%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL680+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:37 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 56 ( 33 ~; 10 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 10 ( 0 !; 9 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(p1_type,type,
p1: $i > $o ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ~ $false
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(3,plain,
( ? [X: $i] : $false
<=> $false ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(4,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ p1(X)
| p1(X) )
<=> $true )),
( ~ ( ~ p1(X)
| p1(X) )
<=> ~ $true )),
rewrite(( ~ $true
<=> $false )),
( ~ ( ~ p1(X)
| p1(X) )
<=> $false )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ? [X: $i] :
~ ( ~ p1(X)
| p1(X) )
<=> ? [X: $i] : $false ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ? [X: $i] :
~ ( ~ p1(X)
| p1(X) )
<=> $false ),
inference(transitivity,[status(thm)],[5,3]) ).
tff(7,plain,
( ~ ? [X: $i] :
~ ( ~ p1(X)
| p1(X) )
<=> ~ $false ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ~ ? [X: $i] :
~ ( ~ p1(X)
| p1(X) )
<=> $true ),
inference(transitivity,[status(thm)],[7,2]) ).
tff(9,plain,
( ~ ~ ? [X: $i] :
~ ( ~ p1(X)
| p1(X) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ~ ~ ? [X: $i] :
~ ( ~ p1(X)
| p1(X) )
<=> $false ),
inference(transitivity,[status(thm)],[9,1]) ).
tff(11,axiom,
~ ~ ? [X: $i] :
~ ( ~ p1(X)
| p1(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
tff(12,plain,
$false,
inference(modus_ponens,[status(thm)],[11,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL680+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n027.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 4 23:04:29 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% See solution above
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------