%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET855-2 : TPTP v9.0.0. Released v3.2.0.
% 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 05:26:32 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 23 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 103 ( 31 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 138 ( 66 ~; 60 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 45 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Union_type,type,
c_Union: ( $i * $i ) > $i ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(v_Y_type,type,
v_Y: $i ).
tff(v_n_type,type,
v_n: $i ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(1,plain,
( ( v_n != c_Union(v_Y,tc_set(t_a)) )
<=> ( v_n != c_Union(v_Y,tc_set(t_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
v_n != c_Union(v_Y,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(3,plain,
v_n != c_Union(v_Y,tc_set(t_a)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a)))
<=> c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(6,plain,
c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
<=> c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(9,plain,
c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(( ( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
<=> ( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
trans(monotonicity(rewrite(( ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
<=> ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) )),
( ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) )
<=> ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ( V_A = V_B ) ) )),
rewrite(( ( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ( V_A = V_B ) )
<=> ( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) )),
( ( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) )
<=> ( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
tff(16,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
| ( v_n = c_Union(v_Y,tc_set(t_a)) )
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
| ( v_n = c_Union(v_Y,tc_set(t_a)) )
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
| ( v_n = c_Union(v_Y,tc_set(t_a)) )
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] :
( ( V_A = V_B )
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) )
| ( v_n = c_Union(v_Y,tc_set(t_a)) )
| ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,19,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SET855-2 : TPTP v9.0.0. Released v3.2.0.
% 0.09/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:47:48 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------