%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV243-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:31:50 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 31 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 40 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 7 ~; 3 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 2 ( 2 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 : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 42 ( 38 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_union_type,type,
c_union: ( $i * $i * $i ) > $i ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
tff(v_H_type,type,
v_H: $i ).
tff(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
tff(c_emptyset_type,type,
c_emptyset: $i ).
tff(1,plain,
^ [T_a: $i,V_y: $i] :
refl(( ( c_union(V_y,c_emptyset,T_a) = V_y )
<=> ( c_union(V_y,c_emptyset,T_a) = V_y ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y )
<=> ! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
tff(5,plain,
! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y )
| ( c_union(v_H,c_emptyset,tc_Message_Omsg) = v_H ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_union(v_H,c_emptyset,tc_Message_Omsg) = v_H,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_Message_Oanalz(c_union(v_H,c_emptyset,tc_Message_Omsg)) = c_Message_Oanalz(v_H),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
c_Message_Oanalz(v_H) = c_Message_Oanalz(c_union(v_H,c_emptyset,tc_Message_Omsg)),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
c_union(c_Message_Oanalz(v_H),c_Message_Osynth(v_H),tc_Message_Omsg) = c_union(c_Message_Oanalz(c_union(v_H,c_emptyset,tc_Message_Omsg)),c_Message_Osynth(v_H),tc_Message_Omsg),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
c_union(c_Message_Oanalz(c_union(v_H,c_emptyset,tc_Message_Omsg)),c_Message_Osynth(v_H),tc_Message_Omsg) = c_union(c_Message_Oanalz(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
^ [V_H: $i,V_G: $i] :
refl(( ( c_Message_Oanalz(c_union(c_Message_Osynth(V_G),V_H,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)),c_Message_Osynth(V_G),tc_Message_Omsg) )
<=> ( c_Message_Oanalz(c_union(c_Message_Osynth(V_G),V_H,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)),c_Message_Osynth(V_G),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [V_H: $i,V_G: $i] : ( c_Message_Oanalz(c_union(c_Message_Osynth(V_G),V_H,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)),c_Message_Osynth(V_G),tc_Message_Omsg) )
<=> ! [V_H: $i,V_G: $i] : ( c_Message_Oanalz(c_union(c_Message_Osynth(V_G),V_H,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)),c_Message_Osynth(V_G),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [V_H: $i,V_G: $i] : ( c_Message_Oanalz(c_union(c_Message_Osynth(V_G),V_H,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)),c_Message_Osynth(V_G),tc_Message_Omsg) )
<=> ! [V_H: $i,V_G: $i] : ( c_Message_Oanalz(c_union(c_Message_Osynth(V_G),V_H,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)),c_Message_Osynth(V_G),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
! [V_H: $i,V_G: $i] : ( c_Message_Oanalz(c_union(c_Message_Osynth(V_G),V_H,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)),c_Message_Osynth(V_G),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__synth__Un_0) ).
tff(18,plain,
! [V_H: $i,V_G: $i] : ( c_Message_Oanalz(c_union(c_Message_Osynth(V_G),V_H,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)),c_Message_Osynth(V_G),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [V_H: $i,V_G: $i] : ( c_Message_Oanalz(c_union(c_Message_Osynth(V_G),V_H,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)),c_Message_Osynth(V_G),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [V_H: $i,V_G: $i] : ( c_Message_Oanalz(c_union(c_Message_Osynth(V_G),V_H,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)),c_Message_Osynth(V_G),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( ~ ! [V_H: $i,V_G: $i] : ( c_Message_Oanalz(c_union(c_Message_Osynth(V_G),V_H,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)),c_Message_Osynth(V_G),tc_Message_Omsg) )
| ( c_Message_Oanalz(c_union(c_Message_Osynth(v_H),c_emptyset,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(v_H,c_emptyset,tc_Message_Omsg)),c_Message_Osynth(v_H),tc_Message_Omsg) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
c_Message_Oanalz(c_union(c_Message_Osynth(v_H),c_emptyset,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(v_H,c_emptyset,tc_Message_Omsg)),c_Message_Osynth(v_H),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_union(V_y,c_emptyset,T_a) = V_y )
| ( c_union(c_Message_Osynth(v_H),c_emptyset,tc_Message_Omsg) = c_Message_Osynth(v_H) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
c_union(c_Message_Osynth(v_H),c_emptyset,tc_Message_Omsg) = c_Message_Osynth(v_H),
inference(unit_resolution,[status(thm)],[23,7]) ).
tff(25,plain,
c_Message_Osynth(v_H) = c_union(c_Message_Osynth(v_H),c_emptyset,tc_Message_Omsg),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
c_Message_Oanalz(c_Message_Osynth(v_H)) = c_Message_Oanalz(c_union(c_Message_Osynth(v_H),c_emptyset,tc_Message_Omsg)),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
c_Message_Oanalz(c_Message_Osynth(v_H)) = c_union(c_Message_Oanalz(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),
inference(transitivity,[status(thm)],[26,22,13]) ).
tff(28,plain,
( ( c_Message_Oanalz(c_Message_Osynth(v_H)) != c_union(c_Message_Oanalz(v_H),c_Message_Osynth(v_H),tc_Message_Omsg) )
<=> ( c_Message_Oanalz(c_Message_Osynth(v_H)) != c_union(c_Message_Oanalz(v_H),c_Message_Osynth(v_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
c_Message_Oanalz(c_Message_Osynth(v_H)) != c_union(c_Message_Oanalz(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(30,plain,
c_Message_Oanalz(c_Message_Osynth(v_H)) != c_union(c_Message_Oanalz(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
$false,
inference(unit_resolution,[status(thm)],[30,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV243-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:36:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% See solution above
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------