%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV262-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:31:54 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 59 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 75 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 28 ( 11 ~; 7 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 3 ( 3 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 : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 92 ( 84 !; 0 ?; 92 :)
% 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_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(v_H_type,type,
v_H: $i ).
tff(c_insert_type,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(c_emptyset_type,type,
c_emptyset: $i ).
tff(v_Y_type,type,
v_Y: $i ).
tff(v_X_type,type,
v_X: $i ).
tff(1,plain,
^ [V_a: $i,T_a: $i,V_B: $i,V_C: $i] :
refl(( ( c_union(c_insert(V_a,V_B,T_a),V_C,T_a) = c_insert(V_a,c_union(V_B,V_C,T_a),T_a) )
<=> ( c_union(c_insert(V_a,V_B,T_a),V_C,T_a) = c_insert(V_a,c_union(V_B,V_C,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] : ( c_union(c_insert(V_a,V_B,T_a),V_C,T_a) = c_insert(V_a,c_union(V_B,V_C,T_a),T_a) )
<=> ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] : ( c_union(c_insert(V_a,V_B,T_a),V_C,T_a) = c_insert(V_a,c_union(V_B,V_C,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] : ( c_union(c_insert(V_a,V_B,T_a),V_C,T_a) = c_insert(V_a,c_union(V_B,V_C,T_a),T_a) )
<=> ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] : ( c_union(c_insert(V_a,V_B,T_a),V_C,T_a) = c_insert(V_a,c_union(V_B,V_C,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] : ( c_union(c_insert(V_a,V_B,T_a),V_C,T_a) = c_insert(V_a,c_union(V_B,V_C,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
tff(5,plain,
! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] : ( c_union(c_insert(V_a,V_B,T_a),V_C,T_a) = c_insert(V_a,c_union(V_B,V_C,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] : ( c_union(c_insert(V_a,V_B,T_a),V_C,T_a) = c_insert(V_a,c_union(V_B,V_C,T_a),T_a) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] : ( c_union(c_insert(V_a,V_B,T_a),V_C,T_a) = c_insert(V_a,c_union(V_B,V_C,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] : ( c_union(c_insert(V_a,V_B,T_a),V_C,T_a) = c_insert(V_a,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_insert(v_X,c_emptyset,tc_Message_Omsg),c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg) = c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_union(c_insert(v_X,c_emptyset,tc_Message_Omsg),c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg) = c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg) = c_union(c_insert(v_X,c_emptyset,tc_Message_Omsg),c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
c_Message_Oparts(c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)) = c_Message_Oparts(c_union(c_insert(v_X,c_emptyset,tc_Message_Omsg),c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg)),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
c_Message_Oparts(c_union(c_insert(v_X,c_emptyset,tc_Message_Omsg),c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg)) = c_Message_Oparts(c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
^ [V_H: $i,V_G: $i] :
refl(( ( c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ( c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_H: $i,V_G: $i] : ( c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_G: $i] : ( c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [V_H: $i,V_G: $i] : ( c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_G: $i] : ( c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
! [V_H: $i,V_G: $i] : ( c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).
tff(17,plain,
! [V_H: $i,V_G: $i] : ( c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [V_H: $i,V_G: $i] : ( c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_H: $i,V_G: $i] : ( c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ~ ! [V_H: $i,V_G: $i] : ( c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ( c_Message_Oparts(c_union(c_insert(v_X,c_emptyset,tc_Message_Omsg),c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg)) = c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
c_Message_Oparts(c_union(c_insert(v_X,c_emptyset,tc_Message_Omsg),c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg)) = c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) = c_Message_Oparts(c_union(c_insert(v_X,c_emptyset,tc_Message_Omsg),c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg)),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) = c_Message_Oparts(c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),
inference(transitivity,[status(thm)],[22,12]) ).
tff(24,plain,
c_union(c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(v_H),tc_Message_Omsg) = c_union(c_Message_Oparts(c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
c_union(c_Message_Oparts(c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(v_H),tc_Message_Omsg) = c_union(c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( ~ ! [V_H: $i,V_G: $i] : ( c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg) )
| ( c_Message_Oparts(c_union(c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(v_H),tc_Message_Omsg) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
c_Message_Oparts(c_union(c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)) = c_union(c_Message_Oparts(c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[26,19]) ).
tff(28,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(29,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)],[28]) ).
tff(30,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(31,axiom,
! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
tff(32,plain,
! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y )
| ( c_union(c_emptyset,v_H,tc_Message_Omsg) = v_H ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
c_union(c_emptyset,v_H,tc_Message_Omsg) = v_H,
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
v_H = c_union(c_emptyset,v_H,tc_Message_Omsg),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
c_insert(v_Y,v_H,tc_Message_Omsg) = c_insert(v_Y,c_union(c_emptyset,v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
c_insert(v_Y,c_union(c_emptyset,v_H,tc_Message_Omsg),tc_Message_Omsg) = c_insert(v_Y,v_H,tc_Message_Omsg),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( ~ ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] : ( c_union(c_insert(V_a,V_B,T_a),V_C,T_a) = c_insert(V_a,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_insert(v_Y,c_emptyset,tc_Message_Omsg),v_H,tc_Message_Omsg) = c_insert(v_Y,c_union(c_emptyset,v_H,tc_Message_Omsg),tc_Message_Omsg) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
c_union(c_insert(v_Y,c_emptyset,tc_Message_Omsg),v_H,tc_Message_Omsg) = c_insert(v_Y,c_union(c_emptyset,v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[40,7]) ).
tff(42,plain,
c_union(c_insert(v_Y,c_emptyset,tc_Message_Omsg),v_H,tc_Message_Omsg) = c_insert(v_Y,v_H,tc_Message_Omsg),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
c_insert(v_X,c_union(c_insert(v_Y,c_emptyset,tc_Message_Omsg),v_H,tc_Message_Omsg),tc_Message_Omsg) = c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ~ ! [V_a: $i,T_a: $i,V_B: $i,V_C: $i] : ( c_union(c_insert(V_a,V_B,T_a),V_C,T_a) = c_insert(V_a,c_union(V_B,V_C,T_a),T_a) )
| ( c_union(c_insert(v_X,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg) = c_insert(v_X,c_union(c_insert(v_Y,c_emptyset,tc_Message_Omsg),v_H,tc_Message_Omsg),tc_Message_Omsg) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
c_union(c_insert(v_X,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg) = c_insert(v_X,c_union(c_insert(v_Y,c_emptyset,tc_Message_Omsg),v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[44,7]) ).
tff(46,plain,
( ~ ! [T_a: $i,V_y: $i] : ( c_union(c_emptyset,V_y,T_a) = V_y )
| ( c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg) = c_insert(v_Y,c_emptyset,tc_Message_Omsg) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg) = c_insert(v_Y,c_emptyset,tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[46,34]) ).
tff(48,plain,
c_insert(v_Y,c_emptyset,tc_Message_Omsg) = c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
c_insert(v_X,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg) = c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg) = c_insert(v_X,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
c_union(c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg) = c_union(c_insert(v_X,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
c_union(c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg) = c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(transitivity,[status(thm)],[51,45,43]) ).
tff(53,plain,
c_Message_Oparts(c_union(c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)) = c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) = c_Message_Oparts(c_union(c_insert(v_X,c_union(c_emptyset,c_insert(v_Y,c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) = c_union(c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(transitivity,[status(thm)],[54,27,25]) ).
tff(56,plain,
( ( c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_union(c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(v_H),tc_Message_Omsg) )
<=> ( c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_union(c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(v_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_union(c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(v_H),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(58,plain,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_union(c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
$false,
inference(unit_resolution,[status(thm)],[58,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV262-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n007.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 09:35:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.46 % SZS status Unsatisfiable
% 0.21/0.46 % SZS output start Proof
% See solution above
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------