%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO086-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:05:33 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 27 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 90 ( 24 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 92 ( 31 ~; 50 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 6 ( 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(open_type,type,
open: $i > $o ).
tff(sk15_type,type,
sk15: $i ).
tff(sk14_type,type,
sk14: $i ).
tff(part_of_type,type,
part_of: ( $i * $i ) > $o ).
tff(1,plain,
( ~ open(sk15)
<=> ~ open(sk15) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ open(sk15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_2_7_2_69) ).
tff(3,plain,
~ open(sk15),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( part_of(sk15,sk14)
<=> part_of(sk15,sk14) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
part_of(sk15,sk14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_2_7_2_68) ).
tff(6,plain,
part_of(sk15,sk14),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [B: $i,A: $i] :
refl(( ( open(A)
| ( A = B )
| ~ part_of(A,B) )
<=> ( open(A)
| ( A = B )
| ~ part_of(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [B: $i,A: $i] :
( open(A)
| ( A = B )
| ~ part_of(A,B) )
<=> ! [B: $i,A: $i] :
( open(A)
| ( A = B )
| ~ part_of(A,B) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [B: $i,A: $i] :
( open(A)
| ( A = B )
| ~ part_of(A,B) )
<=> ! [B: $i,A: $i] :
( open(A)
| ( A = B )
| ~ part_of(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [B: $i,A: $i] :
rewrite(( ( ~ part_of(A,B)
| ( A = B )
| open(A) )
<=> ( open(A)
| ( A = B )
| ~ part_of(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [B: $i,A: $i] :
( ~ part_of(A,B)
| ( A = B )
| open(A) )
<=> ! [B: $i,A: $i] :
( open(A)
| ( A = B )
| ~ part_of(A,B) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [B: $i,A: $i] :
( ~ part_of(A,B)
| ( A = B )
| open(A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax',c1_35) ).
tff(13,plain,
! [B: $i,A: $i] :
( open(A)
| ( A = B )
| ~ part_of(A,B) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [B: $i,A: $i] :
( open(A)
| ( A = B )
| ~ part_of(A,B) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [B: $i,A: $i] :
( open(A)
| ( A = B )
| ~ part_of(A,B) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i] :
( open(A)
| ( A = B )
| ~ part_of(A,B) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [B: $i,A: $i] :
( open(A)
| ( A = B )
| ~ part_of(A,B) )
| open(sk15)
| ( sk15 = sk14 )
| ~ part_of(sk15,sk14) )
<=> ( ~ ! [B: $i,A: $i] :
( open(A)
| ( A = B )
| ~ part_of(A,B) )
| open(sk15)
| ( sk15 = sk14 )
| ~ part_of(sk15,sk14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i] :
( open(A)
| ( A = B )
| ~ part_of(A,B) )
| open(sk15)
| ( sk15 = sk14 )
| ~ part_of(sk15,sk14) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i] :
( open(A)
| ( A = B )
| ~ part_of(A,B) )
| open(sk15)
| ( sk15 = sk14 )
| ~ part_of(sk15,sk14) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
sk15 = sk14,
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
( open(sk15)
<=> open(sk14) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( open(sk14)
<=> open(sk15) ),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( open(sk14)
<=> open(sk14) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
open(sk14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_2_7_2_67) ).
tff(25,plain,
open(sk14),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
open(sk15),
inference(modus_ponens,[status(thm)],[25,22]) ).
tff(27,plain,
$false,
inference(unit_resolution,[status(thm)],[3,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO086-1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.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 : Thu Jun 19 14:16:39 EDT 2025
% 0.11/0.32 % 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
%------------------------------------------------------------------------------