%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN280-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:38:39 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of formulae : 18 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 20 ~; 8 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 20 ( 18 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(q1_type,type,
q1: ( $i * $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(r0_type,type,
r0: $i > $o ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ~ q1(X,b,Y)
<=> ~ q1(X,b,Y) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ~ q1(X,b,Y)
<=> ! [Y: $i,X: $i] : ~ q1(X,b,Y) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ~ q1(X,b,Y)
<=> ! [Y: $i,X: $i] : ~ q1(X,b,Y) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ~ q1(X,b,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(5,plain,
! [Y: $i,X: $i] : ~ q1(X,b,Y),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ~ q1(X,b,Y),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ~ q1(X,b,Y),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( r0(b)
<=> r0(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
r0(b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_9) ).
tff(10,plain,
r0(b),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ r0(b)
| q1(b,b,b) )
<=> ( ~ r0(b)
| q1(b,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ( q1(b,b,b)
| ~ r0(b) )
<=> ( ~ r0(b)
| q1(b,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
( q1(b,b,b)
| ~ r0(b) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_120) ).
tff(14,plain,
( ~ r0(b)
| q1(b,b,b) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
( ~ r0(b)
| q1(b,b,b) ),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
q1(b,b,b),
inference(unit_resolution,[status(thm)],[15,10]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ~ q1(X,b,Y)
| ~ q1(b,b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
$false,
inference(unit_resolution,[status(thm)],[17,16,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SYN280-1 : TPTP v9.0.0. Released v1.1.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:30:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47 % SZS output start Proof
% See solution above
% 0.20/0.47 % E exiting
%------------------------------------------------------------------------------