%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN112-1 : TPTP v9.0.0. Released v1.1.0.
% 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 05:38:16 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.49s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 94 ( 47 ~; 35 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 44 ( 39 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
tff(k2_type,type,
k2: ( $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(l1_type,type,
l1: ( $i * $i ) > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ~ k2(e,X)
<=> ~ k2(e,X) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ~ k2(e,X)
<=> ! [X: $i] : ~ k2(e,X) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ~ k2(e,X)
<=> ! [X: $i] : ~ k2(e,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ~ k2(e,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(5,plain,
! [X: $i] : ~ k2(e,X),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ~ k2(e,X),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ~ k2(e,X),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
^ [H: $i,G: $i] :
refl(( ( ~ n0(H,G)
| l1(G,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(9,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)],[8]) ).
tff(10,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(11,plain,
^ [H: $i,G: $i] :
rewrite(( ( l1(G,G)
| ~ n0(H,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(12,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)],[11]) ).
tff(13,axiom,
! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_002) ).
tff(14,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
( n0(d,e)
<=> n0(d,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
n0(d,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_3) ).
tff(20,plain,
n0(d,e),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,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(22,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,e)
| l1(e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,e)
| l1(e,e) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
l1(e,e),
inference(unit_resolution,[status(thm)],[23,20,17]) ).
tff(25,plain,
( ( ~ l1(e,e)
| k2(e,e) )
<=> ( ~ l1(e,e)
| k2(e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ( k2(e,e)
| ~ l1(e,e) )
<=> ( ~ l1(e,e)
| k2(e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
( k2(e,e)
| ~ l1(e,e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_130) ).
tff(28,plain,
( ~ l1(e,e)
| k2(e,e) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ~ l1(e,e)
| k2(e,e) ),
inference(modus_ponens,[status(thm)],[28,25]) ).
tff(30,plain,
k2(e,e),
inference(unit_resolution,[status(thm)],[29,24]) ).
tff(31,plain,
( ~ ! [X: $i] : ~ k2(e,X)
| ~ k2(e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,30,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN112-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:30:12 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.22/0.49 % SZS status Unsatisfiable
% 0.22/0.49 % SZS output start Proof
% See solution above
% 0.22/0.49 % E exiting
%------------------------------------------------------------------------------