TSTP Solution File: ITP004+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ITP004+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 03:10:11 EDT 2023
% Result : Theorem 0.85s 0.91s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 31
% Syntax : Number of formulae : 62 ( 8 unt; 24 typ; 0 def)
% Number of atoms : 146 ( 6 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 184 ( 76 ~; 79 |; 8 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 17 >; 10 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-4 aty)
% Number of variables : 68 ( 0 sgn; 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
bool: $i ).
tff(decl_23,type,
ne: $i > $o ).
tff(decl_24,type,
ind: $i ).
tff(decl_25,type,
arr: ( $i * $i ) > $i ).
tff(decl_26,type,
mem: ( $i * $i ) > $o ).
tff(decl_27,type,
ap: ( $i * $i ) > $i ).
tff(decl_28,type,
p: $i > $o ).
tff(decl_29,type,
k: ( $i * $i ) > $i ).
tff(decl_30,type,
i: $i > $i ).
tff(decl_31,type,
c_2Emin_2E_3D_3D_3E: $i ).
tff(decl_32,type,
c_2Epred__set_2ESUBSET: $i > $i ).
tff(decl_33,type,
c_2Ebool_2E_7E: $i ).
tff(decl_34,type,
c_2Ebool_2E_2F_5C: $i ).
tff(decl_35,type,
c_2Ebool_2EIN: $i > $i ).
tff(decl_36,type,
c_2Epred__set_2ECHOICE: $i > $i ).
tff(decl_37,type,
c_2Epred__set_2EDELETE: $i > $i ).
tff(decl_38,type,
c_2Epred__set_2EREST: $i > $i ).
tff(decl_39,type,
c_2Emin_2E_3D: $i > $i ).
tff(decl_40,type,
c_2Ebool_2E_21: $i > $i ).
tff(decl_41,type,
esk1_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_42,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
esk4_0: $i ).
tff(decl_45,type,
esk5_0: $i ).
fof(conj_thm_2Epred__set_2EREST__SUBSET,conjecture,
! [X9] :
( ne(X9)
=> ! [X10] :
( mem(X10,arr(X9,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X9),ap(c_2Epred__set_2EREST(X9),X10)),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EREST__SUBSET) ).
fof(ax_thm_2Epred__set_2ESUBSET__DEF,axiom,
! [X9] :
( ne(X9)
=> ! [X10] :
( mem(X10,arr(X9,bool))
=> ! [X11] :
( mem(X11,arr(X9,bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(X9),X10),X11))
<=> ! [X12] :
( mem(X12,X9)
=> ( p(ap(ap(c_2Ebool_2EIN(X9),X12),X10))
=> p(ap(ap(c_2Ebool_2EIN(X9),X12),X11)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Epred__set_2ESUBSET__DEF) ).
fof(ap_tp,axiom,
! [X1,X2,X3] :
( mem(X3,arr(X1,X2))
=> ! [X4] :
( mem(X4,X1)
=> mem(ap(X3,X4),X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',ap_tp) ).
fof(mem_c_2Epred__set_2EREST,axiom,
! [X9] :
( ne(X9)
=> mem(c_2Epred__set_2EREST(X9),arr(arr(X9,bool),arr(X9,bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2EREST) ).
fof(mem_c_2Epred__set_2ECHOICE,axiom,
! [X9] :
( ne(X9)
=> mem(c_2Epred__set_2ECHOICE(X9),arr(arr(X9,bool),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECHOICE) ).
fof(conj_thm_2Epred__set_2EIN__DELETE,axiom,
! [X9] :
( ne(X9)
=> ! [X10] :
( mem(X10,arr(X9,bool))
=> ! [X13] :
( mem(X13,X9)
=> ! [X14] :
( mem(X14,X9)
=> ( p(ap(ap(c_2Ebool_2EIN(X9),X13),ap(ap(c_2Epred__set_2EDELETE(X9),X10),X14)))
<=> ( p(ap(ap(c_2Ebool_2EIN(X9),X13),X10))
& X13 != X14 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EIN__DELETE) ).
fof(ax_thm_2Epred__set_2EREST__DEF,axiom,
! [X9] :
( ne(X9)
=> ! [X10] :
( mem(X10,arr(X9,bool))
=> ap(c_2Epred__set_2EREST(X9),X10) = ap(ap(c_2Epred__set_2EDELETE(X9),X10),ap(c_2Epred__set_2ECHOICE(X9),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Epred__set_2EREST__DEF) ).
fof(c_0_7,negated_conjecture,
~ ! [X9] :
( ne(X9)
=> ! [X10] :
( mem(X10,arr(X9,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X9),ap(c_2Epred__set_2EREST(X9),X10)),X10)) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Epred__set_2EREST__SUBSET]) ).
fof(c_0_8,plain,
! [X52,X53,X54,X55] :
( ( ~ p(ap(ap(c_2Epred__set_2ESUBSET(X52),X53),X54))
| ~ mem(X55,X52)
| ~ p(ap(ap(c_2Ebool_2EIN(X52),X55),X53))
| p(ap(ap(c_2Ebool_2EIN(X52),X55),X54))
| ~ mem(X54,arr(X52,bool))
| ~ mem(X53,arr(X52,bool))
| ~ ne(X52) )
& ( mem(esk3_3(X52,X53,X54),X52)
| p(ap(ap(c_2Epred__set_2ESUBSET(X52),X53),X54))
| ~ mem(X54,arr(X52,bool))
| ~ mem(X53,arr(X52,bool))
| ~ ne(X52) )
& ( p(ap(ap(c_2Ebool_2EIN(X52),esk3_3(X52,X53,X54)),X53))
| p(ap(ap(c_2Epred__set_2ESUBSET(X52),X53),X54))
| ~ mem(X54,arr(X52,bool))
| ~ mem(X53,arr(X52,bool))
| ~ ne(X52) )
& ( ~ p(ap(ap(c_2Ebool_2EIN(X52),esk3_3(X52,X53,X54)),X54))
| p(ap(ap(c_2Epred__set_2ESUBSET(X52),X53),X54))
| ~ mem(X54,arr(X52,bool))
| ~ mem(X53,arr(X52,bool))
| ~ ne(X52) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax_thm_2Epred__set_2ESUBSET__DEF])])])])]) ).
fof(c_0_9,negated_conjecture,
( ne(esk4_0)
& mem(esk5_0,arr(esk4_0,bool))
& ~ p(ap(ap(c_2Epred__set_2ESUBSET(esk4_0),ap(c_2Epred__set_2EREST(esk4_0),esk5_0)),esk5_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,plain,
! [X17,X18,X19,X20] :
( ~ mem(X19,arr(X17,X18))
| ~ mem(X20,X17)
| mem(ap(X19,X20),X18) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])]) ).
fof(c_0_11,plain,
! [X42] :
( ~ ne(X42)
| mem(c_2Epred__set_2EREST(X42),arr(arr(X42,bool),arr(X42,bool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mem_c_2Epred__set_2EREST])]) ).
fof(c_0_12,plain,
! [X40] :
( ~ ne(X40)
| mem(c_2Epred__set_2ECHOICE(X40),arr(arr(X40,bool),X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mem_c_2Epred__set_2ECHOICE])]) ).
cnf(c_0_13,plain,
( p(ap(ap(c_2Ebool_2EIN(X1),esk3_3(X1,X2,X3)),X2))
| p(ap(ap(c_2Epred__set_2ESUBSET(X1),X2),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
mem(esk5_0,arr(esk4_0,bool)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
ne(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( mem(ap(X1,X4),X3)
| ~ mem(X1,arr(X2,X3))
| ~ mem(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( mem(c_2Epred__set_2EREST(X1),arr(arr(X1,bool),arr(X1,bool)))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( mem(esk3_3(X1,X2,X3),X1)
| p(ap(ap(c_2Epred__set_2ESUBSET(X1),X2),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_19,plain,
! [X57,X58,X59,X60] :
( ( p(ap(ap(c_2Ebool_2EIN(X57),X59),X58))
| ~ p(ap(ap(c_2Ebool_2EIN(X57),X59),ap(ap(c_2Epred__set_2EDELETE(X57),X58),X60)))
| ~ mem(X60,X57)
| ~ mem(X59,X57)
| ~ mem(X58,arr(X57,bool))
| ~ ne(X57) )
& ( X59 != X60
| ~ p(ap(ap(c_2Ebool_2EIN(X57),X59),ap(ap(c_2Epred__set_2EDELETE(X57),X58),X60)))
| ~ mem(X60,X57)
| ~ mem(X59,X57)
| ~ mem(X58,arr(X57,bool))
| ~ ne(X57) )
& ( ~ p(ap(ap(c_2Ebool_2EIN(X57),X59),X58))
| X59 = X60
| p(ap(ap(c_2Ebool_2EIN(X57),X59),ap(ap(c_2Epred__set_2EDELETE(X57),X58),X60)))
| ~ mem(X60,X57)
| ~ mem(X59,X57)
| ~ mem(X58,arr(X57,bool))
| ~ ne(X57) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Epred__set_2EIN__DELETE])])])]) ).
fof(c_0_20,plain,
! [X61,X62] :
( ~ ne(X61)
| ~ mem(X62,arr(X61,bool))
| ap(c_2Epred__set_2EREST(X61),X62) = ap(ap(c_2Epred__set_2EDELETE(X61),X62),ap(c_2Epred__set_2ECHOICE(X61),X62)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax_thm_2Epred__set_2EREST__DEF])])]) ).
cnf(c_0_21,plain,
( mem(c_2Epred__set_2ECHOICE(X1),arr(arr(X1,bool),X1))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,negated_conjecture,
( p(ap(ap(c_2Ebool_2EIN(esk4_0),esk3_3(esk4_0,X1,esk5_0)),X1))
| p(ap(ap(c_2Epred__set_2ESUBSET(esk4_0),X1),esk5_0))
| ~ mem(X1,arr(esk4_0,bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_23,plain,
( mem(ap(c_2Epred__set_2EREST(X1),X2),arr(X1,bool))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( p(ap(ap(c_2Epred__set_2ESUBSET(esk4_0),X1),esk5_0))
| mem(esk3_3(esk4_0,X1,esk5_0),esk4_0)
| ~ mem(X1,arr(esk4_0,bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_14]),c_0_15])]) ).
cnf(c_0_25,plain,
( p(ap(ap(c_2Ebool_2EIN(X1),X2),X3))
| ~ p(ap(ap(c_2Ebool_2EIN(X1),X2),ap(ap(c_2Epred__set_2EDELETE(X1),X3),X4)))
| ~ mem(X4,X1)
| ~ mem(X2,X1)
| ~ mem(X3,arr(X1,bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( ap(c_2Epred__set_2EREST(X1),X2) = ap(ap(c_2Epred__set_2EDELETE(X1),X2),ap(c_2Epred__set_2ECHOICE(X1),X2))
| ~ ne(X1)
| ~ mem(X2,arr(X1,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( mem(ap(c_2Epred__set_2ECHOICE(X1),X2),X1)
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( p(ap(ap(c_2Ebool_2EIN(esk4_0),esk3_3(esk4_0,ap(c_2Epred__set_2EREST(esk4_0),X1),esk5_0)),ap(c_2Epred__set_2EREST(esk4_0),X1)))
| p(ap(ap(c_2Epred__set_2ESUBSET(esk4_0),ap(c_2Epred__set_2EREST(esk4_0),X1)),esk5_0))
| ~ mem(X1,arr(esk4_0,bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_15])]) ).
cnf(c_0_29,negated_conjecture,
~ p(ap(ap(c_2Epred__set_2ESUBSET(esk4_0),ap(c_2Epred__set_2EREST(esk4_0),esk5_0)),esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_30,negated_conjecture,
( p(ap(ap(c_2Epred__set_2ESUBSET(esk4_0),ap(c_2Epred__set_2EREST(esk4_0),X1)),esk5_0))
| mem(esk3_3(esk4_0,ap(c_2Epred__set_2EREST(esk4_0),X1),esk5_0),esk4_0)
| ~ mem(X1,arr(esk4_0,bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_15])]) ).
cnf(c_0_31,plain,
( p(ap(ap(c_2Ebool_2EIN(X1),X2),X3))
| ~ p(ap(ap(c_2Ebool_2EIN(X1),X2),ap(c_2Epred__set_2EREST(X1),X3)))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,X1)
| ~ ne(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_32,negated_conjecture,
p(ap(ap(c_2Ebool_2EIN(esk4_0),esk3_3(esk4_0,ap(c_2Epred__set_2EREST(esk4_0),esk5_0),esk5_0)),ap(c_2Epred__set_2EREST(esk4_0),esk5_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_14]),c_0_29]) ).
cnf(c_0_33,negated_conjecture,
mem(esk3_3(esk4_0,ap(c_2Epred__set_2EREST(esk4_0),esk5_0),esk5_0),esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_14]),c_0_29]) ).
cnf(c_0_34,plain,
( p(ap(ap(c_2Epred__set_2ESUBSET(X1),X2),X3))
| ~ p(ap(ap(c_2Ebool_2EIN(X1),esk3_3(X1,X2,X3)),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_35,negated_conjecture,
p(ap(ap(c_2Ebool_2EIN(esk4_0),esk3_3(esk4_0,ap(c_2Epred__set_2EREST(esk4_0),esk5_0),esk5_0)),esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_14]),c_0_33]),c_0_15])]) ).
cnf(c_0_36,negated_conjecture,
~ mem(ap(c_2Epred__set_2EREST(esk4_0),esk5_0),arr(esk4_0,bool)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_14]),c_0_15])]),c_0_29]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_23]),c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP004+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 13:06:51 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.85/0.91 % Version : CSE_E---1.5
% 0.85/0.91 % Problem : theBenchmark.p
% 0.85/0.91 % Proof found
% 0.85/0.91 % SZS status Theorem for theBenchmark.p
% 0.85/0.91 % SZS output start Proof
% See solution above
% 0.85/0.91 % Total time : 0.341000 s
% 0.85/0.91 % SZS output end Proof
% 0.85/0.91 % Total time : 0.345000 s
%------------------------------------------------------------------------------