%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV002^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n010.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 02:56:05 PM UTC 2025
% Result : Theorem 19.49s 19.65s
% Output : Proof 19.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 222 ( 66 equ; 0 cnn)
% Maximal formula atoms : 22 ( 8 avg)
% Number of connectives : 583 ( 84 ~; 18 |; 10 &; 430 @)
% ( 0 <=>; 40 =>; 1 <=; 0 <~>)
% Maximal formula depth : 35 ( 8 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 9 con; 0-2 aty)
% Number of variables : 148 ( 0 ^; 148 !; 0 ?; 148 :)
% 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(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(c_0_3,plain,
( p1
| ~ p2 ),
inference(fof_simplification,[status(thm)],[ax1016]) ).
thf(c_0_4,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax1017]) ).
thf(c_0_5,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_6,plain,
( p1
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_7,plain,
~ p1,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_8,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_5]) ).
thf(c_0_9,plain,
~ p2,
inference(sr,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_10,plain,
! [X1: a] :
( ( ( f__0 @ X1 @ X1 )
= X1 )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_11,plain,
( 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 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_12,plain,
! [X1: a,X2: a,X3: a] :
( ( ( f__0 @ X1 @ ( esk1894_0 @ X2 @ X3 ) )
= ( esk1894_0 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) ) )
| p2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_13,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_8,c_0_9]) ).
thf(c_0_14,plain,
! [X1: a] :
( ( f__0 @ X1 @ X1 )
= X1 ),
inference(sr,[status(thm)],[c_0_10,c_0_9]) ).
thf(c_0_15,plain,
( ( esk1894_0 @ ( f__0 @ esk1895_0 @ esk1896_0 ) @ ( f__0 @ esk1895_0 @ esk1897_0 ) )
!= ( f__0 @ esk1895_0 @ ( esk1894_0 @ esk1896_0 @ ( f__0 @ esk1895_0 @ esk1897_0 ) ) ) ),
inference(sr,[status(thm)],[c_0_11,c_0_9]) ).
thf(c_0_16,plain,
! [X1: a,X2: a,X3: a] :
( ( esk1894_0 @ ( f__0 @ X1 @ X2 ) @ ( f__0 @ X1 @ X3 ) )
= ( f__0 @ X1 @ ( esk1894_0 @ X2 @ X3 ) ) ),
inference(sr,[status(thm)],[c_0_12,c_0_9]) ).
thf(c_0_17,plain,
! [X1: a,X2: a] :
( ( f__0 @ X1 @ ( f__0 @ X1 @ X2 ) )
= ( f__0 @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,plain,
( ( f__0 @ esk1895_0 @ ( esk1894_0 @ esk1896_0 @ ( f__0 @ esk1895_0 @ esk1897_0 ) ) )
!= ( f__0 @ esk1895_0 @ ( esk1894_0 @ esk1896_0 @ esk1897_0 ) ) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_19,plain,
! [X1: a,X2: a,X3: a] :
( ( f__0 @ X1 @ ( esk1894_0 @ X2 @ ( f__0 @ X1 @ X3 ) ) )
= ( f__0 @ X1 @ ( esk1894_0 @ X2 @ X3 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_16]) ).
thf(c_0_20,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[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 v9.2.0. 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 : n010.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 19:18:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 19.49/19.65 % SZS status Theorem
% 19.49/19.65 % Mode: mode485
% 19.49/19.65 % Inferences: 29
% 19.49/19.65 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------