%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : DAT056^2 : TPTP v9.2.0. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 Oct 9 01:25:57 PM UTC 2025
% Result : Theorem 108.18s 108.06s
% Output : Proof 108.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 45 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 343 ( 36 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 346 ( 30 ~; 24 |; 1 &; 284 @)
% ( 0 <=>; 6 =>; 1 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 19 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_lst,type,
lst: $tType ).
thf(ty_eigen__1,type,
eigen__1: lst ).
thf(ty_eigen__0,type,
eigen__0: lst ).
thf(ty_ap,type,
ap: lst > lst > lst ).
thf(ty_xs,type,
xs: lst ).
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(h1,assumption,
~ ! [X1: lst] :
( ( ap @ xs @ ( ap @ eigen__0 @ X1 ) )
= ( ap @ ( ap @ xs @ eigen__0 ) @ X1 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ( ap @ xs @ ( ap @ eigen__0 @ eigen__1 ) )
!= ( ap @ ( ap @ xs @ eigen__0 ) @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(ax81,axiom,
( ~ p4
| p29 ),
file('<stdin>',ax81) ).
thf(pax2,axiom,
( p2
=> ! [X20: lst] :
( ( fap @ fnl @ X20 )
= X20 ) ),
file('<stdin>',pax2) ).
thf(ax31,axiom,
( ~ p29
| p79 ),
file('<stdin>',ax31) ).
thf(ax108,axiom,
p4,
file('<stdin>',ax108) ).
thf(nax1,axiom,
( p1
<= ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) ) ),
file('<stdin>',nax1) ).
thf(ax111,axiom,
~ p1,
file('<stdin>',ax111) ).
thf(pax3,axiom,
( p3
=> ! [X20: lst,X21: lst,X22: a] :
( ( fap @ ( fcns @ X22 @ X21 ) @ X20 )
= ( fcns @ X22 @ ( fap @ X21 @ X20 ) ) ) ),
file('<stdin>',pax3) ).
thf(pax79,axiom,
( p79
=> ( ( ( fap @ ( fap @ fnl @ f__0 ) @ f__1 )
= ( fap @ fnl @ ( fap @ f__0 @ f__1 ) ) )
=> ( ! [X1: a,X2: lst] :
( ( ( fap @ ( fap @ X2 @ f__0 ) @ f__1 )
= ( fap @ X2 @ ( fap @ f__0 @ f__1 ) ) )
=> ( ( fap @ ( fap @ ( fcns @ X1 @ X2 ) @ f__0 ) @ f__1 )
= ( fap @ ( fcns @ X1 @ X2 ) @ ( fap @ f__0 @ f__1 ) ) ) )
=> ( ( fap @ ( fap @ fxs @ f__0 ) @ f__1 )
= ( fap @ fxs @ ( fap @ f__0 @ f__1 ) ) ) ) ) ),
file('<stdin>',pax79) ).
thf(ax110,axiom,
p2,
file('<stdin>',ax110) ).
thf(ax109,axiom,
p3,
file('<stdin>',ax109) ).
thf(c_0_10,plain,
( ~ p4
| p29 ),
inference(fof_simplification,[status(thm)],[ax81]) ).
thf(c_0_11,plain,
! [X261: lst] :
( ~ p2
| ( ( fap @ fnl @ X261 )
= X261 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])]) ).
thf(c_0_12,plain,
( ~ p29
| p79 ),
inference(fof_simplification,[status(thm)],[ax31]) ).
thf(c_0_13,plain,
( p29
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
p4,
inference(split_conjunct,[status(thm)],[ax108]) ).
thf(c_0_15,plain,
( ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
!= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) )
| p1 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])]) ).
thf(c_0_16,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax111]) ).
thf(c_0_17,plain,
! [X255: lst,X256: lst,X257: a] :
( ~ p3
| ( ( fap @ ( fcns @ X257 @ X256 ) @ X255 )
= ( fcns @ X257 @ ( fap @ X256 @ X255 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax3])])]) ).
thf(c_0_18,plain,
( ( ( ( fap @ ( fap @ esk62_0 @ f__0 ) @ f__1 )
= ( fap @ esk62_0 @ ( fap @ f__0 @ f__1 ) ) )
| ( ( fap @ ( fap @ fxs @ f__0 ) @ f__1 )
= ( fap @ fxs @ ( fap @ f__0 @ f__1 ) ) )
| ( ( fap @ ( fap @ fnl @ f__0 ) @ f__1 )
!= ( fap @ fnl @ ( fap @ f__0 @ f__1 ) ) )
| ~ p79 )
& ( ( ( fap @ ( fap @ ( fcns @ esk61_0 @ esk62_0 ) @ f__0 ) @ f__1 )
!= ( fap @ ( fcns @ esk61_0 @ esk62_0 ) @ ( fap @ f__0 @ f__1 ) ) )
| ( ( fap @ ( fap @ fxs @ f__0 ) @ f__1 )
= ( fap @ fxs @ ( fap @ f__0 @ f__1 ) ) )
| ( ( fap @ ( fap @ fnl @ f__0 ) @ f__1 )
!= ( fap @ fnl @ ( fap @ f__0 @ f__1 ) ) )
| ~ p79 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax79])])])]) ).
thf(c_0_19,plain,
! [X2: lst] :
( ( ( fap @ fnl @ X2 )
= X2 )
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_20,plain,
p2,
inference(split_conjunct,[status(thm)],[ax110]) ).
thf(c_0_21,plain,
( p79
| ~ p29 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_22,plain,
p29,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).
thf(c_0_23,plain,
( p1
| ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
!= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_24,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_25,plain,
! [X1: a,X2: lst,X3: lst] :
( ( ( fap @ ( fcns @ X1 @ X2 ) @ X3 )
= ( fcns @ X1 @ ( fap @ X2 @ X3 ) ) )
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_26,plain,
p3,
inference(split_conjunct,[status(thm)],[ax109]) ).
thf(c_0_27,plain,
( ( ( fap @ ( fap @ esk62_0 @ f__0 ) @ f__1 )
= ( fap @ esk62_0 @ ( fap @ f__0 @ f__1 ) ) )
| ( ( fap @ ( fap @ fxs @ f__0 ) @ f__1 )
= ( fap @ fxs @ ( fap @ f__0 @ f__1 ) ) )
| ( ( fap @ ( fap @ fnl @ f__0 ) @ f__1 )
!= ( fap @ fnl @ ( fap @ f__0 @ f__1 ) ) )
| ~ p79 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_28,plain,
! [X2: lst] :
( ( fap @ fnl @ X2 )
= X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).
thf(c_0_29,plain,
p79,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
thf(c_0_30,plain,
( ( fap @ ( fap @ fxs @ f__0 ) @ f__1 )
!= ( fap @ fxs @ ( fap @ f__0 @ f__1 ) ) ),
inference(sr,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_31,plain,
( ( ( fap @ ( fap @ fxs @ f__0 ) @ f__1 )
= ( fap @ fxs @ ( fap @ f__0 @ f__1 ) ) )
| ( ( fap @ ( fap @ ( fcns @ esk61_0 @ esk62_0 ) @ f__0 ) @ f__1 )
!= ( fap @ ( fcns @ esk61_0 @ esk62_0 ) @ ( fap @ f__0 @ f__1 ) ) )
| ( ( fap @ ( fap @ fnl @ f__0 ) @ f__1 )
!= ( fap @ fnl @ ( fap @ f__0 @ f__1 ) ) )
| ~ p79 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_32,plain,
! [X1: a,X2: lst,X3: lst] :
( ( fcns @ X1 @ ( fap @ X2 @ X3 ) )
= ( fap @ ( fcns @ X1 @ X2 ) @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
thf(c_0_33,plain,
( ( fap @ ( fap @ esk62_0 @ f__0 ) @ f__1 )
= ( fap @ esk62_0 @ ( fap @ f__0 @ f__1 ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_28]),c_0_29])]),c_0_30]) ).
thf(c_0_34,plain,
( ( fap @ ( fap @ ( fcns @ esk61_0 @ esk62_0 ) @ f__0 ) @ f__1 )
!= ( fap @ ( fcns @ esk61_0 @ esk62_0 ) @ ( fap @ f__0 @ f__1 ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_28]),c_0_28]),c_0_29])]),c_0_30]) ).
thf(c_0_35,plain,
! [X1: a] :
( ( fap @ ( fap @ ( fcns @ X1 @ esk62_0 ) @ f__0 ) @ f__1 )
= ( fap @ ( fcns @ X1 @ esk62_0 ) @ ( fap @ f__0 @ f__1 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_32]),c_0_32]) ).
thf(c_0_36,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h2,h1,h0])],[]) ).
thf(2,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,1,h2]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,2,h1]) ).
thf(0,theorem,
! [X1: lst,X2: lst] :
( ( ap @ xs @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ xs @ X1 ) @ X2 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : DAT056^2 : TPTP v9.2.0. Released v5.4.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 8 17:34:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 108.18/108.06 % SZS status Theorem
% 108.18/108.06 % Mode: mode447
% 108.18/108.06 % Inferences: 22
% 108.18/108.06 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------