%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ063-2 : TPTP v9.0.0. Released v3.2.0.
% 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 05:23:19 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 19 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 5 ~; 1 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 20 ( 18 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(t_a_type,type,
t_a: $i ).
tff(c_Mutil_Otiling_type,type,
c_Mutil_Otiling: ( $i * $i ) > $i ).
tff(v_A_type,type,
v_A: $i ).
tff(c_union_type,type,
c_union: ( $i * $i * $i ) > $i ).
tff(v_u_type,type,
v_u: $i ).
tff(c_emptyset_type,type,
c_emptyset: $i ).
tff(1,plain,
^ [T_a: $i,V_y: $i] :
refl(( ( c_union(c_emptyset,V_y,T_a) = V_y )
<=> ( c_union(c_emptyset,V_y,T_a) = V_y ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
tff(5,plain,
! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y )
| ( c_union(c_emptyset,v_u,t_a) = v_u ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_union(c_emptyset,v_u,t_a) = v_u,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
<=> c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
<=> c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
<=> c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(14,plain,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
( ~ c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
<=> ~ c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
~ c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(18,plain,
~ c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
$false,
inference(unit_resolution,[status(thm)],[18,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PUZ063-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.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 02:43:24 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
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------