%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV781-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:36:05 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.54s
% Output : Proof 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 36 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 28 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 7 ~; 3 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 50 ( 45 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $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(c_List_OtakeWhile_type,type,
c_List_OtakeWhile: ( $i * $i * $i ) > $i ).
tff(v_P_type,type,
v_P: $i ).
tff(c_Event_OinitState_type,type,
c_Event_OinitState: $i > $i ).
tff(1,plain,
^ [V_A: $i] :
refl(( ( c_Event_Oknows(V_A,c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_OinitState(V_A) )
<=> ( c_Event_Oknows(V_A,c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_OinitState(V_A) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_A: $i] : ( c_Event_Oknows(V_A,c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_OinitState(V_A) )
<=> ! [V_A: $i] : ( c_Event_Oknows(V_A,c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_OinitState(V_A) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_A: $i] : ( c_Event_Oknows(V_A,c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_OinitState(V_A) )
<=> ! [V_A: $i] : ( c_Event_Oknows(V_A,c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_OinitState(V_A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_A: $i] : ( c_Event_Oknows(V_A,c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_OinitState(V_A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Nil_0) ).
tff(5,plain,
! [V_A: $i] : ( c_Event_Oknows(V_A,c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_OinitState(V_A) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_A: $i] : ( c_Event_Oknows(V_A,c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_OinitState(V_A) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_A: $i] : ( c_Event_Oknows(V_A,c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_OinitState(V_A) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_A: $i] : ( c_Event_Oknows(V_A,c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_OinitState(V_A) )
| ( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_OinitState(c_Message_Oagent_OSpy) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)) = c_Event_OinitState(c_Message_Oagent_OSpy),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [T_a: $i,V_P: $i] :
refl(( ( c_List_OtakeWhile(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) )
<=> ( c_List_OtakeWhile(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [T_a: $i,V_P: $i] : ( c_List_OtakeWhile(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) )
<=> ! [T_a: $i,V_P: $i] : ( c_List_OtakeWhile(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [T_a: $i,V_P: $i] : ( c_List_OtakeWhile(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) )
<=> ! [T_a: $i,V_P: $i] : ( c_List_OtakeWhile(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [T_a: $i,V_P: $i] : ( c_List_OtakeWhile(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I1_J_0) ).
tff(14,plain,
! [T_a: $i,V_P: $i] : ( c_List_OtakeWhile(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [T_a: $i,V_P: $i] : ( c_List_OtakeWhile(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [T_a: $i,V_P: $i] : ( c_List_OtakeWhile(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [T_a: $i,V_P: $i] : ( c_List_OtakeWhile(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) )
| ( c_List_OtakeWhile(v_P,c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent) = c_List_Olist_ONil(tc_Event_Oevent) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
c_List_OtakeWhile(v_P,c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent) = c_List_Olist_ONil(tc_Event_Oevent),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(v_P,c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(v_P,c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent)) = c_Event_OinitState(c_Message_Oagent_OSpy),
inference(transitivity,[status(thm)],[19,9]) ).
tff(21,plain,
( c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(v_P,c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent)),c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool))
<=> c_lessequals(c_Event_OinitState(c_Message_Oagent_OSpy),c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( c_lessequals(c_Event_OinitState(c_Message_Oagent_OSpy),c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool))
<=> c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(v_P,c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent)),c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
^ [V_A: $i,V_evs: $i] :
refl(( c_lessequals(c_Event_OinitState(V_A),c_Event_Oknows(V_A,V_evs),tc_fun(tc_Message_Omsg,tc_bool))
<=> c_lessequals(c_Event_OinitState(V_A),c_Event_Oknows(V_A,V_evs),tc_fun(tc_Message_Omsg,tc_bool)) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [V_A: $i,V_evs: $i] : c_lessequals(c_Event_OinitState(V_A),c_Event_Oknows(V_A,V_evs),tc_fun(tc_Message_Omsg,tc_bool))
<=> ! [V_A: $i,V_evs: $i] : c_lessequals(c_Event_OinitState(V_A),c_Event_Oknows(V_A,V_evs),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [V_A: $i,V_evs: $i] : c_lessequals(c_Event_OinitState(V_A),c_Event_Oknows(V_A,V_evs),tc_fun(tc_Message_Omsg,tc_bool))
<=> ! [V_A: $i,V_evs: $i] : c_lessequals(c_Event_OinitState(V_A),c_Event_Oknows(V_A,V_evs),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
! [V_A: $i,V_evs: $i] : c_lessequals(c_Event_OinitState(V_A),c_Event_Oknows(V_A,V_evs),tc_fun(tc_Message_Omsg,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__subset__knows_0) ).
tff(27,plain,
! [V_A: $i,V_evs: $i] : c_lessequals(c_Event_OinitState(V_A),c_Event_Oknows(V_A,V_evs),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [V_A: $i,V_evs: $i] : c_lessequals(c_Event_OinitState(V_A),c_Event_Oknows(V_A,V_evs),tc_fun(tc_Message_Omsg,tc_bool)),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [V_A: $i,V_evs: $i] : c_lessequals(c_Event_OinitState(V_A),c_Event_Oknows(V_A,V_evs),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [V_A: $i,V_evs: $i] : c_lessequals(c_Event_OinitState(V_A),c_Event_Oknows(V_A,V_evs),tc_fun(tc_Message_Omsg,tc_bool))
| c_lessequals(c_Event_OinitState(c_Message_Oagent_OSpy),c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
c_lessequals(c_Event_OinitState(c_Message_Oagent_OSpy),c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(v_P,c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent)),c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[31,22]) ).
tff(33,plain,
( ~ c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(v_P,c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent)),c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool))
<=> ~ c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(v_P,c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent)),c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
~ c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(v_P,c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent)),c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(35,plain,
~ c_lessequals(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(v_P,c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent)),c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
$false,
inference(unit_resolution,[status(thm)],[35,32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SWV781-1 : TPTP v9.0.0. Released v4.1.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 10:51:09 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.54 % SZS status Unsatisfiable
% 0.22/0.54 % SZS output start Proof
% See solution above
% 0.39/0.57 % E exiting
%------------------------------------------------------------------------------