%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV273-1 : TPTP v9.0.0. Released v3.2.0.
% 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 05:31:57 AM UTC 2025
% Result : Unsatisfiable 0.71s 0.90s
% Output : Proof 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 29
% Syntax : Number of formulae : 67 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 248 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 320 ( 151 ~; 143 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 164 ( 149 !; 0 ?; 164 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_set_type,type,
tc_set: $i > $i ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
tff(v_H_type,type,
v_H: $i ).
tff(c_union_type,type,
c_union: ( $i * $i * $i ) > $i ).
tff(1,plain,
^ [V_H: $i] :
refl(( c_lessequals(V_H,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
<=> c_lessequals(V_H,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_H: $i] : c_lessequals(V_H,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
<=> ! [V_H: $i] : c_lessequals(V_H,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_H: $i] : c_lessequals(V_H,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
<=> ! [V_H: $i] : c_lessequals(V_H,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_H: $i] : c_lessequals(V_H,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__increasing_0) ).
tff(5,plain,
! [V_H: $i] : c_lessequals(V_H,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_H: $i] : c_lessequals(V_H,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_H: $i] : c_lessequals(V_H,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_H: $i] : c_lessequals(V_H,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(v_H,c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_lessequals(v_H,c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_H: $i,V_G: $i] :
refl(( ( ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) )
<=> ( ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) )
<=> ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) )
<=> ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV005-1.ax',cls_Message_Osynth__subset__iff_1) ).
tff(14,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(v_H,c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(v_H),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(v_H,c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(v_H),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(v_H,c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(v_H),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,c_Message_Osynth(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(V_G),c_Message_Osynth(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(v_H,c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(v_H),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
c_lessequals(c_Message_Osynth(v_H),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[19,16,9]) ).
tff(21,plain,
^ [V_H: $i,V_G: $i] :
refl(( ( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
<=> ( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
<=> ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
<=> ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__mono_0) ).
tff(25,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_Message_Osynth(v_H),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_Message_Osynth(v_H),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_Message_Osynth(v_H),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_Message_Osynth(v_H),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
( ~ c_lessequals(c_Message_Osynth(v_H),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
inference(unit_resolution,[status(thm)],[30,27]) ).
tff(32,plain,
c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[31,20]) ).
tff(33,plain,
( ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(v_H,c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(v_H,c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(v_H,c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(v_H,c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
( ~ c_lessequals(v_H,c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
inference(unit_resolution,[status(thm)],[35,27]) ).
tff(37,plain,
c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[36,9]) ).
tff(38,plain,
( ~ c_lessequals(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
<=> ~ c_lessequals(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
~ c_lessequals(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(40,plain,
~ c_lessequals(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
^ [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
refl(( ( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
<=> ( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
^ [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
trans(monotonicity(rewrite(( ( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a)) )
<=> ( ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) )),
( ( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a)) )
<=> ( ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a))
| c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a)) ) )),
rewrite(( ( ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a))
| c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a)) )
<=> ( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) )),
( ( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a)) )
<=> ( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a)) )
<=> ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Set_OUn__subset__iff_2) ).
tff(47,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i,V_C: $i] :
( c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) )
| c_lessequals(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
( ~ c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
inference(unit_resolution,[status(thm)],[53,50,40]) ).
tff(55,plain,
~ c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[54,37]) ).
tff(56,plain,
^ [V_H: $i,V_G: $i] :
refl(( ( ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
<=> ( ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
<=> ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
<=> ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV005-1.ax',cls_Message_Oparts__subset__iff_0) ).
tff(60,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
( ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) )
<=> ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| c_lessequals(V_G,c_Message_Oparts(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
( ~ c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
inference(unit_resolution,[status(thm)],[65,62]) ).
tff(67,plain,
$false,
inference(unit_resolution,[status(thm)],[66,55,32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV273-1 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n009.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 09:34:48 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.71/0.90 % SZS status Unsatisfiable
% 0.71/0.90 % SZS output start Proof
% See solution above
% 0.78/1.00 % E exiting
%------------------------------------------------------------------------------