TSTP Solution File: ITP010^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ITP010^1 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:30:32 EDT 2024
% Result : Theorem 0.16s 0.33s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 56
% Syntax : Number of formulae : 64 ( 6 unt; 54 typ; 0 def)
% Number of atoms : 28 ( 7 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 293 ( 29 ~; 0 |; 0 &; 260 @)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 66 ( 66 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 19 con; 0-4 aty)
% Number of variables : 28 ( 0 ^ 16 !; 12 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
d: $tType ).
thf(type_def_7,type,
u: $tType ).
thf(type_def_8,type,
du: $tType ).
thf(func_def_0,type,
u: $tType ).
thf(func_def_1,type,
d: $tType ).
thf(func_def_2,type,
du: $tType ).
thf(func_def_3,type,
tyop_2Emin_2Ebool: d ).
thf(func_def_4,type,
tyop_2Emin_2Efun: d > d > d ).
thf(func_def_5,type,
s: d > u > du ).
thf(func_def_6,type,
app_2E2: du > du > u ).
thf(func_def_7,type,
combin_i_2E0: u ).
thf(func_def_8,type,
combin_k_2E0: u ).
thf(func_def_9,type,
combin_s_2E0: u ).
thf(func_def_10,type,
c_2Ebool_2E_21_2E0: u ).
thf(func_def_11,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(func_def_12,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(func_def_13,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(func_def_14,type,
c_2Emin_2E_3D_2E0: u ).
thf(func_def_15,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(func_def_16,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(func_def_17,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(func_def_18,type,
c_2Ebool_2E_3F_2E0: u ).
thf(func_def_19,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(func_def_20,type,
c_2Ebool_2EF_2E0: u ).
thf(func_def_21,type,
c_2Ebool_2ET_2E0: u ).
thf(func_def_22,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(func_def_23,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(func_def_24,type,
c_2Ecardinal_2Ecardleq_2E0: u ).
thf(func_def_25,type,
c_2Ecardinal_2Ecardleq_2E2: du > du > u ).
thf(func_def_26,type,
c_2Ebool_2E_7E_2E0: u ).
thf(func_def_27,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(func_def_28,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(func_def_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
thf(func_def_30,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_31,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_34,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_35,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(func_def_36,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(func_def_37,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(func_def_38,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
thf(func_def_39,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(func_def_40,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(func_def_41,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
thf(func_def_47,type,
sP0: $o > $o > $o > $o ).
thf(func_def_48,type,
sP1: $o > $o > $o > $o ).
thf(func_def_49,type,
sP2: $o > $o > $o > $o ).
thf(func_def_50,type,
sP3: $o > $o > $o > $o ).
thf(func_def_51,type,
sK4: d > u > u ).
thf(func_def_52,type,
sK5: d ).
thf(func_def_53,type,
sK6: u ).
thf(func_def_54,type,
sK7: u ).
thf(func_def_55,type,
sK8: d ).
thf(func_def_56,type,
sK9: u > d > d > u > u ).
thf(func_def_57,type,
sK10: d > u > u ).
thf(f415,plain,
$false,
inference(trivial_inequality_removal,[],[f197]) ).
thf(f197,plain,
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool ) @ sK7 ) @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ sK6 ) ) ) ) )
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool ) @ sK7 ) @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ sK6 ) ) ) ) ) ),
inference(cnf_transformation,[],[f137]) ).
thf(f137,plain,
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool ) @ sK7 ) @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ sK6 ) ) ) ) )
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool ) @ sK7 ) @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ sK6 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f135,f136]) ).
thf(f136,plain,
( ? [X0: d,X1: u,X2: u,X3: d] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) )
=> ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool ) @ sK7 ) @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ sK6 ) ) ) ) )
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool ) @ sK7 ) @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ sK6 ) ) ) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f135,plain,
? [X0: d,X1: u,X2: u,X3: d] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) ),
inference(rectify,[],[f116]) ).
thf(f116,plain,
? [X2: d,X3: u,X1: u,X0: d] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X3 ) ) ) ) )
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X3 ) ) ) ) ) ),
inference(ennf_transformation,[],[f48]) ).
thf(f48,plain,
~ ! [X3: u,X1: u,X0: d,X2: d] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X3 ) ) ) ) )
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X3 ) ) ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f47,plain,
~ ! [X0: d,X1: u,X2: d,X3: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X3 ) ) ) )
<=> ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X3 ) ) ) ) ),
inference(rectify,[],[f43]) ).
thf(f43,negated_conjecture,
~ ! [X0: d,X16: u,X1: d,X17: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X16 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X17 ) ) ) )
<=> ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X16 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X17 ) ) ) ) ),
inference(negated_conjecture,[],[f42]) ).
thf(f42,conjecture,
! [X0: d,X16: u,X1: d,X17: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X16 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X17 ) ) ) )
<=> ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X16 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X17 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ECARD__NOT__LE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ITP010^1 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.10/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.31 % Computer : n021.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat May 18 18:16:23 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.31 This is a TH0_THM_EQU_NAR problem
% 0.16/0.31 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.33 % (21203)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.33 % (21205)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.16/0.33 % (21208)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.16/0.33 % (21207)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.33 % (21210)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.16/0.33 % (21209)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.33 % (21207)Instruction limit reached!
% 0.16/0.33 % (21207)------------------------------
% 0.16/0.33 % (21207)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33 % (21203)First to succeed.
% 0.16/0.33 % (21207)Termination reason: Unknown
% 0.16/0.33 % (21207)Termination phase: shuffling
% 0.16/0.33
% 0.16/0.33 % (21207)Memory used [KB]: 1023
% 0.16/0.33 % (21207)Time elapsed: 0.003 s
% 0.16/0.33 % (21207)Instructions burned: 2 (million)
% 0.16/0.33 % (21207)------------------------------
% 0.16/0.33 % (21207)------------------------------
% 0.16/0.33 % (21208)Also succeeded, but the first one will report.
% 0.16/0.33 % (21210)Instruction limit reached!
% 0.16/0.33 % (21210)------------------------------
% 0.16/0.33 % (21210)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33 % (21210)Termination reason: Unknown
% 0.16/0.33 % (21210)Termination phase: shuffling
% 0.16/0.33
% 0.16/0.33 % (21210)Memory used [KB]: 1023
% 0.16/0.33 % (21210)Time elapsed: 0.003 s
% 0.16/0.33 % (21210)Instructions burned: 4 (million)
% 0.16/0.33 % (21210)------------------------------
% 0.16/0.33 % (21210)------------------------------
% 0.16/0.33 % (21203)Refutation found. Thanks to Tanya!
% 0.16/0.33 % SZS status Theorem for theBenchmark
% 0.16/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.33 % (21203)------------------------------
% 0.16/0.33 % (21203)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33 % (21203)Termination reason: Refutation
% 0.16/0.33
% 0.16/0.33 % (21203)Memory used [KB]: 5756
% 0.16/0.33 % (21203)Time elapsed: 0.008 s
% 0.16/0.33 % (21203)Instructions burned: 19 (million)
% 0.16/0.33 % (21203)------------------------------
% 0.16/0.33 % (21203)------------------------------
% 0.16/0.33 % (21202)Success in time 0.016 s
% 0.16/0.33 % Vampire---4.8 exiting
%------------------------------------------------------------------------------