%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV432^1 : TPTP v9.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n008.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 02:56:49 PM UTC 2025
% Result : Theorem 19.29s 19.52s
% Output : Proof 19.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 11 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 48 ( 15 ~; 4 |; 0 &; 27 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 9 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(invexists,conjecture,
~ ! [X1: b > a] :
~ ! [X2: b] :
( ( f @ ( X1 @ X2 ) )
= X2 ) ).
thf(h0,negated_conjecture,
! [X1: b > a] :
~ ! [X2: b] :
( ( f @ ( X1 @ X2 ) )
= X2 ),
inference(assume_negation,[status(cth)],[invexists]) ).
thf(pax1,axiom,
( p1
=> ! [X34: b > a] :
~ ! [X35: b] :
( ( ff @ ( X34 @ X35 ) )
= X35 ) ),
file('<stdin>',pax1) ).
thf(pax2,axiom,
( p2
=> ! [X32: b] :
~ ! [X33: a] :
( ( ff @ X33 )
!= X32 ) ),
file('<stdin>',pax2) ).
thf(ax14939,axiom,
p1,
file('<stdin>',ax14939) ).
thf(ax14938,axiom,
p2,
file('<stdin>',ax14938) ).
thf(c_0_4,plain,
! [X168: b > a] :
( ~ p1
| ( ( ff @ ( X168 @ ( esk67_1 @ X168 ) ) )
!= ( esk67_1 @ X168 ) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1])])])]) ).
thf(c_0_5,plain,
! [X164: b] :
( ~ p2
| ( ( ff @ ( esk65_1 @ X164 ) )
= X164 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax2])])])])]) ).
thf(c_0_6,plain,
! [X34: b > a] :
( ~ p1
| ( ( ff @ ( X34 @ ( esk67_1 @ X34 ) ) )
!= ( esk67_1 @ X34 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_7,plain,
p1,
inference(split_conjunct,[status(thm)],[ax14939]) ).
thf(c_0_8,plain,
! [X2: b] :
( ( ( ff @ ( esk65_1 @ X2 ) )
= X2 )
| ~ p2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
p2,
inference(split_conjunct,[status(thm)],[ax14938]) ).
thf(c_0_10,plain,
! [X34: b > a] :
( ( ff @ ( X34 @ ( esk67_1 @ X34 ) ) )
!= ( esk67_1 @ X34 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7])]) ).
thf(c_0_11,plain,
! [X2: b] :
( ( ff @ ( esk65_1 @ X2 ) )
= X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9])]) ).
thf(c_0_12,plain,
$false,
inference(spm,[status(thm)],[c_0_10,c_0_11]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
~ ! [X1: b > a] :
~ ! [X2: b] :
( ( f @ ( X1 @ X2 ) )
= X2 ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : SEV432^1 : TPTP v9.2.0. Released v5.2.0.
% 0.14/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 19:13:53 EDT 2025
% 0.14/0.36 % CPUTime :
% 19.29/19.52 % SZS status Theorem
% 19.29/19.52 % Mode: mode485
% 19.29/19.52 % Inferences: 14636
% 19.29/19.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------