%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN120-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:38:17 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 20 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 66 ( 31 ~; 27 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 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 : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 34 ( 30 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(l1_type,type,
l1: ( $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(1,plain,
( ~ l1(e,e)
<=> ~ l1(e,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ l1(e,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(3,plain,
~ l1(e,e),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [H: $i,G: $i] :
refl(( ( ~ n0(H,G)
| l1(G,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [H: $i,G: $i] :
rewrite(( ( l1(G,G)
| ~ n0(H,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_002) ).
tff(10,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( n0(d,e)
<=> n0(d,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
n0(d,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_3) ).
tff(16,plain,
n0(d,e),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,e)
| l1(e,e) )
<=> ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,e)
| l1(e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,e)
| l1(e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,e)
| l1(e,e) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
$false,
inference(unit_resolution,[status(thm)],[19,16,13,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN120-1 : TPTP v9.0.0. Released v1.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:28:57 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47 % SZS output start Proof
% See solution above
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------