TSTP Solution File: SWV251-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV251-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 : Thu Sep 29 15:10:36 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 49
% Syntax : Number of formulae : 96 ( 33 unt; 13 typ; 0 def)
% Number of atoms : 238 ( 38 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 274 ( 126 ~; 119 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 8 >; 10 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 251 ( 228 !; 0 ?; 251 :)
% 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_union_type,type,
c_union: ( $i * $i * $i ) > $i ).
tff(v_H_type,type,
v_H: $i ).
tff(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
tff(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
tff(v_G_type,type,
v_G: $i ).
tff(c_insert_type,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(v_X_type,type,
v_X: $i ).
tff(c_minus_type,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(v_x_type,type,
v_x: $i ).
tff(1,plain,
^ [T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
<=> ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
<=> ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
tff(5,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
| ( c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_minus(v_H,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)),tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_minus(v_H,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)),tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg)
<=> c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(12,plain,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( ~ c_in(V_x,V_B,T_a)
| ( c_minus(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) )
<=> ( ~ c_in(V_x,V_B,T_a)
| ( c_minus(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_B,T_a)
| ( c_minus(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_B,T_a)
| ( c_minus(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_B,T_a)
| ( c_minus(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_B,T_a)
| ( c_minus(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_B,T_a)
| ( c_minus(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
tff(17,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_B,T_a)
| ( c_minus(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_B,T_a)
| ( c_minus(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_B,T_a)
| ( c_minus(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_B,T_a)
| ( c_minus(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) )
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg)
| ( c_minus(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)) = c_minus(v_H,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_B,T_a)
| ( c_minus(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) )
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg)
| ( c_minus(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)) = c_minus(v_H,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_B,T_a)
| ( c_minus(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) )
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg)
| ( c_minus(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)) = c_minus(v_H,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_x,V_B,T_a)
| ( c_minus(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) = c_minus(V_A,V_B,tc_set(T_a)) ) )
| ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg)
| ( c_minus(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)) = c_minus(v_H,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
c_minus(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)) = c_minus(v_H,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[22,19,12]) ).
tff(24,plain,
c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_minus(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)),tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_minus(v_H,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)),tc_Message_Omsg),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ~ ! [T_a: $i,V_B: $i,V_A: $i] : ( c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) )
| ( c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_minus(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)),tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_minus(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)),tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[25,7]) ).
tff(27,plain,
c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_minus(c_insert(v_X,v_H,tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)),tc_Message_Omsg),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),
inference(transitivity,[status(thm)],[27,24,9]) ).
tff(29,plain,
( c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
<=> c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
<=> c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
^ [T_a: $i,V_A: $i] :
refl(
( c_lessequals(V_A,V_A,tc_set(T_a))
<=> c_lessequals(V_A,V_A,tc_set(T_a)) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a))
<=> ! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a))
<=> ! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
tff(35,plain,
! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ~ ! [T_a: $i,V_A: $i] : c_lessequals(V_A,V_A,tc_set(T_a))
| c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[39,30]) ).
tff(41,plain,
( ~ c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
<=> ~ c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
~ c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(43,plain,
~ c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg)
<=> c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(46,plain,
c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
<=> ( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
rewrite(
( ( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) )
<=> ( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
tff(53,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
| c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
| c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
| c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) )
| c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[59,56,46,43]) ).
tff(61,plain,
^ [V_H: $i,V_G: $i] :
refl(
( ( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) )
<=> ( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(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_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(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_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__mono_0) ).
tff(65,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
( ( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),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_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
( ~ ! [V_H: $i,V_G: $i] :
( ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg)) )
| ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[70,67,60]) ).
tff(72,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_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_B,V_C,tc_set(T_a)) ) )),
inference(bind,[status(th)],]) ).
tff(73,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_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_B,V_C,tc_set(T_a)) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,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_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_B,V_C,tc_set(T_a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
! [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_B,V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
tff(76,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_B,V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,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_B,V_C,tc_set(T_a)) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,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_B,V_C,tc_set(T_a)) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,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_B,V_C,tc_set(T_a)) )
| ~ c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),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_B,V_C,tc_set(T_a)) )
| ~ c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,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_B,V_C,tc_set(T_a)) )
| ~ c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,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_B,V_C,tc_set(T_a)) )
| ~ c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
~ c_lessequals(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[81,78,71]) ).
tff(83,plain,
$false,
inference(unit_resolution,[status(thm)],[82,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV251-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Sep 4 02:10:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43 % SZS output start Proof
% See solution above
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