%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV772-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:36:04 AM UTC 2025
% Result : Unsatisfiable 0.23s 0.52s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 25 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 33 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 6 ~; 2 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 70 ( 63 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Event_Oknows_type,type,
c_Event_Oknows: ( $i * $i ) > $i ).
tff(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
tff(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
tff(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
tff(v_X_type,type,
v_X: $i ).
tff(c_List_Oappend_type,type,
c_List_Oappend: ( $i * $i * $i ) > $i ).
tff(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(c_Event_Oevent_OSays_type,type,
c_Event_Oevent_OSays: ( $i * $i * $i ) > $i ).
tff(v_B_type,type,
v_B: $i ).
tff(v_A_type,type,
v_A: $i ).
tff(1,plain,
^ [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
refl(( ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
<=> ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).
tff(5,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(V_A,V_B,V_X),V_evs,tc_Event_Oevent)) = c_Set_Oinsert(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
| ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent)) = c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent)) = c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_x: $i,V_xs: $i,T_a: $i] :
refl(( ( c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) )
<=> ( c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) )
<=> ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) )
<=> ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
tff(14,plain,
! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) )
| ( c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent) = c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent) = c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent) = c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent)),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) = c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg),
inference(transitivity,[status(thm)],[20,9]) ).
tff(22,plain,
( ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) != c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg) )
<=> ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) != c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) != c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(24,plain,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) != c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
$false,
inference(unit_resolution,[status(thm)],[24,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SWV772-1 : TPTP v9.0.0. Released v4.1.0.
% 0.09/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n015.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 10:50:55 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.23/0.52 % SZS status Unsatisfiable
% 0.23/0.52 % SZS output start Proof
% See solution above
% 0.23/0.55 % E exiting
%------------------------------------------------------------------------------