%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP004_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 : Fri Sep 25 01:47:30 PM UTC 2026
% Result : Theorem 7.07s 1.80s
% Output : CNFRefutation 8.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 368 ( 42 equ)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 123 ( 46 ~; 58 |; 12 &)
% ( 4 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 242 ( 242 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 54 ( 54 usr; 26 con; 0-4 aty)
% Number of variables : 104 ( 0 sgn 100 !; 4 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
tyop_2Emin_2Ebool: d ).
tff(pred_def_1,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(func_def_2,type,
s: ( u * d ) > du ).
tff(func_def_3,type,
app_2E2: ( du * du ) > u ).
tff(func_def_4,type,
combin_i_2E0: u ).
tff(func_def_5,type,
combin_k_2E0: u ).
tff(func_def_6,type,
combin_s_2E0: u ).
tff(func_def_7,type,
c_2Ebool_2E_21_2E0: u ).
tff(func_def_8,type,
c_2Ebool_2E_21_2E1: du > u ).
tff(func_def_9,type,
c_2Ebool_2E_2F_5C_2E0: u ).
tff(func_def_10,type,
c_2Ebool_2E_2F_5C_2E2: ( du * du ) > u ).
tff(func_def_11,type,
c_2Emin_2E_3D_2E0: u ).
tff(func_def_12,type,
c_2Emin_2E_3D_2E2: ( du * du ) > u ).
tff(func_def_13,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
tff(func_def_14,type,
c_2Emin_2E_3D_3D_3E_2E2: ( du * du ) > u ).
tff(func_def_15,type,
c_2Ebool_2E_3F_2E0: u ).
tff(func_def_16,type,
c_2Ebool_2E_3F_2E1: du > u ).
tff(func_def_17,type,
c_2Epred__set_2ECHOICE_2E0: u ).
tff(func_def_18,type,
c_2Epred__set_2ECHOICE_2E1: du > u ).
tff(func_def_19,type,
c_2Epred__set_2EDELETE_2E0: u ).
tff(func_def_20,type,
c_2Epred__set_2EDELETE_2E2: ( du * du ) > u ).
tff(func_def_21,type,
c_2Ebool_2EF_2E0: u ).
tff(func_def_22,type,
c_2Ebool_2EIN_2E0: u ).
tff(func_def_23,type,
c_2Ebool_2EIN_2E2: ( du * du ) > u ).
tff(func_def_24,type,
c_2Epred__set_2EREST_2E0: u ).
tff(func_def_25,type,
c_2Epred__set_2EREST_2E1: du > u ).
tff(func_def_26,type,
c_2Epred__set_2ESUBSET_2E0: u ).
tff(func_def_27,type,
c_2Epred__set_2ESUBSET_2E2: ( du * du ) > u ).
tff(func_def_28,type,
c_2Ebool_2ET_2E0: u ).
tff(func_def_29,type,
c_2Ebool_2E_5C_2F_2E0: u ).
tff(func_def_30,type,
c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).
tff(func_def_31,type,
c_2Ebool_2E_7E_2E0: u ).
tff(func_def_32,type,
c_2Ebool_2E_7E_2E1: du > u ).
tff(func_def_33,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_34,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_35,type,
mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_36,type,
mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_37,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_38,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_39,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_40,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_41,type,
mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_42,type,
mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_43,type,
mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_44,type,
mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_45,type,
i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).
tff(func_def_46,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).
tff(func_def_47,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(func_def_48,type,
j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_49,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_50,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_51,type,
sK0: d ).
tff(func_def_52,type,
sK1: u ).
tff(func_def_53,type,
sK2: ( u * ( u * ( d * d ) ) ) > u ).
tff(func_def_54,type,
sK3: ( u * ( u * d ) ) > u ).
tff(f2,axiom,
! [X0: mono_2Etyop_2Emin_2Ebool,X1: mono_2Etyop_2Emin_2Ebool] :
( ( p(X0)
<=> p(X1) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
tff(f36,axiom,
! [X0: d,X1: u,X2: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))))
<=> ! [X3: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))))
=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__DEF) ).
tff(f37,axiom,
! [X0: d,X1: u,X2: u,X3: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3)))))))
<=> ( ( s(X0,X2) != s(X0,X3) )
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__DELETE) ).
tff(f38,axiom,
! [X0: d,X1: u] : ( s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__DEF) ).
tff(f39,conjecture,
! [X0: d,X1: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__SUBSET) ).
tff(f40,negated_conjecture,
~ ! [X0: d,X1: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))),
inference(negated_conjecture,[status(cth)],[f39]) ).
tff(f41,plain,
? [X0: d,X1: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))),
inference(ennf_transformation,[],[f40]) ).
tff(f42,plain,
! [X0: mono_2Etyop_2Emin_2Ebool,X1: mono_2Etyop_2Emin_2Ebool] :
( ( p(X0)
<~> p(X1) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f44,plain,
! [X0: d,X1: u,X2: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))))
<=> ! [X3: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))) ) ),
inference(ennf_transformation,[],[f36]) ).
tff(f45,plain,
~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f41]) ).
tff(f46,plain,
! [X0: mono_2Etyop_2Emin_2Ebool,X1: mono_2Etyop_2Emin_2Ebool] :
( ( ( p(X0)
| p(X1) )
& ( ~ p(X0)
| ~ p(X1) ) )
| ( X0 = X1 ) ),
inference(nnf_transformation,[],[f42]) ).
tff(f48,plain,
! [X0: d,X1: u,X2: u] :
( ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))))
| ! [X3: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))) ) )
& ( ? [X3: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))))
& ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))) )
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))) ) ),
inference(nnf_transformation,[],[f44]) ).
tff(f49,plain,
! [X0: d,X1: u,X2: u] :
( ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))))
| ! [X4: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X4),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X4),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))) ) )
& ( ? [X3: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))))
& ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X3),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))) )
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))) ) ),
inference(rectify,[],[f48]) ).
tff(f50,plain,
! [X0: d,X1: u,X2: u] :
( ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))))
| ! [X4: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X4),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X4),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))) ) )
& ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,sK3(X0,X1,X2)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))))
& ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,sK3(X0,X1,X2)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))) )
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f49]) ).
tff(f51,plain,
! [X0: d,X1: u,X2: u,X3: u] :
( ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3)))))))
| ( ( s(X0,X2) != s(X0,X3) )
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))) ) )
& ( ( s(X0,X2) = s(X0,X3) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3))))))) ) ),
inference(nnf_transformation,[],[f37]) ).
tff(f52,plain,
! [X0: d,X1: u,X2: u,X3: u] :
( ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3)))))))
| ( ( s(X0,X2) != s(X0,X3) )
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))) ) )
& ( ( s(X0,X2) = s(X0,X3) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3))))))) ) ),
inference(flattening,[],[f51]) ).
tff(f53,plain,
~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))),
inference(cnf_transformation,[],[f45]) ).
tff(f54,plain,
! [X0: mono_2Etyop_2Emin_2Ebool,X1: mono_2Etyop_2Emin_2Ebool] :
( p(X0)
| p(X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f46]) ).
tff(f57,plain,
! [X0: d,X1: u] : ( s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))) = s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))) ),
inference(cnf_transformation,[],[f38]) ).
tff(f59,plain,
! [X2: u,X0: d,X1: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,sK3(X0,X1,X2)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))) ),
inference(cnf_transformation,[],[f50]) ).
tff(f60,plain,
! [X2: u,X0: d,X1: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,sK3(X0,X1,X2)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2)))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))) ),
inference(cnf_transformation,[],[f50]) ).
tff(f62,plain,
! [X2: u,X3: u,X0: d,X1: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3)))))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_49,negated_conjecture,
~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))),
inference(cnf_transformation,[],[f53]) ).
tcf(c_51,plain,
! [X0_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool,X1_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool] :
( p(X1_mono_2Etyop_2Emin_2Ebool)
| p(X0_mono_2Etyop_2Emin_2Ebool)
| ( X0_mono_2Etyop_2Emin_2Ebool = X1_mono_2Etyop_2Emin_2Ebool ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_53,plain,
! [X0_u: u,X0_d: d] : s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X0_u),s(X0_d,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X0_u))))) = s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X0_u))),
inference(cnf_transformation,[],[f57]) ).
tcf(c_54,plain,
! [X0_u: u,X0_d: d,X1_u: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X0_u),s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X1_u)))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0_d,sK3(X0_d,X0_u,X1_u)),s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X1_u))))) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_55,plain,
! [X0_u: u,X0_d: d,X1_u: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X0_u),s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X1_u)))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0_d,sK3(X0_d,X0_u,X1_u)),s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X0_u))))) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_58,plain,
! [X0_u: u,X0_d: d,X1_u: u,X2_u: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0_d,X0_u),s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X1_u)))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0_d,X0_u),s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X1_u),s(X0_d,X2_u))))))) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_163,plain,
! [X0_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool,X1_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool,X2_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool] :
( ( X2_mono_2Etyop_2Emin_2Ebool = X0_mono_2Etyop_2Emin_2Ebool )
| ( X2_mono_2Etyop_2Emin_2Ebool != X1_mono_2Etyop_2Emin_2Ebool )
| ( X0_mono_2Etyop_2Emin_2Ebool != X1_mono_2Etyop_2Emin_2Ebool ) ),
theory(equality) ).
tcf(c_172,plain,
! [X0_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool,X1_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool] :
( p(X0_mono_2Etyop_2Emin_2Ebool)
| ~ p(X1_mono_2Etyop_2Emin_2Ebool)
| ( X0_mono_2Etyop_2Emin_2Ebool != X1_mono_2Etyop_2Emin_2Ebool ) ),
theory(equality) ).
tcf(c_302,plain,
! [X0_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool] :
( p(X0_mono_2Etyop_2Emin_2Ebool)
| ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) = X0_mono_2Etyop_2Emin_2Ebool ) ),
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_497,plain,
! [X0_u: u,X0_d: d,X1_u: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X0_u),s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X1_u)))))
| ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0_d,sK3(X0_d,X0_u,X1_u)),s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X1_u)))) ) ),
inference(superposition,[status(thm)],[c_302,c_54]) ).
tcf(c_667,plain,
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))))) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_808,plain,
! [X0_u: u,X0_d: d,X0_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool,X1_u: u] :
( p(X0_mono_2Etyop_2Emin_2Ebool)
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X0_u),s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X1_u)))))
| ( X0_mono_2Etyop_2Emin_2Ebool = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X0_u),s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X1_u)))) ) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_1335,plain,
! [X0_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool] :
( p(X0_mono_2Etyop_2Emin_2Ebool)
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))))
| ( X0_mono_2Etyop_2Emin_2Ebool = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) ) ),
inference(instantiation,[status(thm)],[c_808]) ).
tcf(c_1411,plain,
! [X0_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))))
| ~ p(X0_mono_2Etyop_2Emin_2Ebool)
| ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) != X0_mono_2Etyop_2Emin_2Ebool ) ),
inference(instantiation,[status(thm)],[c_172]) ).
tcf(c_1464,plain,
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))))
| ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) ) ),
inference(instantiation,[status(thm)],[c_1335]) ).
tcf(c_1500,plain,
! [X0_du: du] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(X0_du))
| ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) != j_mono_2Etyop_2Emin_2Ebool(X0_du) ) ),
inference(instantiation,[status(thm)],[c_1411]) ).
tcf(c_1702,plain,
! [X0_u: u,X0_d: d,X1_u: u,X2_u: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0_d,X0_u),s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X1_u)))))
| ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0_d,X0_u),s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0_d,tyop_2Emin_2Ebool),X1_u),s(X0_d,X2_u)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) ) ),
inference(superposition,[status(thm)],[c_302,c_58]) ).
tcf(c_1935,plain,
! [X0_u: u,X0_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool,X1_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool] :
( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),X0_u)))) = X1_mono_2Etyop_2Emin_2Ebool )
| ( X1_mono_2Etyop_2Emin_2Ebool != X0_mono_2Etyop_2Emin_2Ebool )
| ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),X0_u)))) != X0_mono_2Etyop_2Emin_2Ebool ) ),
inference(instantiation,[status(thm)],[c_163]) ).
tcf(c_2364,plain,
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))))))
| ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) != j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))))) ) ),
inference(instantiation,[status(thm)],[c_1500]) ).
tcf(c_3140,plain,
j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))),
inference(superposition,[status(thm)],[c_497,c_49]) ).
tcf(c_3250,plain,
! [X0_u: u,X0_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool] :
( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),X0_u)))) = X0_mono_2Etyop_2Emin_2Ebool )
| ( X0_mono_2Etyop_2Emin_2Ebool != j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) )
| ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),X0_u)))) != j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) ) ),
inference(instantiation,[status(thm)],[c_1935]) ).
tcf(c_3496,plain,
! [X0_u: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))))
| ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1),s(sK0,X0_u)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) ) ),
inference(superposition,[status(thm)],[c_3140,c_1702]) ).
tcf(c_3525,plain,
! [X0_u: u] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1),s(sK0,X0_u)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))),
inference(forward_subsumption_resolution,[status(thm)],[c_3496,c_49]) ).
tcf(c_5700,plain,
! [X0_u: u] :
( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),X0_u)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))))) )
| ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),X0_u)))) != j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) )
| ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))))) != j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) ) ),
inference(instantiation,[status(thm)],[c_3250]) ).
tcf(c_5701,plain,
( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))))) )
| ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) != j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) )
| ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))))) != j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) ) ),
inference(instantiation,[status(thm)],[c_5700]) ).
tcf(c_5754,plain,
j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK3(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))),
inference(superposition,[status(thm)],[c_53,c_3525]) ).
tcf(c_5764,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5754,c_5701,c_2364,c_1464,c_667,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP004_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n011.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 17:28:42 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 7.07/1.80 % SZS status Started for theBenchmark.p
% 7.07/1.80 % SZS status Theorem for theBenchmark.p
% 7.07/1.80
% 7.07/1.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.07/1.80
% 7.07/1.80 % ------ iProver source info
% 7.07/1.80
% 7.07/1.80 % git: date: 2026-07-19 20:42:38 +0200
% 7.07/1.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.07/1.80 % git: non_committed_changes: false
% 7.07/1.80
% 7.07/1.80 % ------ Parsing...
% 7.07/1.80 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 7.07/1.80 %
% 7.07/1.80
% 7.07/1.80 % ------ Preprocessing... sup_sim: 0 pe_s pe_e %
% 7.07/1.80
% 7.07/1.80 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 7.07/1.80 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 7.07/1.80 %
% 7.07/1.80
% 7.07/1.80 % ------ Preprocessing...
% 7.07/1.80 % ------ Proving...
% 7.07/1.80 % ------ Problem Properties
% 7.07/1.80
% 7.07/1.80 %
% 7.07/1.80 % clauses 11
% 7.07/1.80 % conjectures 1
% 7.07/1.80 % EPR 2
% 7.07/1.80 % Horn 8
% 7.07/1.80 % unary 2
% 7.07/1.80 % binary 5
% 7.07/1.80 % lits 24
% 7.07/1.80 % lits eq 7
% 7.07/1.80 % fd_pure 0
% 7.07/1.80 % fd_pseudo 0
% 7.07/1.80 % fd_cond 0
% 7.07/1.80 % fd_pseudo_cond 2
% 7.07/1.80 % AC symbols 0
% 7.07/1.80
% 7.07/1.80 % ------ Schedule dynamic 5 is on
% 7.07/1.80
% 7.07/1.80 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.07/1.80
% 7.07/1.80
% 7.07/1.80 % ------
% 7.07/1.80 % Current options:
% 7.07/1.80 % ------
% 7.07/1.80
% 7.07/1.80
% 7.07/1.80 %
% 7.07/1.80
% 7.07/1.80 % ------ Proving...
% 7.07/1.80 %
% 7.07/1.80
% 7.07/1.80 % SZS status Theorem for theBenchmark.p
% 7.07/1.80
% 7.07/1.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.31/1.80
% 8.31/1.80
%------------------------------------------------------------------------------