%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL055-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : 300s
% DateTime : Sat Jun 21 05:00:39 AM UTC 2025
% Result : Unsatisfiable 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 19 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 24 ~; 4 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 21 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
tff(b_type,type,
b: $i ).
tff(response_type,type,
response: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( ( response(a,b) = b )
<=> ( response(a,b) = b ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
response(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fond_bird_exists) ).
tff(3,plain,
response(a,b) = b,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
response(a,response(a,b)) = response(a,b),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
response(a,response(a,b)) = b,
inference(transitivity,[status(thm)],[4,3]) ).
tff(6,plain,
^ [Z: $i] :
refl(( ( response(a,response(a,Z)) != Z )
<=> ( response(a,response(a,Z)) != Z ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [Z: $i] : ( response(a,response(a,Z)) != Z )
<=> ! [Z: $i] : ( response(a,response(a,Z)) != Z ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [Z: $i] : ( response(a,response(a,Z)) != Z )
<=> ! [Z: $i] : ( response(a,response(a,Z)) != Z ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,plain,
( ! [W: $i,Z: $i] : ( response(a,response(a,Z)) != Z )
<=> ! [Z: $i] : ( response(a,response(a,Z)) != Z ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(10,plain,
( ! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) )
<=> ! [W: $i,Z: $i] : ( response(a,response(a,Z)) != Z ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(11,plain,
( ! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) )
<=> ! [Z: $i] : ( response(a,response(a,Z)) != Z ) ),
inference(transitivity,[status(thm)],[10,9]) ).
tff(12,axiom,
! [W: $i,Z: $i] :
( ( response(a,Z) != W )
| ( response(a,W) != Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_happiness) ).
tff(13,plain,
! [Z: $i] : ( response(a,response(a,Z)) != Z ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [Z: $i] : ( response(a,response(a,Z)) != Z ),
inference(modus_ponens,[status(thm)],[13,8]) ).
tff(15,plain,
! [Z: $i] : ( response(a,response(a,Z)) != Z ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i] : ( response(a,response(a,Z)) != Z ),
inference(modus_ponens,[status(thm)],[15,7]) ).
tff(17,plain,
( ~ ! [Z: $i] : ( response(a,response(a,Z)) != Z )
| ( response(a,response(a,b)) != b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
response(a,response(a,b)) != b,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
$false,
inference(unit_resolution,[status(thm)],[18,5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COL055-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 12:09:11 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.39 % SZS status Unsatisfiable
% 0.14/0.39 % SZS output start Proof
% See solution above
% 0.14/0.39 % E exiting
%------------------------------------------------------------------------------