%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV776-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:09:05 AM UTC 2026
% Result : Unsatisfiable 3.60s 6.41s
% Output : CNFRefutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 13 unt; 0 def)
% Number of atoms : 68 ( 35 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 27 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 57 ( 7 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_2,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_ONotes(v_A,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_ONotes(v_A,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_ONil(tc_Event_Oevent)) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_74,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_ONotes(v_A,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_ONotes(v_A,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_ONil(tc_Event_Oevent)) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
( ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,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('theBenchmark.p',cls_conjecture_1) ).
cnf(c_75,plain,
( ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,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(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
( c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,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_ONil(tc_Event_Oevent)) ),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_76,plain,
( c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,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_ONil(tc_Event_Oevent)) ),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_insert__absorb_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_in(VAR_0,VAR_1,VAR_2)
| c_Set_Oinsert(VAR_0,VAR_1,VAR_2) = VAR_1 ),
file('theBenchmark.p',cls_insert__absorb_0) ).
cnf(c_83,plain,
( ~ c_in(A,B,C)
| c_Set_Oinsert(A,B,C) = B ),
inference(clausify,[status(thm)],[cls_insert__absorb_0]) ).
fof(cls_knows__Spy__Notes_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_0,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(VAR_0,VAR_1),VAR_2,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,VAR_2) ),
file('theBenchmark.p',cls_knows__Spy__Notes_1) ).
cnf(c_90,plain,
( c_in(A,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(A,B),C,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,C) ),
inference(clausify,[status(thm)],[cls_knows__Spy__Notes_1]) ).
fof(cls_knows__Spy__Notes_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_in(VAR_0,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(VAR_0,VAR_1),VAR_2,tc_Event_Oevent)) = c_Set_Oinsert(VAR_1,c_Event_Oknows(c_Message_Oagent_OSpy,VAR_2),tc_Message_Omsg) ),
file('theBenchmark.p',cls_knows__Spy__Notes_0) ).
cnf(c_94,plain,
( ~ c_in(A,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(A,B),C,tc_Event_Oevent)) = c_Set_Oinsert(B,c_Event_Oknows(c_Message_Oagent_OSpy,C),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_knows__Spy__Notes_0]) ).
fof(cls_eq__Nil__appendI_0,axiom,
! [VAR_0,VAR_1] : VAR_0 = c_List_Oappend(c_List_Olist_ONil(VAR_1),VAR_0,VAR_1),
file('theBenchmark.p',cls_eq__Nil__appendI_0) ).
cnf(c_99,plain,
A = c_List_Oappend(c_List_Olist_ONil(B),A,B),
inference(clausify,[status(thm)],[cls_eq__Nil__appendI_0]) ).
cnf(c_100,plain,
c_List_Oappend(c_List_Olist_ONil(A),B,A) = B,
inference(copy,[status(thm)],[c_99]) ).
fof(cls_subset__refl_0,axiom,
! [VAR_0,VAR_1] : c_lessequals(VAR_0,VAR_0,tc_fun(VAR_1,tc_bool)),
file('theBenchmark.p',cls_subset__refl_0) ).
cnf(c_196,plain,
c_lessequals(A,A,tc_fun(B,tc_bool)),
inference(clausify,[status(thm)],[cls_subset__refl_0]) ).
fof(cls_psubset__insert__iff_3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_1,VAR_2,VAR_3)
| c_in(VAR_1,VAR_0,VAR_3)
| ~ c_lessequals(VAR_0,VAR_2,tc_fun(VAR_3,tc_bool))
| c_HOL_Oord__class_Oless(VAR_0,c_Set_Oinsert(VAR_1,VAR_2,VAR_3),tc_fun(VAR_3,tc_bool)) ),
file('theBenchmark.p',cls_psubset__insert__iff_3) ).
cnf(c_279,plain,
( c_in(B,C,D)
| c_in(B,A,D)
| ~ c_lessequals(A,C,tc_fun(D,tc_bool))
| c_HOL_Oord__class_Oless(A,c_Set_Oinsert(B,C,D),tc_fun(D,tc_bool)) ),
inference(clausify,[status(thm)],[cls_psubset__insert__iff_3]) ).
fof(cls_psubset__eq_1,axiom,
! [VAR_0,VAR_1] : ~ c_HOL_Oord__class_Oless(VAR_0,VAR_0,tc_fun(VAR_1,tc_bool)),
file('theBenchmark.p',cls_psubset__eq_1) ).
cnf(c_394,plain,
~ c_HOL_Oord__class_Oless(A,A,tc_fun(B,tc_bool)),
inference(clausify,[status(thm)],[cls_psubset__eq_1]) ).
cnf(c_4229,plain,
( c_in(B,A,C)
| ~ c_lessequals(A,A,tc_fun(C,tc_bool))
| c_HOL_Oord__class_Oless(A,c_Set_Oinsert(B,A,C),tc_fun(C,tc_bool)) ),
inference(factor,[status(thm)],[c_279]) ).
cnf(c_530,plain,
( c_in(B,A,C)
| c_HOL_Oord__class_Oless(A,c_Set_Oinsert(B,A,C),tc_fun(C,tc_bool)) ),
inference(resolve,[status(thm)],[c_196,c_4229]) ).
cnf(c_565,plain,
( c_Set_Oinsert(A,c_Event_Obad,tc_Message_Oagent) = c_Event_Obad
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(A,B),C,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,C) ),
inference(resolve,[status(thm)],[c_90,c_83]) ).
cnf(c_566,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_ONotes(v_A,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_Olist_OCons(c_Event_Oevent_ONotes(v_A,A),B,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,B) ),
inference(resolve,[status(thm)],[c_90,c_75]) ).
cnf(c_578,plain,
( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,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)
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,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_ONil(tc_Event_Oevent)) ),
inference(paramod,[status(thm)],[c_100,c_74]) ).
cnf(c_579,plain,
( c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,v_X),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(paramod,[status(thm)],[c_100,c_76]) ).
cnf(c_3530,plain,
( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,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)
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,A),B,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,B) ),
inference(paramod,[status(thm)],[c_100,c_566]) ).
cnf(c_4077,plain,
( c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,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)
| c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,v_X),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(paramod,[status(thm)],[c_100,c_578]) ).
cnf(c_4132,plain,
( c_Set_Oinsert(v_A,c_Event_Obad,tc_Message_Oagent) = c_Event_Obad
| c_in(v_A,c_Event_Obad,tc_Message_Oagent) ),
inference(resolve,[status(thm)],[c_579,c_565]) ).
cnf(c_4230,plain,
( c_Set_Oinsert(v_A,c_Event_Obad,tc_Message_Oagent) = c_Event_Obad
| c_Set_Oinsert(v_A,c_Event_Obad,tc_Message_Oagent) = c_Event_Obad ),
inference(resolve,[status(thm)],[c_4132,c_83]) ).
cnf(c_4208,plain,
c_Set_Oinsert(v_A,c_Event_Obad,tc_Message_Oagent) = c_Event_Obad,
inference(copy,[status(thm)],[c_4230]) ).
cnf(c_4231,plain,
( c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| c_HOL_Oord__class_Oless(c_Event_Obad,c_Event_Obad,tc_fun(tc_Message_Oagent,tc_bool)) ),
inference(paramod,[status(thm)],[c_4208,c_530]) ).
cnf(c_4215,plain,
c_in(v_A,c_Event_Obad,tc_Message_Oagent),
inference(resolve,[status(thm)],[c_394,c_4231]) ).
cnf(c_4225,plain,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,A),B,tc_Event_Oevent)) = c_Set_Oinsert(A,c_Event_Oknows(c_Message_Oagent_OSpy,B),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_4215,c_94]) ).
cnf(c_4226,plain,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,v_X),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(resolve,[status(thm)],[c_4225,c_4077]) ).
cnf(c_4227,plain,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_ONotes(v_A,A),B,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,B),
inference(resolve,[status(thm)],[c_4225,c_3530]) ).
cnf(c_4228,plain,
$false,
inference(resolve,[status(thm)],[c_4227,c_4226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV776-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.82 % Computer : n019.cluster.edu
% 0.13/5.82 % Model : x86_64 x86_64
% 0.13/5.82 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.82 % Memory : 8046.5625MB
% 0.13/5.82 % OS : Linux 6.8.0-71-generic
% 0.13/5.82 % CPULimit : 300
% 0.13/5.82 % WCLimit : 300
% 0.13/5.82 % DateTime : Sat Sep 26 14:56:41 UTC 2026
% 0.13/5.83 % CPUTime :
% 0.13/5.83 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/5.83 % Process 1594858 was started by sandbox2 on n019,
% 0.13/5.83 % Sat Sep 26 14:56:41 2026
% 0.13/5.83 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/5.86
% 0.13/5.86 % From the command line: assign(max_seconds, 300).
% 3.60/6.41
% 3.60/6.41 % given #500 (A,wt=29): 555 c_List_Olinorder__class_Osorted(c_List_Oremdups(c_List_Olist_OCons(A,c_List_Olist_ONil(tc_nat),tc_nat),tc_nat),tc_nat). [resolve(64,a,43,b)].
% 3.60/6.41
% 3.60/6.41 % SZS status Unsatisfiable for theBenchmark
% 3.60/6.41
% 3.60/6.41 % Proof 1 at 0.43 (+ 0.10) seconds.
% 3.60/6.41 % Length of proof is 25.
% 3.60/6.41 % Level of proof is 8.
% 3.60/6.41 % Maximum clause weight is 64.000.
% 3.60/6.41 % Given clauses 586.
% 3.60/6.41
% 3.60/6.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------