%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN346-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:38:50 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of formulae : 23 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 100 ( 59 ~; 31 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 54 ( 50 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: ( $i * $i ) > $o ).
tff(z2_type,type,
z2: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
^ [Y2: $i,Y1: $i] :
refl(( f(Y1,z2(Y1,Y2))
<=> f(Y1,z2(Y1,Y2)) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y2: $i,Y1: $i] : f(Y1,z2(Y1,Y2))
<=> ! [Y2: $i,Y1: $i] : f(Y1,z2(Y1,Y2)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y2: $i,Y1: $i] : f(Y1,z2(Y1,Y2))
<=> ! [Y2: $i,Y1: $i] : f(Y1,z2(Y1,Y2)) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y2: $i,Y1: $i] : f(Y1,z2(Y1,Y2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
tff(5,plain,
! [Y2: $i,Y1: $i] : f(Y1,z2(Y1,Y2)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y2: $i,Y1: $i] : f(Y1,z2(Y1,Y2)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y2: $i,Y1: $i] : f(Y1,z2(Y1,Y2)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y2: $i,Y1: $i] : f(Y1,z2(Y1,Y2))
| f(b,z2(b,b)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
f(b,z2(b,b)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y2: $i,Y1: $i] :
refl(( ( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) )
<=> ( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) )
<=> ! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) )
<=> ! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
tff(14,plain,
! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) )
| ~ f(b,z2(b,b)) )
<=> ( ~ ! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) )
| ~ f(b,z2(b,b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ f(b,z2(b,b))
| ~ f(b,z2(b,b)) )
<=> ~ f(b,z2(b,b)) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) )
| ~ f(b,z2(b,b))
| ~ f(b,z2(b,b)) )
<=> ( ~ ! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) )
| ~ f(b,z2(b,b)) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) )
| ~ f(b,z2(b,b))
| ~ f(b,z2(b,b)) )
<=> ( ~ ! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) )
| ~ f(b,z2(b,b)) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) )
| ~ f(b,z2(b,b))
| ~ f(b,z2(b,b)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [Y2: $i,Y1: $i] :
( ~ f(b,z2(Y1,Y2))
| ~ f(Y2,z2(Y1,Y2)) )
| ~ f(b,z2(b,b)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,16,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN346-1 : TPTP v9.0.0. Released v1.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:33:27 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37 % SZS output start Proof
% See solution above
% 0.18/0.37 % E exiting
%------------------------------------------------------------------------------