%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : REL049-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:23:49 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 22 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 28 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 5 ~; 1 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 27 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk2_type,type,
sk2: $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(1,plain,
( ( join(sk1,sk2) = sk2 )
<=> ( join(sk1,sk2) = sk2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
join(sk1,sk2) = sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
tff(3,plain,
join(sk1,sk2) = sk2,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( join(sk3,sk2) = sk2 )
<=> ( join(sk3,sk2) = sk2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
join(sk3,sk2) = sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_15) ).
tff(6,plain,
join(sk3,sk2) = sk2,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
join(sk1,join(sk3,sk2)) = join(sk1,sk2),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( join(A,join(B,C)) = join(join(A,B),C) )
<=> ( join(A,join(B,C)) = join(join(A,B),C) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux2_join_associativity_2) ).
tff(12,plain,
! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
| ( join(sk1,join(sk3,sk2)) = join(join(sk1,sk3),sk2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
join(sk1,join(sk3,sk2)) = join(join(sk1,sk3),sk2),
inference(unit_resolution,[status(thm)],[15,14]) ).
tff(17,plain,
join(join(sk1,sk3),sk2) = join(sk1,join(sk3,sk2)),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
join(join(sk1,sk3),sk2) = sk2,
inference(transitivity,[status(thm)],[17,7,3]) ).
tff(19,plain,
( ( join(join(sk1,sk3),sk2) != sk2 )
<=> ( join(join(sk1,sk3),sk2) != sk2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
join(join(sk1,sk3),sk2) != sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_16) ).
tff(21,plain,
join(join(sk1,sk3),sk2) != sk2,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
$false,
inference(unit_resolution,[status(thm)],[21,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : REL049-1 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 03:03:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------