%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP006_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 : Tue Sep 29 11:27:49 AM UTC 2026
% Result : Theorem 1.69s 1.13s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 194 ( 20 equ)
% Maximal formula atoms : 32 ( 9 avg)
% Number of connectives : 259 ( 85 ~; 76 |; 76 &)
% ( 12 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 71 ( 71 usr; 30 con; 0-4 aty)
% Number of variables : 201 ( 153 !; 48 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
u: $tType ).
tff(type_def_6,type,
d: $tType ).
tff(type_def_7,type,
du: $tType ).
tff(type_def_8,type,
mono_2Etyop_2Emin_2Ebool: $tType ).
tff(type_def_9,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(type_def_10,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).
tff(func_def_0,type,
tyop_2Emin_2Ebool: d ).
tff(func_def_1,type,
tyop_2Emin_2Efun: ( d * d ) > d ).
tff(func_def_2,type,
s: ( d * u ) > 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_2Ebool_2EF_2E0: u ).
tff(func_def_18,type,
c_2EquantHeuristics_2EGUESS__EXISTS_2E0: u ).
tff(func_def_19,type,
c_2EquantHeuristics_2EGUESS__EXISTS_2E2: ( du * du ) > u ).
tff(func_def_20,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E0: u ).
tff(func_def_21,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2: ( du * du ) > u ).
tff(func_def_22,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E0: u ).
tff(func_def_23,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2: ( du * du ) > u ).
tff(func_def_24,type,
c_2EquantHeuristics_2EGUESS__FORALL_2E0: u ).
tff(func_def_25,type,
c_2EquantHeuristics_2EGUESS__FORALL_2E2: ( du * du ) > u ).
tff(func_def_26,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E0: u ).
tff(func_def_27,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2: ( du * du ) > u ).
tff(func_def_28,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0: u ).
tff(func_def_29,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2: ( du * du ) > u ).
tff(func_def_30,type,
c_2Ebool_2ET_2E0: u ).
tff(func_def_31,type,
c_2Ebool_2E_5C_2F_2E0: u ).
tff(func_def_32,type,
c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).
tff(func_def_33,type,
c_2Ebool_2E_7E_2E0: u ).
tff(func_def_34,type,
c_2Ebool_2E_7E_2E1: du > u ).
tff(func_def_35,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_36,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_37,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_38,type,
mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_39,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_40,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_41,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_42,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_43,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_44,type,
mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_45,type,
mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_46,type,
mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_47,type,
i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).
tff(func_def_48,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_49,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_50,type,
j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_51,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_52,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_53,type,
sK10: ( d * d * u * u ) > u ).
tff(func_def_54,type,
sK11: ( d * u ) > u ).
tff(func_def_55,type,
sK12: ( d * u ) > u ).
tff(func_def_56,type,
sK13: ( d * d * u * u ) > u ).
tff(func_def_57,type,
sK14: ( d * d * u * u ) > u ).
tff(func_def_58,type,
sK15: ( d * d * u * u ) > u ).
tff(func_def_59,type,
sK16: ( d * d * u * u ) > u ).
tff(func_def_60,type,
sK17: ( d * d * u * u ) > u ).
tff(func_def_61,type,
sK18: ( d * d * u * u ) > u ).
tff(func_def_62,type,
sK19: ( d * d * u * u ) > u ).
tff(func_def_63,type,
sK20: ( d * d * u * u ) > u ).
tff(func_def_64,type,
sK21: ( d * d * u * u ) > u ).
tff(func_def_65,type,
sK22: ( d * d * u * u ) > u ).
tff(func_def_66,type,
sK23: d ).
tff(func_def_67,type,
sK24: d ).
tff(func_def_68,type,
sK25: u ).
tff(func_def_69,type,
sK26: u ).
tff(func_def_70,type,
sK27: u ).
tff(pred_def_1,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(pred_def_2,type,
sP0: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_3,type,
sP1: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_4,type,
sP2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_5,type,
sP3: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_6,type,
sP4: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_7,type,
sP5: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_8,type,
sP6: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_9,type,
sP7: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_10,type,
sP8: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_11,type,
sP9: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_12,type,
sQ28_eqProxy: ( du * du ) > $o ).
tff(pred_def_13,type,
sQ29_eqProxy: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_14,type,
sQ30_eqProxy: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) > $o ).
tff(pred_def_15,type,
sQ31_eqProxy: ( 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 ) > $o ).
tff(f45,axiom,
! [X0: d,X1: d,X2: u,X3: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))))
<=> ! [X4: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4)))))
=> ? [X5: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5))))))) ) )
& ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))))
<=> ! [X6: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6)))))
=> ? [X7: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X7))))))) ) )
& ! [X8: u,X9: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9)))))
<=> ! [X10: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(X0,X10))))))) )
& ! [X11: u,X12: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12)))))
<=> ! [X13: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(X0,X13))))))) )
& ! [X14: u,X15: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15)))))
<=> ! [X16: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15),s(X1,X16)))))
=> ? [X17: u] : ( s(X1,X16) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(X0,X17))) ) ) )
& ! [X18: u,X19: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19)))))
<=> ! [X20: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19),s(X1,X20)))))
=> ? [X21: u] : ( s(X1,X20) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(X0,X21))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__REWRITES) ).
tff(f57,conjecture,
! [X0: d,X1: d,X2: u,X3: u,X4: u] :
( ! [X5: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4),s(X0,X5)))))
=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3),s(X0,X5))))) )
=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3)))))
=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT) ).
tff(f58,negated_conjecture,
~ ! [X0: d,X1: d,X2: u,X3: u,X4: u] :
( ! [X5: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4),s(X0,X5)))))
=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3),s(X0,X5))))) )
=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3)))))
=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4))))) ) ),
inference(negated_conjecture,[status(cth)],[f57]) ).
tff(f68,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))))
<=> ! [X4: u] :
( ? [X5: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5)))))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4))))) ) )
& ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))))
<=> ! [X6: u] :
( ? [X7: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X7)))))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))) ) )
& ! [X8: u,X9: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9)))))
<=> ! [X10: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(X0,X10))))))) )
& ! [X11: u,X12: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12)))))
<=> ! [X13: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(X0,X13))))))) )
& ! [X14: u,X15: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15)))))
<=> ! [X16: u] :
( ? [X17: u] : ( s(X1,X16) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(X0,X17))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15),s(X1,X16))))) ) )
& ! [X18: u,X19: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19)))))
<=> ! [X20: u] :
( ? [X21: u] : ( s(X1,X20) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(X0,X21))) )
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19),s(X1,X20))))) ) ) ),
inference(ennf_transformation,[],[f45]) ).
tff(f82,plain,
? [X0: d,X1: d,X2: u,X3: u,X4: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4)))))
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3)))))
& ! [X5: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3),s(X0,X5)))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4),s(X0,X5))))) ) ),
inference(ennf_transformation,[],[f58]) ).
tff(f83,plain,
? [X0: d,X1: d,X2: u,X3: u,X4: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4)))))
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X1,X0),X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3)))))
& ! [X5: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3),s(X0,X5)))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4),s(X0,X5))))) ) ),
inference(flattening,[],[f82]) ).
tff(f134,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))))
| ? [X4: u] :
( ! [X5: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5)))))))
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4))))) ) )
& ( ! [X4: u] :
( ? [X5: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5)))))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))) )
& ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))))
| ? [X6: u] :
( ! [X7: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X7)))))))
& ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))) ) )
& ( ! [X6: u] :
( ? [X7: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X7)))))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))) )
& ! [X8: u,X9: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9)))))
| ? [X10: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(X0,X10))))))) )
& ( ! [X10: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(X0,X10)))))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9))))) ) )
& ! [X11: u,X12: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12)))))
| ? [X13: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(X0,X13))))))) )
& ( ! [X13: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(X0,X13)))))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12))))) ) )
& ! [X14: u,X15: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15)))))
| ? [X16: u] :
( ! [X17: u] : ( s(X1,X16) != s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(X0,X17))) )
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15),s(X1,X16))))) ) )
& ( ! [X16: u] :
( ? [X17: u] : ( s(X1,X16) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(X0,X17))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15),s(X1,X16))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15))))) ) )
& ! [X18: u,X19: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19)))))
| ? [X20: u] :
( ! [X21: u] : ( s(X1,X20) != s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(X0,X21))) )
& ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19),s(X1,X20))))) ) )
& ( ! [X20: u] :
( ? [X21: u] : ( s(X1,X20) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(X0,X21))) )
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19),s(X1,X20))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19))))) ) ) ),
inference(nnf_transformation,[],[f68]) ).
tff(f135,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))))
| ? [X4: u] :
( ! [X5: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5)))))))
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4))))) ) )
& ( ! [X4: u] :
( ? [X5: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5)))))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))) )
& ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))))
| ? [X6: u] :
( ! [X7: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X7)))))))
& ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))) ) )
& ( ! [X6: u] :
( ? [X7: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X7)))))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))) )
& ! [X8: u,X9: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9)))))
| ? [X10: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(X0,X10))))))) )
& ( ! [X10: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(X0,X10)))))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X8),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X9))))) ) )
& ! [X11: u,X12: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12)))))
| ? [X13: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(X0,X13))))))) )
& ( ! [X13: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(X0,X13)))))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X11),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X12))))) ) )
& ! [X14: u,X15: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15)))))
| ? [X16: u] :
( ! [X17: u] : ( s(X1,X16) != s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(X0,X17))) )
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15),s(X1,X16))))) ) )
& ( ! [X16: u] :
( ? [X17: u] : ( s(X1,X16) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(X0,X17))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15),s(X1,X16))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X14),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X15))))) ) )
& ! [X18: u,X19: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19)))))
| ? [X20: u] :
( ! [X21: u] : ( s(X1,X20) != s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(X0,X21))) )
& ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19),s(X1,X20))))) ) )
& ( ! [X20: u] :
( ? [X21: u] : ( s(X1,X20) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(X0,X21))) )
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19),s(X1,X20))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X18),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X19))))) ) ) ),
inference(flattening,[],[f134]) ).
tff(f136,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))))
| ? [X4: u] :
( ! [X5: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5)))))))
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X4))))) ) )
& ( ! [X6: u] :
( ? [X7: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X7)))))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))) )
& ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))))
| ? [X8: u] :
( ! [X9: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X9)))))))
& ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X8))))) ) )
& ( ! [X10: u] :
( ? [X11: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X11)))))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X10))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))) )
& ! [X12: u,X13: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13)))))
| ? [X14: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(X0,X14))))))) )
& ( ! [X15: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(X0,X15)))))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13))))) ) )
& ! [X16: u,X17: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17)))))
| ? [X18: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(X0,X18))))))) )
& ( ! [X19: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(X0,X19)))))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17))))) ) )
& ! [X20: u,X21: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21)))))
| ? [X22: u] :
( ! [X23: u] : ( s(X1,X22) != s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(X0,X23))) )
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21),s(X1,X22))))) ) )
& ( ! [X24: u] :
( ? [X25: u] : ( s(X1,X24) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(X0,X25))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21),s(X1,X24))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21))))) ) )
& ! [X26: u,X27: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27)))))
| ? [X28: u] :
( ! [X29: u] : ( s(X1,X28) != s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(X0,X29))) )
& ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27),s(X1,X28))))) ) )
& ( ! [X30: u] :
( ? [X31: u] : ( s(X1,X30) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(X0,X31))) )
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27),s(X1,X30))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27))))) ) ) ),
inference(rectify,[],[f135]) ).
tff(f137,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))))
| ( ! [X5: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X5)))))))
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,sK13(X0,X1,X2,X3)))))) ) )
& ( ! [X6: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,sK14(X0,X1,X2,X3))))))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X6))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))) )
& ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3)))))
| ( ! [X9: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,X9)))))))
& ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,sK15(X0,X1,X2,X3)))))) ) )
& ( ! [X10: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,sK16(X0,X1,X2,X3))))))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3),s(X1,X10))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X3))))) )
& ! [X12: u,X13: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13)))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(X0,sK17(X0,X1,X12,X13)))))))) )
& ( ! [X15: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(X0,X15)))))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X12),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X13))))) ) )
& ! [X16: u,X17: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17)))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(X0,sK18(X0,X1,X16,X17)))))))) )
& ( ! [X19: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(X0,X19)))))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17))))) ) )
& ! [X20: u,X21: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21)))))
| ( ! [X23: u] : ( s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(X0,X23))) != s(X1,sK19(X0,X1,X20,X21)) )
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21),s(X1,sK19(X0,X1,X20,X21)))))) ) )
& ( ! [X24: u] :
( ( s(X1,X24) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(X0,sK20(X0,X1,X20,X24)))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21),s(X1,X24))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X20),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X21))))) ) )
& ! [X26: u,X27: u] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27)))))
| ( ! [X29: u] : ( s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(X0,X29))) != s(X1,sK21(X0,X1,X26,X27)) )
& ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27),s(X1,sK21(X0,X1,X26,X27)))))) ) )
& ( ! [X30: u] :
( ( s(X1,X30) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(X0,sK22(X0,X1,X26,X30)))) )
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27),s(X1,X30))))) )
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X27))))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17,sK18,sK19,sK20,sK21,sK22]),skolemize(X4,sK13(X0,X1,X2,X3)),skolemize(X7,sK14(X0,X1,X2,X3)),skolemize(X8,sK15(X0,X1,X2,X3)),skolemize(X11,sK16(X0,X1,X2,X3)),skolemize(X14,sK17(X0,X1,X12,X13)),skolemize(X18,sK18(X0,X1,X16,X17)),skolemize(X22,sK19(X0,X1,X20,X21)),skolemize(X25,sK20(X0,X1,X20,X24)),skolemize(X28,sK21(X0,X1,X26,X27)),skolemize(X31,sK22(X0,X1,X26,X30))],[f136]) ).
tff(f178,plain,
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27)))))
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26)))))
& ! [X5: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26),s(sK23,X5)))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27),s(sK23,X5))))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23,sK24,sK25,sK26,sK27]),skolemize(X0,sK23),skolemize(X1,sK24),skolemize(X2,sK25),skolemize(X3,sK26),skolemize(X4,sK27)],[f83]) ).
tff(f287,plain,
! [X0: d,X1: d,X19: u,X16: u,X17: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(X0,X19)))))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17))))) ),
inference(cnf_transformation,[],[f137]) ).
tff(f288,plain,
! [X0: d,X1: d,X16: u,X17: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17),s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(X0,sK18(X0,X1,X16,X17))))))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,X1),X16),s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17))))) ),
inference(cnf_transformation,[],[f137]) ).
tff(f388,plain,
! [X5: u] :
( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27),s(sK23,X5)))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26),s(sK23,X5))))) ),
inference(cnf_transformation,[],[f178]) ).
tff(f389,plain,
p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26))))),
inference(cnf_transformation,[],[f178]) ).
tff(f390,plain,
~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27))))),
inference(cnf_transformation,[],[f178]) ).
tff(f776,plain,
! [X0: d,X1: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26),s(sK23,app_2E2(s(tyop_2Emin_2Efun(X0,sK23),X1),s(X0,sK18(X0,sK23,X1,sK27))))))))
| p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,sK23),X1),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27))))) ),
inference(resolution,[],[f288,f388]) ).
tff(f793,plain,
! [X0: d,X1: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,sK23),X1),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK27)))))
| ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(X0,sK23),X1),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26))))) ),
inference(resolution,[],[f776,f287]) ).
tff(f795,plain,
~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(sK24,sK23),sK25),s(tyop_2Emin_2Efun(sK23,tyop_2Emin_2Ebool),sK26))))),
inference(resolution,[],[f793,f390]) ).
tff(f796,plain,
$false,
inference(resolution,[],[f795,f389]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP006_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n016.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 11:57:32 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.69/1.13 % (2497483)Detected formulas, will run a generic FOF schedule.
% 1.69/1.13 % (2497494)dis-21_1_sil=8000:lcm=predicate:random_seed=3148093669:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.69/1.13 % (2497494)First to succeed.
% 1.69/1.13 % (2497494)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2497483"
% 1.69/1.13 % (2497493)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4045092159:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.69/1.13 % (2497489)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1265967257:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.69/1.13 % (2497490)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1183154226:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.69/1.13 % (2497488)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2777605709:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.69/1.13 % (2497492)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1746569014:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.69/1.13 % (2497491)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3096642570:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.69/1.13 % (2497491)Refutation not found, incomplete strategy
% 1.69/1.13 % (2497491)------------------------------
% 1.69/1.13 % (2497491)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.69/1.13 % (2497491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/1.13 % (2497491)CaDiCaL version: 2.1.3
% 1.69/1.13 % (2497491)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.13 % (2497491)Time elapsed: 0.003 s
% 1.69/1.13 % (2497491)Peak memory usage: 88 MB
% 1.69/1.13 % (2497491)Instructions burned: 4 (million)
% 1.69/1.13 % (2497492)Refutation not found, incomplete strategy
% 1.69/1.13 % (2497492)------------------------------
% 1.69/1.13 % (2497492)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.69/1.13 % (2497492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/1.13 % (2497492)CaDiCaL version: 2.1.3
% 1.69/1.13 % (2497492)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.13 % (2497492)Time elapsed: 0.005 s
% 1.69/1.13 % (2497492)Peak memory usage: 88 MB
% 1.69/1.13 % (2497492)Instructions burned: 7 (million)
% 1.69/1.13 % (2497493)Instruction limit reached!
% 1.69/1.13 % (2497493)------------------------------
% 1.69/1.13 % (2497493)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.69/1.13 % (2497493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/1.13 % (2497493)CaDiCaL version: 2.1.3
% 1.69/1.13 % (2497493)Termination reason: Instruction limit
% 1.69/1.13 % (2497493)Termination phase: Saturation
% 1.69/1.13 % (2497493)Time elapsed: 0.091 s
% 1.69/1.13 % (2497493)Peak memory usage: 89 MB
% 1.69/1.13 % (2497493)Instructions burned: 140 (million)
% 1.69/1.13 % (2497494)Refutation found. Thanks to Tanya!
% 1.69/1.13 % SZS status Theorem for theBenchmark
% 1.69/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.31 % (2497494)------------------------------
% 2.56/1.31 % (2497494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.31 % (2497494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.31 % (2497494)CaDiCaL version: 2.1.3
% 2.56/1.31 % (2497494)Termination reason: Refutation
% 2.56/1.31 % (2497494)Time elapsed: 0.009 s
% 2.56/1.31 % (2497494)Peak memory usage: 89 MB
% 2.56/1.31 % (2497494)Instructions burned: 26 (million)
% 2.56/1.31 % (2497494)------------------------------
% 2.56/1.31 % (2497494)------------------------------
% 2.56/1.31 % (2497483)Success in time 0.278 s
% 2.56/1.31 % Vampire exiting
%------------------------------------------------------------------------------