i * $i ) > $o ).
tff(decl_26,type,
cons: ( $i * $i ) > $i ).
tff(decl_27,type,
app: ( $i * $i ) > $i ).
tff(decl_28,type,
singletonP: $i > $o ).
tff(decl_29,type,
nil: $i ).
tff(decl_30,type,
frontsegP: ( $i * $i ) > $o ).
tff(decl_31,type,
rearsegP: ( $i * $i ) > $o ).
tff(decl_32,type,
segmentP: ( $i * $i ) > $o ).
tff(decl_33,type,
cyclefreeP: $i > $o ).
tff(decl_34,type,
leq: ( $i * $i ) > $o ).
tff(decl_35,type,
totalorderP: $i > $o ).
tff(decl_36,type,
strictorderP: $i > $o ).
tff(decl_37,type,
lt: ( $i * $i ) > $o ).
tff(decl_38,type,
totalorderedP: $i > $o ).
tff(decl_39,type,
strictorderedP: $i > $o ).
tff(decl_40,type,
duplicatefreeP: $i > $o ).
tff(decl_41,type,
equalelemsP: $i > $o ).
tff(decl_42,type,
hd: $i > $i ).
tff(decl_43,type,
tl: $i > $i ).
tff(decl_44,type,
geq: ( $i * $i ) > $o ).
tff(decl_45,type,
gt: ( $i * $i ) > $o ).
tff(decl_46,type,
esk1_0: $i ).
tff(decl_47,type,
esk2_0: $i ).
tff(decl_48,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk5_1: $i > $i ).
tff(decl_51,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk10_1: $i > $i ).
tff(decl_56,type,
esk11_1: $i > $i ).
tff(decl_57,type,
esk12_1: $i > $i ).
tff(decl_58,type,
esk13_1: $i > $i ).
tff(decl_59,type,
esk14_1: $i > $i ).
tff(decl_60,type,
esk15_1: $i > $i ).
tff(decl_61,type,
esk16_1: $i > $i ).
tff(decl_62,type,
esk17_1: $i > $i ).
tff(decl_63,type,
esk18_1: $i > $i ).
tff(decl_64,type,
esk19_1: $i > $i ).
tff(decl_65,type,
esk20_1: $i > $i ).
tff(decl_66,type,
esk21_1: $i > $i ).
tff(decl_67,type,
esk22_1: $i > $i ).
tff(decl_68,type,
esk23_1: $i > $i ).
tff(decl_69,type,
esk24_1: $i > $i ).
tff(decl_70,type,
esk25_1: $i > $i ).
tff(decl_71,type,
esk26_1: $i > $i ).
tff(decl_72,type,
esk27_1: $i > $i ).
tff(decl_73,type,
esk28_1: $i > $i ).
tff(decl_74,type,
esk29_1: $i > $i ).
tff(decl_75,type,
esk30_1: $i > $i ).
tff(decl_76,type,
esk31_1: $i > $i ).
tff(decl_77,type,
esk32_1: $i > $i ).
tff(decl_78,type,
esk33_1: $i > $i ).
tff(decl_79,type,
esk34_1: $i > $i ).
tff(decl_80,type,
esk35_1: $i > $i ).
tff(decl_81,type,
esk36_1: $i > $i ).
tff(decl_82,type,
esk37_1: $i > $i ).
tff(decl_83,type,
esk38_1: $i > $i ).
tff(decl_84,type,
esk39_1: $i > $i ).
tff(decl_85,type,
esk40_1: $i > $i ).
tff(decl_86,type,
esk41_1: $i > $i ).
tff(decl_87,type,
esk42_1: $i > $i ).
tff(decl_88,type,
esk43_1: $i > $i ).
tff(decl_89,type,
esk44_1: $i > $i ).
tff(decl_90,type,
esk45_1: $i > $i ).
tff(decl_91,type,
esk46_1: $i > $i ).
tff(decl_92,type,
esk47_1: $i > $i ).
tff(decl_93,type,
esk48_0: $i ).
tff(decl_94,type,
esk49_0: $i ).
tff(decl_95,type,
esk50_0: $i ).
tff(decl_96,type,
esk51_0: $i ).
tff(decl_97,type,
esk52_0: $i ).
tff(decl_98,type,
esk53_0: $i ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X5,X3),X6) != X4
| ~ strictorderedP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X3
& lt(X7,X9) ) ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X6
& ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(X14,cons(X13,nil)) = X3
& lt(X13,X11) ) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X15] :
( ssList(X15)
& neq(X15,nil)
& segmentP(X2,X15)
& segmentP(X1,X15) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax58,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X5,X3),X6) != X4
| ~ strictorderedP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X3
& lt(X7,X9) ) ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X6
& ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(X14,cons(X13,nil)) = X3
& lt(X13,X11) ) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X15] :
( ssList(X15)
& neq(X15,nil)
& segmentP(X2,X15)
& segmentP(X1,X15) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_7,negated_conjecture,
! [X266,X267,X268,X269,X270,X271,X272,X273,X274] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssList(esk52_0)
& ssList(esk53_0)
& app(app(esk52_0,esk50_0),esk53_0) = esk51_0
& strictorderedP(esk50_0)
& ( ~ ssItem(X266)
| ~ ssList(X267)
| app(X267,cons(X266,nil)) != esk52_0
| ~ ssItem(X268)
| ~ ssList(X269)
| app(cons(X268,nil),X269) != esk50_0
| ~ lt(X266,X268) )
& ( ~ ssItem(X270)
| ~ ssList(X271)
| app(cons(X270,nil),X271) != esk53_0
| ~ ssItem(X272)
| ~ ssList(X273)
| app(X273,cons(X272,nil)) != esk50_0
| ~ lt(X272,X270) )
& ( nil = esk51_0
| nil != esk50_0 )
& ( neq(esk49_0,nil)
| nil = esk49_0 )
& ( ~ ssList(X274)
| ~ neq(X274,nil)
| ~ segmentP(esk49_0,X274)
| ~ segmentP(esk48_0,X274)
| nil = esk49_0 )
& ( neq(esk49_0,nil)
| nil != esk48_0 )
& ( ~ ssList(X274)
| ~ neq(X274,nil)
| ~ segmentP(esk49_0,X274)
| ~ segmentP(esk48_0,X274)
| nil != esk48_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
fof(c_0_8,plain,
! [X37,X38,X41,X42] :
( ( ssList(esk8_2(X37,X38))
| ~ segmentP(X37,X38)
| ~ ssList(X38)
| ~ ssList(X37) )
& ( ssList(esk9_2(X37,X38))
| ~ segmentP(X37,X38)
| ~ ssList(X38)
| ~ ssList(X37) )
& ( app(app(esk8_2(X37,X38),X38),esk9_2(X37,X38)) = X37
| ~ segmentP(X37,X38)
| ~ ssList(X38)
| ~ ssList(X37) )
& ( ~ ssList(X41)
| ~ ssList(X42)
| app(app(X41,X38),X42) != X37
| segmentP(X37,X38)
| ~ ssList(X38)
| ~ ssList(X37) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).
cnf(c_0_9,negated_conjecture,
( nil = esk49_0
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X198] :
( ~ ssList(X198)
| segmentP(X198,X198) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])]) ).
cnf(c_0_12,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( segmentP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,X3),X2) != X4
| ~ ssList(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
app(app(esk52_0,esk50_0),esk53_0) = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
( esk49_0 = nil
| ~ segmentP(esk50_0,X1)
| ~ segmentP(esk49_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_17,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_19,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(app(app(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
app(app(esk52_0,esk50_0),esk53_0) = esk49_0,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
ssList(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
( esk49_0 = nil
| ~ segmentP(esk49_0,esk50_0)
| ~ neq(esk50_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_25,negated_conjecture,
segmentP(esk49_0,esk50_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_18]),c_0_22]),c_0_23])]) ).
fof(c_0_26,plain,
! [X118,X119] :
( ( ~ neq(X118,X119)
| X118 != X119
| ~ ssList(X119)
| ~ ssList(X118) )
& ( X118 = X119
| neq(X118,X119)
| ~ ssList(X119)
| ~ ssList(X118) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_27,negated_conjecture,
( nil = esk51_0
| nil != esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_28,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_29,negated_conjecture,
( esk49_0 = nil
| ~ neq(esk50_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_30,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_32,negated_conjecture,
( esk49_0 = nil
| esk50_0 != nil ),
inference(rw,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_33,negated_conjecture,
( esk50_0 != nil
| ~ segmentP(esk50_0,X1)
| ~ segmentP(esk49_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_10]),c_0_10]) ).
fof(c_0_34,plain,
! [X204] :
( ( ~ segmentP(nil,X204)
| nil = X204
| ~ ssList(X204) )
& ( nil != X204
| segmentP(nil,X204)
| ~ ssList(X204) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])]) ).
cnf(c_0_35,negated_conjecture,
esk49_0 = nil,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_18])]),c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( esk50_0 != nil
| ~ segmentP(esk49_0,esk50_0)
| ~ neq(esk50_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_17]),c_0_18])]) ).
cnf(c_0_37,plain,
( nil = X1
| ~ segmentP(nil,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,negated_conjecture,
segmentP(nil,esk50_0),
inference(rw,[status(thm)],[c_0_25,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( neq(esk49_0,nil)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_40,negated_conjecture,
( esk50_0 != nil
| ~ neq(esk50_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_25])]) ).
cnf(c_0_41,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_18])]) ).
cnf(c_0_42,negated_conjecture,
( neq(esk49_0,nil)
| esk50_0 != nil ),
inference(rw,[status(thm)],[c_0_39,c_0_10]) ).
cnf(c_0_43,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_41])]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_35]),c_0_41])]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWC067+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n006.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 : Mon Aug 28 16:50:21 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.59 start to proof: theBenchmark
% 0.56/0.67 % Version : CSE_E---1.5
% 0.56/0.67 % Problem : theBenchmark.p
% 0.56/0.67 % Proof found
% 0.56/0.67 % SZS status Theorem for theBenchmark.p
% 0.56/0.67 % SZS output start Proof
% See solution above
% 0.56/0.68 % Total time : 0.066000 s
% 0.56/0.68 % SZS output end Proof
% 0.56/0.68 % Total time : 0.071000 s
%------------------------------------------------------------------------------