%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU957^5 : 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 : n017.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 02:53:01 PM UTC 2025
% Result : Theorem 23.73s 23.91s
% Output : Proof 23.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 21 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 118 ( 47 ~; 9 |; 2 &; 45 @)
% ( 0 <=>; 14 =>; 1 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 9 con; 0-2 aty)
% Number of variables : 41 ( 0 ^; 41 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(cTHM607_pme,conjecture,
( ~ ! [X1: ( a > $o ) > a] :
~ ! [X2: a > $o] :
( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) )
=> ( ~ ! [X1: a > b] :
~ ! [X2: b] :
~ ! [X3: a] :
( ( X1 @ X3 )
!= X2 )
=> ~ ! [X1: b > a] :
~ ! [X2: b,X3: b] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ! [X1: ( a > $o ) > a] :
~ ! [X2: a > $o] :
( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) )
=> ( ~ ! [X1: a > b] :
~ ! [X2: b] :
~ ! [X3: a] :
( ( X1 @ X3 )
!= X2 )
=> ~ ! [X1: b > a] :
~ ! [X2: b,X3: b] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM607_pme]) ).
thf(ax15,axiom,
( p1
| ~ p3 ),
file('<stdin>',ax15) ).
thf(ax17,axiom,
~ p1,
file('<stdin>',ax17) ).
thf(nax3,axiom,
( p3
<= ( ~ ! [X13: a > b] :
~ ! [X7: b] :
~ ! [X14: a] :
( ( X13 @ X14 )
!= X7 )
=> ~ ! [X15: b > a] :
~ ! [X7: b,X16: b] :
( ( ( X15 @ X7 )
= ( X15 @ X16 ) )
=> ( X7 = X16 ) ) ) ),
file('<stdin>',nax3) ).
thf(c_0_3,plain,
( p1
| ~ p3 ),
inference(fof_simplification,[status(thm)],[ax15]) ).
thf(c_0_4,plain,
~ p1,
inference(fof_simplification,[status(thm)],[ax17]) ).
thf(c_0_5,plain,
! [X50: b,X52: b > a] :
( ( ( ( esk16_0 @ ( esk17_1 @ X50 ) )
= X50 )
| p3 )
& ( ( ( X52 @ ( esk18_1 @ X52 ) )
= ( X52 @ ( esk19_1 @ X52 ) ) )
| p3 )
& ( ( ( esk18_1 @ X52 )
!= ( esk19_1 @ X52 ) )
| 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_6,plain,
( p1
| ~ p3 ),
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: b] :
( ( ( esk16_0 @ ( esk17_1 @ X1 ) )
= X1 )
| p3 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
~ p3,
inference(sr,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_10,plain,
! [X6: b > a] :
( ( ( X6 @ ( esk18_1 @ X6 ) )
= ( X6 @ ( esk19_1 @ X6 ) ) )
| p3 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_11,plain,
! [X6: b > a] :
( p3
| ( ( esk18_1 @ X6 )
!= ( esk19_1 @ X6 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_12,plain,
! [X1: b] :
( ( esk16_0 @ ( esk17_1 @ X1 ) )
= X1 ),
inference(sr,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_13,plain,
! [X6: b > a] :
( ( X6 @ ( esk18_1 @ X6 ) )
= ( X6 @ ( esk19_1 @ X6 ) ) ),
inference(sr,[status(thm)],[c_0_10,c_0_9]) ).
thf(c_0_14,plain,
! [X6: b > a] :
( ( esk18_1 @ X6 )
!= ( esk19_1 @ X6 ) ),
inference(sr,[status(thm)],[c_0_11,c_0_9]) ).
thf(c_0_15,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_12]),c_0_14]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
( ~ ! [X1: ( a > $o ) > a] :
~ ! [X2: a > $o] :
( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ( X2 @ ( X1 @ X2 ) ) )
=> ( ~ ! [X1: a > b] :
~ ! [X2: b] :
~ ! [X3: a] :
( ( X1 @ X3 )
!= X2 )
=> ~ ! [X1: b > a] :
~ ! [X2: b,X3: b] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU957^5 : TPTP v9.2.0. Released v4.0.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n017.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 : 300
% 0.12/0.34 % DateTime : Wed Oct 8 20:37:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 23.73/23.91 % SZS status Theorem
% 23.73/23.91 % Mode: mode371
% 23.73/23.91 % Inferences: 15
% 23.73/23.91 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------