TSTP Solution File: SEV002^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV002^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n012.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 : Tue Jul 19 18:04:24 EDT 2022
% Result : Theorem 36.91s 37.47s
% Output : Proof 36.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 68 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 471 ( 97 equ; 0 cnn)
% Maximal formula atoms : 22 ( 6 avg)
% Number of connectives : 903 ( 138 ~; 63 |; 20 &; 628 @)
% ( 0 <=>; 52 =>; 2 <=; 0 <~>)
% Maximal formula depth : 35 ( 5 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 26 con; 0-2 aty)
% Number of variables : 204 ( 0 ^ 204 !; 0 ?; 204 :)
% Comments :
%------------------------------------------------------------------------------
thf(cMODULAR_THM_DEF2_pme,conjecture,
! [X1: a > a > a,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ X3 @ ( X1 @ X4 @ X5 ) )
= ( X1 @ ( X2 @ X3 @ X4 ) @ ( X2 @ X3 @ X5 ) ) ) )
=> ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ ( X1 @ X3 @ X5 ) ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > a > a,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ X3 @ ( X1 @ X4 @ X5 ) )
= ( X1 @ ( X2 @ X3 @ X4 ) @ ( X2 @ X3 @ X5 ) ) ) )
=> ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ ( X1 @ X3 @ X5 ) ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) ),
inference(assume_negation,[status(cth)],[cMODULAR_THM_DEF2_pme]) ).
thf(ax1016,axiom,
( p1
| ~ p2 ),
file('<stdin>',ax1016) ).
thf(ax1017,axiom,
~ p1,
file('<stdin>',ax1017) ).
thf(ax1015,axiom,
( p2
| ~ p3 ),
file('<stdin>',ax1015) ).
thf(ax930,axiom,
( ~ p37
| p92 ),
file('<stdin>',ax930) ).
thf(ax1013,axiom,
( p3
| ~ p5 ),
file('<stdin>',ax1013) ).
thf(ax843,axiom,
( ~ p92
| p177 ),
file('<stdin>',ax843) ).
thf(ax987,axiom,
p37,
file('<stdin>',ax987) ).
thf(ax1010,axiom,
( p5
| ~ p8 ),
file('<stdin>',ax1010) ).
thf(nax3,axiom,
( p3
<= ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: a] :
( ( f__0 @ X1 @ X1 )
= X1 )
=> ~ ! [X1: a] :
( ( f__1 @ X1 @ X1 )
= X1 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( f__1 @ ( f__1 @ X1 @ X2 ) @ X3 )
= ( f__1 @ X1 @ ( f__1 @ X2 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ( f__0 @ X1 @ X2 )
= ( f__0 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( f__1 @ X1 @ X2 )
= ( f__1 @ X2 @ X1 ) ) )
=> ~ ! [X1: a,X2: a] :
( ( f__0 @ ( f__1 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ ! [X1: a,X2: a] :
( ( f__1 @ ( f__0 @ X1 @ X2 ) @ X2 )
= X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( f__0 @ X1 @ ( f__1 @ X2 @ X3 ) )
= ( f__1 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ( f__1 @ X1 @ ( f__0 @ X2 @ X3 ) )
= ( f__0 @ ( f__1 @ X1 @ X2 ) @ ( f__1 @ X1 @ X3 ) ) ) )
=> ! [X1: a,X2: a,X3: a] :
( ( f__0 @ X1 @ ( f__1 @ X2 @ ( f__0 @ X1 @ X3 ) ) )
= ( f__1 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) ) ) ) ),
file('<stdin>',nax3) ).
thf(ax842,axiom,
( ~ p177
| p11
| p176 ),
file('<stdin>',ax842) ).
thf(ax1007,axiom,
( p8
| ~ p11 ),
file('<stdin>',ax1007) ).
thf(nax2,axiom,
( p2
<= ! [X4: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X2: a] :
( ( f__0 @ X2 @ X2 )
= X2 )
=> ~ ! [X2: a] :
( ( X4 @ X2 @ X2 )
= X2 ) )
=> ~ ! [X2: a,X3: a,X5: a] :
( ( f__0 @ ( f__0 @ X2 @ X3 ) @ X5 )
= ( f__0 @ X2 @ ( f__0 @ X3 @ X5 ) ) ) )
=> ~ ! [X2: a,X3: a,X5: a] :
( ( X4 @ ( X4 @ X2 @ X3 ) @ X5 )
= ( X4 @ X2 @ ( X4 @ X3 @ X5 ) ) ) )
=> ~ ! [X2: a,X3: a] :
( ( f__0 @ X2 @ X3 )
= ( f__0 @ X3 @ X2 ) ) )
=> ~ ! [X2: a,X3: a] :
( ( X4 @ X2 @ X3 )
= ( X4 @ X3 @ X2 ) ) )
=> ~ ! [X2: a,X3: a] :
( ( f__0 @ ( X4 @ X2 @ X3 ) @ X3 )
= X3 ) )
=> ~ ! [X2: a,X3: a] :
( ( X4 @ ( f__0 @ X2 @ X3 ) @ X3 )
= X3 ) )
=> ~ ! [X2: a,X3: a,X5: a] :
( ( f__0 @ X2 @ ( X4 @ X3 @ X5 ) )
= ( X4 @ ( f__0 @ X2 @ X3 ) @ ( f__0 @ X2 @ X5 ) ) ) )
=> ~ ! [X2: a,X3: a,X5: a] :
( ( X4 @ X2 @ ( f__0 @ X3 @ X5 ) )
= ( f__0 @ ( X4 @ X2 @ X3 ) @ ( X4 @ X2 @ X5 ) ) ) )
=> ! [X2: a,X3: a,X5: a] :
( ( f__0 @ X2 @ ( X4 @ X3 @ ( f__0 @ X2 @ X5 ) ) )
= ( X4 @ ( f__0 @ X2 @ X3 ) @ ( f__0 @ X2 @ X5 ) ) ) ) ),
file('<stdin>',nax2) ).
thf(pax175,axiom,
( p175
=> ( ( ( f__1 @ ( f__0 @ f__4 @ f__2 ) @ f__2 )
= f__2 )
=> ~ ! [X1: a] :
( ( f__0 @ ( f__1 @ ( f__0 @ f__4 @ f__2 ) @ f__2 ) @ ( f__1 @ f__3 @ ( f__0 @ f__2 @ X1 ) ) )
= ( f__1 @ ( f__0 @ f__2 @ f__3 ) @ ( f__0 @ f__2 @ X1 ) ) ) ) ),
file('<stdin>',pax175) ).
thf(ax841,axiom,
( ~ p176
| p175 ),
file('<stdin>',ax841) ).
thf(c_0_14,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1016]) ).
thf(c_0_15,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1017]) ).
thf(c_0_16,plain,
( p2
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax1015]) ).
thf(c_0_17,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_19,plain,
( ~ p37
| p92 ),
inference(fof_simplification,[status(thm)],[ax930]) ).
thf(c_0_20,plain,
( p3
| ~ p5 ),
inference(fof_simplification,[status(thm)],[ax1013]) ).
thf(c_0_21,plain,
( p2
| ~ p3 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_22,plain,
~ p2,
inference(sr,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_23,plain,
( ~ p92
| p177 ),
inference(fof_simplification,[status(thm)],[ax843]) ).
thf(c_0_24,plain,
( p92
| ~ p37 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_25,plain,
p37,
inference(split_conjunct,[status(thm)],[ax987]) ).
thf(c_0_26,plain,
( p5
| ~ p8 ),
inference(fof_simplification,[status(thm)],[ax1010]) ).
thf(c_0_27,plain,
( p3
| ~ p5 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_28,plain,
~ p3,
inference(sr,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_29,plain,
! [X3725: a,X3726: a,X3727: a,X3728: a,X3729: a,X3730: a,X3731: a,X3732: a,X3733: a,X3734: a,X3735: a,X3736: a,X3737: a,X3738: a,X3739: a,X3740: a,X3741: a,X3742: a,X3743: a,X3744: a,X3745: a,X3746: a] :
( ( ( ( f__0 @ X3725 @ X3725 )
= X3725 )
| p3 )
& ( ( ( f__1 @ X3726 @ X3726 )
= X3726 )
| p3 )
& ( ( ( f__0 @ ( f__0 @ X3727 @ X3728 ) @ X3729 )
= ( f__0 @ X3727 @ ( f__0 @ X3728 @ X3729 ) ) )
| p3 )
& ( ( ( f__1 @ ( f__1 @ X3730 @ X3731 ) @ X3732 )
= ( f__1 @ X3730 @ ( f__1 @ X3731 @ X3732 ) ) )
| p3 )
& ( ( ( f__0 @ X3733 @ X3734 )
= ( f__0 @ X3734 @ X3733 ) )
| p3 )
& ( ( ( f__1 @ X3735 @ X3736 )
= ( f__1 @ X3736 @ X3735 ) )
| p3 )
& ( ( ( f__0 @ ( f__1 @ X3737 @ X3738 ) @ X3738 )
= X3738 )
| p3 )
& ( ( ( f__1 @ ( f__0 @ X3739 @ X3740 ) @ X3740 )
= X3740 )
| p3 )
& ( ( ( f__0 @ X3741 @ ( f__1 @ X3742 @ X3743 ) )
= ( f__1 @ ( f__0 @ X3741 @ X3742 ) @ ( f__0 @ X3741 @ X3743 ) ) )
| p3 )
& ( ( ( f__1 @ X3744 @ ( f__0 @ X3745 @ X3746 ) )
= ( f__0 @ ( f__1 @ X3744 @ X3745 ) @ ( f__1 @ X3744 @ X3746 ) ) )
| p3 )
& ( ( ( f__0 @ esk1869_0 @ ( f__1 @ esk1870_0 @ ( f__0 @ esk1869_0 @ esk1871_0 ) ) )
!= ( f__1 @ ( f__0 @ esk1869_0 @ esk1870_0 ) @ ( f__0 @ esk1869_0 @ esk1871_0 ) ) )
| p3 ) ),
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)],[nax3])])])])])]) ).
thf(c_0_30,plain,
( ~ p177
| p11
| p176 ),
inference(fof_simplification,[status(thm)],[ax842]) ).
thf(c_0_31,plain,
( p177
| ~ p92 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_32,plain,
p92,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
thf(c_0_33,plain,
( p8
| ~ p11 ),
inference(fof_simplification,[status(thm)],[ax1007]) ).
thf(c_0_34,plain,
( p5
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_35,plain,
~ p5,
inference(sr,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_36,plain,
! [X2: a,X1: a] :
( ( ( f__1 @ X1 @ X2 )
= ( f__1 @ X2 @ X1 ) )
| p3 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_37,plain,
( p11
| p176
| ~ p177 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_38,plain,
p177,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
thf(c_0_39,plain,
( p8
| ~ p11 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_40,plain,
~ p8,
inference(sr,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_41,plain,
! [X3777: a,X3778: a,X3779: a,X3780: a,X3781: a,X3782: a,X3783: a,X3784: a,X3785: a,X3786: a,X3787: a,X3788: a,X3789: a,X3790: a,X3791: a,X3792: a,X3793: a,X3794: a,X3795: a,X3796: a,X3797: a,X3798: a] :
( ( ( ( f__0 @ X3777 @ X3777 )
= X3777 )
| p2 )
& ( ( ( esk1894_0 @ X3778 @ X3778 )
= X3778 )
| p2 )
& ( ( ( f__0 @ ( f__0 @ X3779 @ X3780 ) @ X3781 )
= ( f__0 @ X3779 @ ( f__0 @ X3780 @ X3781 ) ) )
| p2 )
& ( ( ( esk1894_0 @ ( esk1894_0 @ X3782 @ X3783 ) @ X3784 )
= ( esk1894_0 @ X3782 @ ( esk1894_0 @ X3783 @ X3784 ) ) )
| p2 )
& ( ( ( f__0 @ X3785 @ X3786 )
= ( f__0 @ X3786 @ X3785 ) )
| p2 )
& ( ( ( esk1894_0 @ X3787 @ X3788 )
= ( esk1894_0 @ X3788 @ X3787 ) )
| p2 )
& ( ( ( f__0 @ ( esk1894_0 @ X3789 @ X3790 ) @ X3790 )
= X3790 )
| p2 )
& ( ( ( esk1894_0 @ ( f__0 @ X3791 @ X3792 ) @ X3792 )
= X3792 )
| p2 )
& ( ( ( f__0 @ X3793 @ ( esk1894_0 @ X3794 @ X3795 ) )
= ( esk1894_0 @ ( f__0 @ X3793 @ X3794 ) @ ( f__0 @ X3793 @ X3795 ) ) )
| p2 )
& ( ( ( esk1894_0 @ X3796 @ ( f__0 @ X3797 @ X3798 ) )
= ( f__0 @ ( esk1894_0 @ X3796 @ X3797 ) @ ( esk1894_0 @ X3796 @ X3798 ) ) )
| p2 )
& ( ( ( f__0 @ esk1895_0 @ ( esk1894_0 @ esk1896_0 @ ( f__0 @ esk1895_0 @ esk1897_0 ) ) )
!= ( esk1894_0 @ ( f__0 @ esk1895_0 @ esk1896_0 ) @ ( f__0 @ esk1895_0 @ esk1897_0 ) ) )
| p2 ) ),
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)],[nax2])])])])])]) ).
thf(c_0_42,plain,
( ~ p175
| ( ( f__1 @ ( f__0 @ f__4 @ f__2 ) @ f__2 )
!= f__2 )
| ( ( f__0 @ ( f__1 @ ( f__0 @ f__4 @ f__2 ) @ f__2 ) @ ( f__1 @ f__3 @ ( f__0 @ f__2 @ esk1584_0 ) ) )
!= ( f__1 @ ( f__0 @ f__2 @ f__3 ) @ ( f__0 @ f__2 @ esk1584_0 ) ) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax175])])]) ).
thf(c_0_43,plain,
! [X1: a,X2: a] :
( ( ( f__1 @ ( f__0 @ X1 @ X2 ) @ X2 )
= X2 )
| p3 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_44,plain,
! [X2: a,X1: a] :
( ( f__1 @ X1 @ X2 )
= ( f__1 @ X2 @ X1 ) ),
inference(sr,[status(thm)],[c_0_36,c_0_28]) ).
thf(c_0_45,plain,
! [X1: a,X2: a,X3: a] :
( ( ( f__0 @ X1 @ ( f__1 @ X2 @ X3 ) )
= ( f__1 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) ) )
| p3 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_46,plain,
( ~ p176
| p175 ),
inference(fof_simplification,[status(thm)],[ax841]) ).
thf(c_0_47,plain,
( p176
| p11 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
thf(c_0_48,plain,
~ p11,
inference(sr,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_49,plain,
! [X1: a,X2: a,X3: a] :
( ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_50,plain,
! [X1: a] :
( ( ( f__0 @ X1 @ X1 )
= X1 )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_51,plain,
( ~ p175
| ( ( f__1 @ ( f__0 @ f__4 @ f__2 ) @ f__2 )
!= f__2 )
| ( ( f__0 @ ( f__1 @ ( f__0 @ f__4 @ f__2 ) @ f__2 ) @ ( f__1 @ f__3 @ ( f__0 @ f__2 @ esk1584_0 ) ) )
!= ( f__1 @ ( f__0 @ f__2 @ f__3 ) @ ( f__0 @ f__2 @ esk1584_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_52,plain,
! [X2: a,X1: a] :
( ( f__1 @ X1 @ ( f__0 @ X2 @ X1 ) )
= X1 ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_28]) ).
thf(c_0_53,plain,
! [X1: a,X2: a,X3: a] :
( ( f__1 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) )
= ( f__0 @ X1 @ ( f__1 @ X2 @ X3 ) ) ),
inference(sr,[status(thm)],[c_0_45,c_0_28]) ).
thf(c_0_54,plain,
( p175
| ~ p176 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_55,plain,
p176,
inference(sr,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_56,plain,
! [X1: a,X2: a,X3: a] :
( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
= ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ),
inference(sr,[status(thm)],[c_0_49,c_0_22]) ).
thf(c_0_57,plain,
! [X1: a] :
( ( f__0 @ X1 @ X1 )
= X1 ),
inference(sr,[status(thm)],[c_0_50,c_0_22]) ).
thf(c_0_58,plain,
( ( ( f__0 @ f__2 @ ( f__1 @ f__3 @ ( f__0 @ f__2 @ esk1584_0 ) ) )
!= ( f__0 @ f__2 @ ( f__1 @ f__3 @ esk1584_0 ) ) )
| ~ p175 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_44]),c_0_52]),c_0_44]),c_0_52]),c_0_53])]) ).
thf(c_0_59,plain,
p175,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
thf(c_0_60,plain,
! [X1: a,X2: a] :
( ( f__0 @ X1 @ ( f__0 @ X1 @ X2 ) )
= ( f__0 @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
thf(c_0_61,plain,
( f__0 @ f__2 @ ( f__1 @ f__3 @ ( f__0 @ f__2 @ esk1584_0 ) ) )
!= ( f__0 @ f__2 @ ( f__1 @ f__3 @ esk1584_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]) ).
thf(c_0_62,plain,
! [X1: a,X2: a,X3: a] :
( ( f__0 @ X1 @ ( f__1 @ X2 @ ( f__0 @ X1 @ X3 ) ) )
= ( f__0 @ X1 @ ( f__1 @ X2 @ X3 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_60]),c_0_53]) ).
thf(c_0_63,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],]) ).
thf(0,theorem,
! [X1: a > a > a,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: a] :
( ( X1 @ X3 @ X3 )
= X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 @ X3 )
= X3 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
= ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ X3 @ ( X2 @ X4 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
= ( X1 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ X3 @ X4 )
= ( X2 @ X4 @ X3 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( X2 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a] :
( ( X2 @ ( X1 @ X3 @ X4 ) @ X4 )
= X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ X5 ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ( X2 @ X3 @ ( X1 @ X4 @ X5 ) )
= ( X1 @ ( X2 @ X3 @ X4 ) @ ( X2 @ X3 @ X5 ) ) ) )
=> ! [X3: a,X4: a,X5: a] :
( ( X1 @ X3 @ ( X2 @ X4 @ ( X1 @ X3 @ X5 ) ) )
= ( X2 @ ( X1 @ X3 @ X4 ) @ ( X1 @ X3 @ X5 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV002^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n012.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 : 600
% 0.12/0.33 % DateTime : Tue Jun 28 16:03:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 36.91/37.47 % SZS status Theorem
% 36.91/37.47 % Mode: mode485
% 36.91/37.47 % Inferences: 29
% 36.91/37.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------