%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP004_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 11:27:44 AM UTC 2026
% Result : Theorem 5.61s 1.84s
% Output : Refutation 7.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 60 ( 26 ~; 19 |; 11 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 57 ( 57 usr; 26 con; 0-4 aty)
% Number of variables : 55 ( 51 !; 4 ?; 55 :)
% 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_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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Ebool ) > 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_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_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 * d * u * u ) > u ).
tff(func_def_52,type,
sK1: ( d * u ) > u ).
tff(func_def_53,type,
sK2: ( d * u ) > u ).
tff(func_def_54,type,
sK3: ( d * u * u ) > u ).
tff(func_def_55,type,
sK4: d ).
tff(func_def_56,type,
sK5: u ).
tff(pred_def_1,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
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/sandbox/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)))))))
<=> ( 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) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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(f45,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),X2)))))
| ~ 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))))) ) ),
inference(ennf_transformation,[],[f36]) ).
tff(f46,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(f71,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),X2)))))
& 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))))) ) )
& ( ! [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),X2)))))
| ~ 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_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,[],[f45]) ).
tff(f72,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),X2)))))
& 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))))) ) )
& ( ! [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),X2)))))
| ~ 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_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))) ) ),
inference(rectify,[],[f71]) ).
tff(f73,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)))))
| ( ~ 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_2Ebool_2EIN_2E2(s(X0,sK3(X0,X1,X2)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))) ) )
& ( ! [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),X2)))))
| ~ 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_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))],[f72]) ).
tff(f74,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)))))))
| ~ 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)))))
& ( 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),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3))))))) ) ),
inference(nnf_transformation,[],[f37]) ).
tff(f75,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)))))))
| ~ 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)))))
& ( 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),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3))))))) ) ),
inference(flattening,[],[f74]) ).
tff(f76,plain,
~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),sK5))),s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),sK5))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f46]) ).
tff(f132,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,[],[f73]) ).
tff(f133,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,[],[f73]) ).
tff(f135,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,[],[f75]) ).
tff(f137,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(f138,plain,
~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),sK5))),s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),sK5))))),
inference(cnf_transformation,[],[f76]) ).
tff(f146,plain,
p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK4,sK3(sK4,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),sK5)),sK5)),s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),sK5))))))),
inference(unit_resulting_resolution,[],[f132,f138]) ).
tff(f149,plain,
~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK4,sK3(sK4,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),sK5)),sK5)),s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),sK5))))),
inference(unit_resulting_resolution,[],[f133,f138]) ).
tff(f203,plain,
! [X0: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK4,sK3(sK4,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),sK5)),sK5)),s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),sK5),s(sK4,X0))))))),
inference(unit_resulting_resolution,[],[f135,f149]) ).
tff(f241,plain,
~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK4,sK3(sK4,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),sK5)),sK5)),s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK4,tyop_2Emin_2Ebool),sK5))))))),
inference(superposition,[],[f203,f137]) ).
tff(f242,plain,
$false,
inference(forward_subsumption_resolution,[],[f241,f146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP004_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n010.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 : Sun Sep 27 11:50:01 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.61/1.84 % (827899)Detected formulas, will run a generic FOF schedule.
% 5.61/1.84 % (827984)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3705015412:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.61/1.84 % (827982)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=2804759298:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.61/1.84 % (827984)Instruction limit reached!
% 5.61/1.84 % (827984)------------------------------
% 5.61/1.84 % (827984)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.61/1.84 % (827984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.61/1.84 % (827984)CaDiCaL version: 2.1.3
% 5.61/1.84 % (827984)Termination reason: Instruction limit
% 5.61/1.84 % (827984)Termination phase: Saturation
% 5.61/1.84 % (827984)Time elapsed: 0.058 s
% 5.61/1.84 % (827984)Peak memory usage: 89 MB
% 5.61/1.84 % (827984)Instructions burned: 120 (million)
% 5.61/1.84 % (827981)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=4130414902:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.61/1.84 % (827983)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1208823349:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.61/1.84 % (827983)Refutation not found, incomplete strategy
% 5.61/1.84 % (827983)------------------------------
% 5.61/1.84 % (827983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.61/1.84 % (827983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.61/1.84 % (827983)CaDiCaL version: 2.1.3
% 5.61/1.84 % (827983)Termination reason: Refutation not found, incomplete strategy
% 5.61/1.84 % (827983)Time elapsed: 0.002 s
% 5.61/1.84 % (827983)Peak memory usage: 88 MB
% 5.61/1.84 % (827983)Instructions burned: 1 (million)
% 5.61/1.84 % (827985)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=110983978:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.61/1.84 % (827987)dis-21_1_sil=8000:lcm=predicate:random_seed=3693952781: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)
% 5.61/1.84 % (827979)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=2896536682:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.61/1.84 % (827987)Instruction limit reached!
% 5.61/1.84 % (827987)------------------------------
% 5.61/1.84 % (827987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.61/1.84 % (827987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.61/1.84 % (827987)CaDiCaL version: 2.1.3
% 5.61/1.84 % (827987)Termination reason: Instruction limit
% 5.61/1.84 % (827987)Termination phase: Saturation
% 5.61/1.84 % (827987)Time elapsed: 0.119 s
% 5.61/1.84 % (827987)Peak memory usage: 89 MB
% 5.61/1.84 % (827987)Instructions burned: 129 (million)
% 5.61/1.84 % (827985)Instruction limit reached!
% 5.61/1.84 % (827985)------------------------------
% 5.61/1.84 % (827985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.61/1.84 % (827985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.61/1.84 % (827985)CaDiCaL version: 2.1.3
% 5.61/1.84 % (827985)Termination reason: Instruction limit
% 5.61/1.84 % (827985)Termination phase: Saturation
% 5.61/1.84 % (827985)Time elapsed: 0.135 s
% 5.61/1.84 % (827985)Peak memory usage: 89 MB
% 5.61/1.84 % (827985)Instructions burned: 141 (million)
% 5.61/1.84 % (828006)lrs+10_1_sil=8000:sp=occurrence:random_seed=1964888155:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 5.61/1.84 % (828006)Instruction limit reached!
% 5.61/1.84 % (828006)------------------------------
% 5.61/1.84 % (828006)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.61/1.84 % (828006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.61/1.84 % (828006)CaDiCaL version: 2.1.3
% 5.61/1.84 % (828006)Termination reason: Instruction limit
% 5.61/1.84 % (828006)Termination phase: Saturation
% 5.61/1.84 % (828006)Time elapsed: 0.104 s
% 5.61/1.84 % (828006)Peak memory usage: 88 MB
% 5.61/1.84 % (828006)Instructions burned: 285 (million)
% 5.61/1.84 % (827983)------------------------------
% 5.61/1.84 % (827983)------------------------------
% 5.61/1.84 % (828018)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1033551421:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 5.61/1.84 % (828019)lrs+1011_1_sil=32000:sp=occurrence:random_seed=435722338:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 5.61/1.84 % (828018)Refutation not found, incomplete strategy
% 5.61/1.84 % (828018)------------------------------
% 5.61/1.84 % (828018)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.61/1.84 % (828018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.61/1.84 % (828018)CaDiCaL version: 2.1.3
% 5.61/1.84 % (828018)Termination reason: Refutation not found, incomplete strategy
% 5.61/1.84 % (828018)Time elapsed: 0.010 s
% 5.61/1.84 % (828018)Peak memory usage: 88 MB
% 5.61/1.84 % (828018)Instructions burned: 7 (million)
% 5.61/1.84 % (828027)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1261775119:s2a=on:i=248:s2at=1.23:gtg=position_2994 on theBenchmark for (2994ds/248Mi)
% 5.61/1.84 % (828027)First to succeed.
% 5.61/1.84 % (828027)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-827899"
% 5.61/1.84 % (828030)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=990807307:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 5.61/1.84 % (828030)Refutation not found, incomplete strategy
% 5.61/1.84 % (828030)------------------------------
% 5.61/1.84 % (828030)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.61/1.84 % (828030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.61/1.84 % (828030)CaDiCaL version: 2.1.3
% 5.61/1.84 % (828030)Termination reason: Refutation not found, incomplete strategy
% 5.61/1.84 % (828030)Time elapsed: 0.005 s
% 5.61/1.84 % (828030)Peak memory usage: 88 MB
% 5.61/1.84 % (828030)Instructions burned: 3 (million)
% 5.61/1.84 % (828019)Instruction limit reached!
% 5.61/1.84 % (828019)------------------------------
% 5.61/1.84 % (828019)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.61/1.84 % (828019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.61/1.84 % (828019)CaDiCaL version: 2.1.3
% 5.61/1.84 % (828019)Termination reason: Instruction limit
% 5.61/1.84 % (828019)Termination phase: Saturation
% 5.61/1.84 % (828019)Time elapsed: 0.281 s
% 5.61/1.84 % (828019)Peak memory usage: 91 MB
% 5.61/1.84 % (828019)Instructions burned: 325 (million)
% 5.61/1.84 % (828027)Refutation found. Thanks to Tanya!
% 5.61/1.84 % SZS status Theorem for theBenchmark
% 5.61/1.84 % SZS output start Proof for theBenchmark
% See solution above
% 7.62/2.13 % (828027)------------------------------
% 7.62/2.13 % (828027)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/2.13 % (828027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/2.13 % (828027)CaDiCaL version: 2.1.3
% 7.62/2.13 % (828027)Termination reason: Refutation
% 7.62/2.13 % (828027)Time elapsed: 0.008 s
% 7.62/2.13 % (828027)Peak memory usage: 89 MB
% 7.62/2.13 % (828027)Instructions burned: 12 (million)
% 7.62/2.13 % (828027)------------------------------
% 7.62/2.13 % (828027)------------------------------
% 7.62/2.13 % (827899)Success in time 0.976 s
% 7.62/2.13 % Vampire exiting
%------------------------------------------------------------------------------