%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV270-1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:31:56 AM UTC 2025
% Result : Unsatisfiable 0.68s 0.91s
% Output : Proof 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 37
% Syntax : Number of formulae : 83 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 338 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 411 ( 164 ~; 214 |; 0 &)
% ( 33 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 304 ( 277 !; 0 ?; 304 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(v_H_type,type,
v_H: $i ).
tff(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: ( $i * $i ) > $i ).
tff(v_Y_type,type,
v_Y: $i ).
tff(v_X_type,type,
v_X: $i ).
tff(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(c_union_type,type,
c_union: ( $i * $i * $i ) > $i ).
tff(1,plain,
( ~ c_in(v_X,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)
<=> ~ c_in(v_X,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_in(v_X,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(3,plain,
~ c_in(v_X,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(( ( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
<=> ( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Set_OUn__iff_1) ).
tff(8,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg)
| c_in(v_X,c_union(c_Message_Oparts(v_H),c_Message_Osynth(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_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg)
| c_in(v_X,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg)
| c_in(v_X,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg)
| c_in(v_X,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [V_Y: $i,V_H: $i,V_X: $i] :
refl(( ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV005-0.ax',cls_Message_OMPair__parts_1) ).
tff(19,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg)
| c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) )
<=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg)
| c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg)
| c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg)
| c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,plain,
( c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)
<=> c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(28,plain,
c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(( ( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
<=> ( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
^ [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
rewrite(( ( ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a) )
<=> ( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| c_in(V_c,V_B,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_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Set_OUn__iff_0) ).
tff(35,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg) )
<=> ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) )
<=> ( ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_union(c_Message_Oparts(v_H),c_Message_Osynth(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_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_union(c_Message_Oparts(v_H),c_Message_Osynth(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_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_c,V_B,T_a)
| c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(unit_resolution,[status(thm)],[44,38,28]) ).
tff(46,plain,
c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[45,25]) ).
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_in(V_c,c_union(V_A,V_B,T_a),T_a) )
<=> ( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_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_in(V_c,c_union(V_A,V_B,T_a),T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_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_in(V_c,c_union(V_A,V_B,T_a),T_a) )
<=> ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_Set_OUn__iff_2) ).
tff(51,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(v_X,c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(v_X,c_union(c_Message_Oparts(v_H),c_Message_Osynth(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_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(v_X,c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(v_X,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(v_X,c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(v_X,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [V_c: $i,T_a: $i,V_B: $i,V_A: $i] :
( ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_union(V_A,V_B,T_a),T_a) )
| ~ c_in(v_X,c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(v_X,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
~ c_in(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[56,53,3]) ).
tff(58,plain,
^ [V_Y: $i,V_H: $i,V_X: $i] :
refl(( ( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) )
<=> ( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
^ [V_Y: $i,V_H: $i,V_X: $i] :
rewrite(( ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg) )
<=> ( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV005-1.ax',cls_Message_OMPair__synth_1) ).
tff(64,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) )
| c_in(v_X,c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),v_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg) )
<=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) )
| c_in(v_X,c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),v_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) )
| c_in(v_X,c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),v_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( c_in(V_X,c_Message_Osynth(V_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(V_X,V_Y),V_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Osynth(V_H),tc_Message_Omsg) )
| c_in(v_X,c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),v_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
( c_in(c_Message_Omsg_OMPair(v_X,v_Y),v_H,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Osynth(v_H),tc_Message_Omsg) ),
inference(unit_resolution,[status(thm)],[70,67,57]) ).
tff(72,plain,
c_in(c_Message_Omsg_OMPair(v_X,v_Y),v_H,tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[71,46]) ).
tff(73,plain,
^ [V_H: $i,V_X: $i] :
refl(( ( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,axiom,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV005-0.ax',cls_Message_Oparts_OInj_0) ).
tff(77,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
( ( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),v_H,tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),v_H,tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),v_H,tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(v_X,v_Y),v_H,tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(v_X,v_Y),c_Message_Oparts(v_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
$false,
inference(unit_resolution,[status(thm)],[82,79,25,72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV270-1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:34:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.68/0.91 % SZS status Unsatisfiable
% 0.68/0.91 % SZS output start Proof
% See solution above
% 0.83/0.99 % E exiting
%------------------------------------------------------------------------------