TSTP Solution File: DAT056^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : DAT056^1 : TPTP v8.1.0. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n021.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 : 600s
% DateTime : Sat Jul 16 01:24:20 EDT 2022
% Result : Theorem 2.39s 2.64s
% Output : Proof 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 47 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 226 ( 23 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 245 ( 32 ~; 27 |; 1 &; 180 @)
% ( 0 <=>; 3 =>; 2 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 22 con; 0-2 aty)
% Number of variables : 39 ( 0 ^ 39 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(conj_0,conjecture,
! [X1: lst,X2: lst] :
( ( ap @ xs @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ xs @ X1 ) @ X2 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: lst,X2: lst] :
( ( ap @ xs @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ xs @ X1 ) @ X2 ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(ax1150,axiom,
( ~ p2
| p28 ),
file('<stdin>',ax1150) ).
thf(pax4,axiom,
( p4
=> ! [X124: lst] :
( ( fap @ fnl @ X124 )
= X124 ) ),
file('<stdin>',pax4) ).
thf(ax1151,axiom,
( ~ p28
| ~ p25
| p27 ),
file('<stdin>',ax1151) ).
thf(ax1177,axiom,
p2,
file('<stdin>',ax1177) ).
thf(nax25,axiom,
( p25
<= ! [X124: lst,X54: lst] :
( ( fap @ fnl @ ( fap @ X124 @ X54 ) )
= ( fap @ ( fap @ fnl @ X124 ) @ X54 ) ) ),
file('<stdin>',nax25) ).
thf(ax1175,axiom,
p4,
file('<stdin>',ax1175) ).
thf(ax1152,axiom,
( ~ p27
| ~ p26
| p1 ),
file('<stdin>',ax1152) ).
thf(ax1178,axiom,
~ p1,
file('<stdin>',ax1178) ).
thf(pax3,axiom,
( p3
=> ! [X124: lst,X54: lst,X125: a] :
( ( fap @ ( fcns @ X125 @ X54 ) @ X124 )
= ( fcns @ X125 @ ( fap @ X54 @ X124 ) ) ) ),
file('<stdin>',pax3) ).
thf(nax26,axiom,
( p26
<= ! [X123: a,X54: lst] :
( ! [X46: lst,X5: lst] :
( ( fap @ X54 @ ( fap @ X46 @ X5 ) )
= ( fap @ ( fap @ X54 @ X46 ) @ X5 ) )
=> ! [X46: lst,X5: lst] :
( ( fap @ ( fcns @ X123 @ X54 ) @ ( fap @ X46 @ X5 ) )
= ( fap @ ( fap @ ( fcns @ X123 @ X54 ) @ X46 ) @ X5 ) ) ) ),
file('<stdin>',nax26) ).
thf(ax1176,axiom,
p3,
file('<stdin>',ax1176) ).
thf(c_0_11,plain,
( ~ p2
| p28 ),
inference(fof_simplification,[status(thm)],[ax1150]) ).
thf(c_0_12,plain,
! [X2335: lst] :
( ~ p4
| ( ( fap @ fnl @ X2335 )
= X2335 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])]) ).
thf(c_0_13,plain,
( ~ p28
| ~ p25
| p27 ),
inference(fof_simplification,[status(thm)],[ax1151]) ).
thf(c_0_14,plain,
( p28
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
p2,
inference(split_conjunct,[status(thm)],[ax1177]) ).
thf(c_0_16,plain,
( ( ( fap @ fnl @ ( fap @ esk1092_0 @ esk1093_0 ) )
!= ( fap @ ( fap @ fnl @ esk1092_0 ) @ esk1093_0 ) )
| p25 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax25])])])]) ).
thf(c_0_17,plain,
! [X1: lst] :
( ( ( fap @ fnl @ X1 )
= X1 )
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,plain,
p4,
inference(split_conjunct,[status(thm)],[ax1175]) ).
thf(c_0_19,plain,
( ~ p27
| ~ p26
| p1 ),
inference(fof_simplification,[status(thm)],[ax1152]) ).
thf(c_0_20,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1178]) ).
thf(c_0_21,plain,
( p27
| ~ p28
| ~ p25 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_22,plain,
p28,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
thf(c_0_23,plain,
( p25
| ( ( fap @ fnl @ ( fap @ esk1092_0 @ esk1093_0 ) )
!= ( fap @ ( fap @ fnl @ esk1092_0 ) @ esk1093_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_24,plain,
! [X1: lst] :
( ( fap @ fnl @ X1 )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
thf(c_0_25,plain,
( p1
| ~ p27
| ~ p26 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_26,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_27,plain,
( p27
| ~ p25 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
thf(c_0_28,plain,
p25,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24])]) ).
thf(c_0_29,plain,
! [X2337: lst,X2338: lst,X2339: a] :
( ~ p3
| ( ( fap @ ( fcns @ X2339 @ X2338 ) @ X2337 )
= ( fcns @ X2339 @ ( fap @ X2338 @ X2337 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax3])])]) ).
thf(c_0_30,plain,
! [X2309: lst,X2310: lst] :
( ( ( ( fap @ esk1089_0 @ ( fap @ X2309 @ X2310 ) )
= ( fap @ ( fap @ esk1089_0 @ X2309 ) @ X2310 ) )
| p26 )
& ( ( ( fap @ ( fcns @ esk1088_0 @ esk1089_0 ) @ ( fap @ esk1090_0 @ esk1091_0 ) )
!= ( fap @ ( fap @ ( fcns @ esk1088_0 @ esk1089_0 ) @ esk1090_0 ) @ esk1091_0 ) )
| p26 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax26])])])])])]) ).
thf(c_0_31,plain,
( ~ p26
| ~ p27 ),
inference(sr,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_32,plain,
p27,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
thf(c_0_33,plain,
! [X1: lst,X3: a,X2: lst] :
( ( ( fap @ ( fcns @ X3 @ X1 ) @ X2 )
= ( fcns @ X3 @ ( fap @ X1 @ X2 ) ) )
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_34,plain,
p3,
inference(split_conjunct,[status(thm)],[ax1176]) ).
thf(c_0_35,plain,
! [X1: lst,X2: lst] :
( ( ( fap @ esk1089_0 @ ( fap @ X1 @ X2 ) )
= ( fap @ ( fap @ esk1089_0 @ X1 ) @ X2 ) )
| p26 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_36,plain,
~ p26,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
thf(c_0_37,plain,
( p26
| ( ( fap @ ( fcns @ esk1088_0 @ esk1089_0 ) @ ( fap @ esk1090_0 @ esk1091_0 ) )
!= ( fap @ ( fap @ ( fcns @ esk1088_0 @ esk1089_0 ) @ esk1090_0 ) @ esk1091_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_38,plain,
! [X1: lst,X3: a,X2: lst] :
( ( fcns @ X3 @ ( fap @ X1 @ X2 ) )
= ( fap @ ( fcns @ X3 @ X1 ) @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
thf(c_0_39,plain,
! [X1: lst,X2: lst] :
( ( fap @ ( fap @ esk1089_0 @ X1 ) @ X2 )
= ( fap @ esk1089_0 @ ( fap @ X1 @ X2 ) ) ),
inference(sr,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_40,plain,
( fap @ ( fap @ ( fcns @ esk1088_0 @ esk1089_0 ) @ esk1090_0 ) @ esk1091_0 )
!= ( fap @ ( fcns @ esk1088_0 @ esk1089_0 ) @ ( fap @ esk1090_0 @ esk1091_0 ) ),
inference(sr,[status(thm)],[c_0_37,c_0_36]) ).
thf(c_0_41,plain,
! [X1: lst,X3: a,X2: lst] :
( ( fap @ ( fap @ ( fcns @ X3 @ esk1089_0 ) @ X1 ) @ X2 )
= ( fap @ ( fcns @ X3 @ esk1089_0 ) @ ( fap @ X1 @ X2 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_38]),c_0_38]) ).
thf(c_0_42,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
! [X1: lst,X2: lst] :
( ( ap @ xs @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ xs @ X1 ) @ X2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : DAT056^1 : TPTP v8.1.0. Released v5.4.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n021.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 : 600
% 0.12/0.34 % DateTime : Fri Jul 1 20:32:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.39/2.64 % SZS status Theorem
% 2.39/2.64 % Mode: mode506
% 2.39/2.64 % Inferences: 8206
% 2.39/2.64 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------