TSTP Solution File: DAT056^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : DAT056^2 : 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 : n007.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 40.43s 40.19s
% Output : Proof 40.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 65 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 444 ( 38 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 408 ( 53 ~; 41 |; 1 &; 300 @)
% ( 0 <=>; 11 =>; 2 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 25 con; 0-2 aty)
% Number of variables : 29 ( 0 ^ 29 !; 0 ?; 29 :)
% 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(ax1055,axiom,
( ~ p2
| p29 ),
file('<stdin>',ax1055) ).
thf(ax1081,axiom,
( p1
| ~ p5 ),
file('<stdin>',ax1081) ).
thf(ax1085,axiom,
~ p1,
file('<stdin>',ax1085) ).
thf(ax813,axiom,
( ~ p29
| p234 ),
file('<stdin>',ax813) ).
thf(ax1084,axiom,
p2,
file('<stdin>',ax1084) ).
thf(pax4,axiom,
( p4
=> ! [X7: lst] :
( ( fap @ fnl @ X7 )
= X7 ) ),
file('<stdin>',pax4) ).
thf(ax1080,axiom,
( p5
| ~ p6 ),
file('<stdin>',ax1080) ).
thf(ax444,axiom,
( ~ p234
| ~ p379
| p614 ),
file('<stdin>',ax444) ).
thf(nax379,axiom,
( p379
<= ( ( fap @ fnl @ ( fap @ f__0 @ f__1 ) )
= ( fap @ ( fap @ fnl @ f__0 ) @ f__1 ) ) ),
file('<stdin>',nax379) ).
thf(ax1082,axiom,
p4,
file('<stdin>',ax1082) ).
thf(ax607,axiom,
( ~ p71
| p6
| p434 ),
file('<stdin>',ax607) ).
thf(nax71,axiom,
( p71
<= ( ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
!= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) )
=> ( ! [X6: a,X2: lst] :
( ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
!= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) )
=> ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
!= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) ) )
=> ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
!= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) ) ) ) ),
file('<stdin>',nax71) ).
thf(pax434,axiom,
( p434
=> ( ! [X6: a,X2: lst] :
( ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
!= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) )
=> ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
!= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) ) )
=> ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
!= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) ) ) ),
file('<stdin>',pax434) ).
thf(pax3,axiom,
( p3
=> ! [X7: lst,X2: lst,X8: a] :
( ( fap @ ( fcns @ X8 @ X2 ) @ X7 )
= ( fcns @ X8 @ ( fap @ X2 @ X7 ) ) ) ),
file('<stdin>',pax3) ).
thf(pax614,axiom,
( p614
=> ( ! [X6: a,X2: lst] :
( ( ( fap @ X2 @ ( fap @ f__0 @ f__1 ) )
= ( fap @ ( fap @ X2 @ f__0 ) @ f__1 ) )
=> ( ( fap @ ( fcns @ X6 @ X2 ) @ ( fap @ f__0 @ f__1 ) )
= ( fap @ ( fap @ ( fcns @ X6 @ X2 ) @ f__0 ) @ f__1 ) ) )
=> ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) ) ) ),
file('<stdin>',pax614) ).
thf(ax1083,axiom,
p3,
file('<stdin>',ax1083) ).
thf(c_0_16,plain,
( ~ p2
| p29 ),
inference(fof_simplification,[status(thm)],[ax1055]) ).
thf(c_0_17,plain,
( p1
| ~ p5 ),
inference(fof_simplification,[status(thm)],[ax1081]) ).
thf(c_0_18,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1085]) ).
thf(c_0_19,plain,
( ~ p29
| p234 ),
inference(fof_simplification,[status(thm)],[ax813]) ).
thf(c_0_20,plain,
( p29
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_21,plain,
p2,
inference(split_conjunct,[status(thm)],[ax1084]) ).
thf(c_0_22,plain,
! [X3599: lst] :
( ~ p4
| ( ( fap @ fnl @ X3599 )
= X3599 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])]) ).
thf(c_0_23,plain,
( p5
| ~ p6 ),
inference(fof_simplification,[status(thm)],[ax1080]) ).
thf(c_0_24,plain,
( p1
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_25,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_26,plain,
( ~ p234
| ~ p379
| p614 ),
inference(fof_simplification,[status(thm)],[ax444]) ).
thf(c_0_27,plain,
( p234
| ~ p29 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_28,plain,
p29,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
thf(c_0_29,plain,
( ( ( fap @ fnl @ ( fap @ f__0 @ f__1 ) )
!= ( fap @ ( fap @ fnl @ f__0 ) @ f__1 ) )
| p379 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax379])]) ).
thf(c_0_30,plain,
! [X2: lst] :
( ( ( fap @ fnl @ X2 )
= X2 )
| ~ p4 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_31,plain,
p4,
inference(split_conjunct,[status(thm)],[ax1082]) ).
thf(c_0_32,plain,
( ~ p71
| p6
| p434 ),
inference(fof_simplification,[status(thm)],[ax607]) ).
thf(c_0_33,plain,
p71,
inference(fof_simplification,[status(thm)],[nax71]) ).
thf(c_0_34,plain,
( p5
| ~ p6 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_35,plain,
~ p5,
inference(sr,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_36,plain,
( p614
| ~ p234
| ~ p379 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_37,plain,
p234,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
thf(c_0_38,plain,
( p379
| ( ( fap @ fnl @ ( fap @ f__0 @ f__1 ) )
!= ( fap @ ( fap @ fnl @ f__0 ) @ f__1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_39,plain,
! [X2: lst] :
( ( fap @ fnl @ X2 )
= X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
thf(c_0_40,plain,
( ~ p434
| ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
!= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax434])]) ).
thf(c_0_41,plain,
( p6
| p434
| ~ p71 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_42,plain,
p71,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_43,plain,
~ p6,
inference(sr,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_44,plain,
! [X3601: lst,X3602: lst,X3603: a] :
( ~ p3
| ( ( fap @ ( fcns @ X3603 @ X3602 ) @ X3601 )
= ( fcns @ X3603 @ ( fap @ X3602 @ X3601 ) ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax3])])]) ).
thf(c_0_45,plain,
( ( ( ( fap @ esk762_0 @ ( fap @ f__0 @ f__1 ) )
= ( fap @ ( fap @ esk762_0 @ f__0 ) @ f__1 ) )
| ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) )
| ~ p614 )
& ( ( ( fap @ ( fcns @ esk761_0 @ esk762_0 ) @ ( fap @ f__0 @ f__1 ) )
!= ( fap @ ( fap @ ( fcns @ esk761_0 @ esk762_0 ) @ f__0 ) @ f__1 ) )
| ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) )
| ~ p614 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax614])])])]) ).
thf(c_0_46,plain,
( p614
| ~ p379 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
thf(c_0_47,plain,
p379,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_39])]) ).
thf(c_0_48,plain,
( ~ p434
| ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
!= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_49,plain,
p434,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]),c_0_43]) ).
thf(c_0_50,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_44]) ).
thf(c_0_51,plain,
p3,
inference(split_conjunct,[status(thm)],[ax1083]) ).
thf(c_0_52,plain,
( ( ( fap @ esk762_0 @ ( fap @ f__0 @ f__1 ) )
= ( fap @ ( fap @ esk762_0 @ f__0 ) @ f__1 ) )
| ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) )
| ~ p614 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_53,plain,
p614,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
thf(c_0_54,plain,
( fap @ ( fap @ fxs @ f__0 ) @ f__1 )
!= ( fap @ fxs @ ( fap @ f__0 @ f__1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).
thf(c_0_55,plain,
( ( ( fap @ fxs @ ( fap @ f__0 @ f__1 ) )
= ( fap @ ( fap @ fxs @ f__0 ) @ f__1 ) )
| ( ( fap @ ( fcns @ esk761_0 @ esk762_0 ) @ ( fap @ f__0 @ f__1 ) )
!= ( fap @ ( fap @ ( fcns @ esk761_0 @ esk762_0 ) @ f__0 ) @ f__1 ) )
| ~ p614 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_56,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_50,c_0_51])]) ).
thf(c_0_57,plain,
( ( fap @ ( fap @ esk762_0 @ f__0 ) @ f__1 )
= ( fap @ esk762_0 @ ( fap @ f__0 @ f__1 ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53])]),c_0_54]) ).
thf(c_0_58,plain,
( fap @ ( fap @ ( fcns @ esk761_0 @ esk762_0 ) @ f__0 ) @ f__1 )
!= ( fap @ ( fcns @ esk761_0 @ esk762_0 ) @ ( fap @ f__0 @ f__1 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_53])]),c_0_54]) ).
thf(c_0_59,plain,
! [X1: a] :
( ( fap @ ( fap @ ( fcns @ X1 @ esk762_0 ) @ f__0 ) @ f__1 )
= ( fap @ ( fcns @ X1 @ esk762_0 ) @ ( fap @ f__0 @ f__1 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_56]),c_0_56]) ).
thf(c_0_60,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]),
[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
% 0.07/0.12 % Problem : DAT056^2 : TPTP v8.1.0. Released v5.4.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 1 19:33:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 40.43/40.19 % SZS status Theorem
% 40.43/40.19 % Mode: mode485
% 40.43/40.19 % Inferences: 425
% 40.43/40.19 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------