%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP001_4 : 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 : n013.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 11:27:38 AM UTC 2026
% Result : Theorem 3.69s 1.52s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 7 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 7 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 86 ( 86 usr; 39 con; 0-3 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% 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(type_def_11,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(type_def_12,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_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_2Ebool_2ET_2E0: u ).
tff(func_def_19,type,
c_2Ebool_2E_5C_2F_2E0: u ).
tff(func_def_20,type,
c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).
tff(func_def_21,type,
c_2Ebool_2E_7E_2E0: u ).
tff(func_def_22,type,
c_2Ebool_2E_7E_2E1: du > u ).
tff(func_def_23,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_24,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_25,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_26,type,
mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_27,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_28,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_29,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_30,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_31,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_32,type,
mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_33,type,
mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_34,type,
mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_35,type,
i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).
tff(func_def_36,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_37,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_38,type,
j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_39,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_40,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_41,type,
tyop_2Emin_2Eind: d ).
tff(func_def_42,type,
c_2Ebool_2E_3F_21_2E0: u ).
tff(func_def_43,type,
c_2Ebool_2E_3F_21_2E1: du > u ).
tff(func_def_44,type,
c_2Emin_2E_40_2E0: u ).
tff(func_def_45,type,
c_2Emin_2E_40_2E1: du > u ).
tff(func_def_46,type,
c_2Ebool_2EBOUNDED_2E0: u ).
tff(func_def_47,type,
c_2Ebool_2EBOUNDED_2E1: du > u ).
tff(func_def_48,type,
c_2Ebool_2ECOND_2E0: u ).
tff(func_def_49,type,
c_2Ebool_2ECOND_2E3: ( du * du * du ) > u ).
tff(func_def_50,type,
c_2Ebool_2EDATATYPE_2E0: u ).
tff(func_def_51,type,
c_2Ebool_2EDATATYPE_2E1: du > u ).
tff(func_def_52,type,
c_2Ebool_2EIN_2E0: u ).
tff(func_def_53,type,
c_2Ebool_2EIN_2E2: ( du * du ) > u ).
tff(func_def_54,type,
c_2Ebool_2ELET_2E0: u ).
tff(func_def_55,type,
c_2Ebool_2ELET_2E2: ( du * du ) > u ).
tff(func_def_56,type,
c_2Ebool_2EONE__ONE_2E0: u ).
tff(func_def_57,type,
c_2Ebool_2EONE__ONE_2E1: du > u ).
tff(func_def_58,type,
c_2Ebool_2EONTO_2E0: u ).
tff(func_def_59,type,
c_2Ebool_2EONTO_2E1: du > u ).
tff(func_def_60,type,
c_2Ebool_2ERES__EXISTS_2E0: u ).
tff(func_def_61,type,
c_2Ebool_2ERES__EXISTS_2E2: ( du * du ) > u ).
tff(func_def_62,type,
c_2Ebool_2ERES__EXISTS__UNIQUE_2E0: u ).
tff(func_def_63,type,
c_2Ebool_2ERES__EXISTS__UNIQUE_2E2: ( du * du ) > u ).
tff(func_def_64,type,
c_2Ebool_2ERES__FORALL_2E0: u ).
tff(func_def_65,type,
c_2Ebool_2ERES__FORALL_2E2: ( du * du ) > u ).
tff(func_def_66,type,
c_2Ebool_2ERES__SELECT_2E0: u ).
tff(func_def_67,type,
c_2Ebool_2ERES__SELECT_2E2: ( du * du ) > u ).
tff(func_def_68,type,
c_2Ebool_2ETYPE__DEFINITION_2E0: u ).
tff(func_def_69,type,
c_2Ebool_2ETYPE__DEFINITION_2E2: ( du * du ) > u ).
tff(func_def_70,type,
c_2Ebool_2Eliteral__case_2E0: u ).
tff(func_def_71,type,
c_2Ebool_2Eliteral__case_2E2: ( du * du ) > u ).
tff(func_def_72,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29 ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_73,type,
mono_2Ec_2Ebool_2EBOUNDED_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_74,type,
mono_2Ec_2Ebool_2EBOUNDED_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_75,type,
mono_2Ec_2Ebool_2EONE__ONE_2E0_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_76,type,
mono_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29 > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_77,type,
mono_2Ec_2Ebool_2EONTO_2E0_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_78,type,
mono_2Ec_2Ebool_2EONTO_2E1_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29 > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_79,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29_2Ctyop_2Emin_2Ebool_29 > u ).
tff(func_def_80,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29 > u ).
tff(func_def_81,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_82,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Eind_2Ctyop_2Emin_2Eind_29 ).
tff(func_def_83,type,
sK1: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_84,type,
sK2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_85,type,
sK3: mono_2Etyop_2Emin_2Ebool ).
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(f33,axiom,
p(mono_2Ec_2Ebool_2ET_2E0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
tff(f112,conjecture,
p(mono_2Ec_2Ebool_2ET_2E0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
tff(f113,negated_conjecture,
~ p(mono_2Ec_2Ebool_2ET_2E0),
inference(negated_conjecture,[status(cth)],[f112]) ).
tff(f114,plain,
~ p(mono_2Ec_2Ebool_2ET_2E0),
inference(flattening,[],[f113]) ).
tff(f137,plain,
~ p(mono_2Ec_2Ebool_2ET_2E0),
inference(cnf_transformation,[],[f114]) ).
tff(f161,plain,
p(mono_2Ec_2Ebool_2ET_2E0),
inference(cnf_transformation,[],[f33]) ).
tff(f165,plain,
$false,
inference(forward_subsumption_resolution,[],[f161,f137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP001_4 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 % Computer : n013.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 11:46:51 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 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
% 3.69/1.52 % (86361)Detected formulas, will run a generic FOF schedule.
% 3.69/1.52 % (86366)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=2703857077:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.69/1.52 % (86372)dis-21_1_sil=8000:lcm=predicate:random_seed=2198733271: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)
% 3.69/1.52 % (86368)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=1444460913:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.69/1.52 % (86367)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=1502308274:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.69/1.52 % (86369)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2831195575:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.69/1.52 % (86370)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2645343219:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.69/1.52 % (86370)First to succeed.
% 3.69/1.52 % (86369)Also succeeded, but the first one will report.
% 3.69/1.52 % (86370)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-86361"
% 3.69/1.52 % (86372)Also succeeded, but the first one will report.
% 3.69/1.52 % (86371)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2051880194:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.69/1.52 % (86371)Also succeeded, but the first one will report.
% 3.69/1.52 % (86370)Refutation found. Thanks to Tanya!
% 3.69/1.52 % SZS status Theorem for theBenchmark
% 3.69/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.52 % (86370)------------------------------
% 3.69/1.52 % (86370)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.52 % (86370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.52 % (86370)CaDiCaL version: 2.1.3
% 3.69/1.52 % (86370)Termination reason: Refutation
% 3.69/1.52 % (86370)Time elapsed: 0.003 s
% 3.69/1.52 % (86370)Peak memory usage: 88 MB
% 3.69/1.52 % (86370)Instructions burned: 1 (million)
% 3.69/1.52 % (86370)------------------------------
% 3.69/1.52 % (86370)------------------------------
% 3.69/1.52 % (86361)Success in time 0.443 s
% 3.69/1.52 % Vampire exiting
%------------------------------------------------------------------------------