%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT056^1 : TPTP v9.2.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n027.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 : Wed Feb 25 08:44:45 AM UTC 2026
% Result : Theorem 1.50s 1.29s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 16 unt; 0 typ; 4 def)
% Number of atoms : 100 ( 67 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 679 ( 43 ~; 32 |; 6 &; 584 @)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 15 con; 0-2 aty)
% Number of variables : 117 ( 0 ^; 85 !; 32 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
lst: $tType ).
thf(type_def_7,type,
a: $tType ).
thf(func_def_0,type,
lst: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
ap: lst > lst > lst ).
thf(func_def_3,type,
cns: a > lst > lst ).
thf(func_def_4,type,
nl: lst ).
thf(func_def_5,type,
xs: lst ).
thf(func_def_9,type,
sK0: lst ).
thf(func_def_10,type,
sK1: lst ).
thf(func_def_11,type,
sK2: lst ).
thf(func_def_12,type,
sK3: lst ).
thf(func_def_13,type,
sK4: a ).
thf(func_def_14,type,
sK5: lst ).
thf(func_def_15,type,
sK6: lst ).
thf(func_def_16,type,
sK7: lst ).
thf(f60,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f38,f42,f45,f53,f59]) ).
thf(f59,plain,
( spl8_2
| ~ spl8_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
| spl8_2
| ~ spl8_4 ),
inference(trivial_inequality_removal,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( cns @ sK4 @ ( ap @ sK5 @ ( ap @ sK7 @ sK6 ) ) )
!= ( cns @ sK4 @ ( ap @ sK5 @ ( ap @ sK7 @ sK6 ) ) ) )
| spl8_2
| ~ spl8_4 ),
inference(superposition,[status(thm)],[f56,f41]) ).
thf(f41,plain,
( ! [X8: lst,X7: lst] :
( ( ap @ ( ap @ sK5 @ X8 ) @ X7 )
= ( ap @ sK5 @ ( ap @ X8 @ X7 ) ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl8_4
<=> ! [X7: lst,X8: lst] :
( ( ap @ ( ap @ sK5 @ X8 ) @ X7 )
= ( ap @ sK5 @ ( ap @ X8 @ X7 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition]) ).
thf(f56,plain,
( ( ( cns @ sK4 @ ( ap @ sK5 @ ( ap @ sK7 @ sK6 ) ) )
!= ( cns @ sK4 @ ( ap @ ( ap @ sK5 @ sK7 ) @ sK6 ) ) )
| spl8_2 ),
inference(superposition,[status(thm)],[f55,f22]) ).
thf(f22,plain,
! [X2: a,X0: lst,X1: lst] :
( ( ap @ ( cns @ X2 @ X0 ) @ X1 )
= ( cns @ X2 @ ( ap @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: lst,X1: lst,X2: a] :
( ( ap @ ( cns @ X2 @ X0 ) @ X1 )
= ( cns @ X2 @ ( ap @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: lst,X2: lst,X1: a] :
( ( ap @ ( cns @ X1 @ X0 ) @ X2 )
= ( cns @ X1 @ ( ap @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X8: lst,X9: a,X7: lst] :
( ( ap @ ( cns @ X9 @ X8 ) @ X7 )
= ( cns @ X9 @ ( ap @ X8 @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ueLwQxY4i2/DTF2THF_27460.p',fact_1p_Osimps_I2_J) ).
thf(f55,plain,
( ( ( ap @ ( cns @ sK4 @ sK5 ) @ ( ap @ sK7 @ sK6 ) )
!= ( cns @ sK4 @ ( ap @ ( ap @ sK5 @ sK7 ) @ sK6 ) ) )
| spl8_2 ),
inference(superposition,[status(thm)],[f54,f22]) ).
thf(f54,plain,
( ( ( ap @ ( cns @ sK4 @ sK5 ) @ ( ap @ sK7 @ sK6 ) )
!= ( ap @ ( cns @ sK4 @ ( ap @ sK5 @ sK7 ) ) @ sK6 ) )
| spl8_2 ),
inference(superposition,[status(thm)],[f34,f22]) ).
thf(f34,plain,
( ( ( ap @ ( ap @ ( cns @ sK4 @ sK5 ) @ sK7 ) @ sK6 )
!= ( ap @ ( cns @ sK4 @ sK5 ) @ ( ap @ sK7 @ sK6 ) ) )
| spl8_2 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl8_2
<=> ( ( ap @ ( ap @ ( cns @ sK4 @ sK5 ) @ sK7 ) @ sK6 )
= ( ap @ ( cns @ sK4 @ sK5 ) @ ( ap @ sK7 @ sK6 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).
thf(f53,plain,
~ spl8_3,
inference(avatar_contradiction_clause,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
| ~ spl8_3 ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( ap @ xs @ ( ap @ sK0 @ sK1 ) )
!= ( ap @ xs @ ( ap @ sK0 @ sK1 ) ) )
| ~ spl8_3 ),
inference(superposition,[status(thm)],[f23,f37]) ).
thf(f37,plain,
( ! [X10: lst,X0: lst,X9: lst] :
( ( ap @ X0 @ ( ap @ X9 @ X10 ) )
= ( ap @ ( ap @ X0 @ X9 ) @ X10 ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl8_3
<=> ! [X9: lst,X0: lst,X10: lst] :
( ( ap @ X0 @ ( ap @ X9 @ X10 ) )
= ( ap @ ( ap @ X0 @ X9 ) @ X10 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition]) ).
thf(f23,plain,
( ( ap @ ( ap @ xs @ sK0 ) @ sK1 )
!= ( ap @ xs @ ( ap @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ap @ ( ap @ xs @ sK0 ) @ sK1 )
!= ( ap @ xs @ ( ap @ sK0 @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f15]) ).
thf(f15,plain,
( ? [X0: lst,X1: lst] :
( ( ap @ xs @ ( ap @ X0 @ X1 ) )
!= ( ap @ ( ap @ xs @ X0 ) @ X1 ) )
=> ( ( ap @ ( ap @ xs @ sK0 ) @ sK1 )
!= ( ap @ xs @ ( ap @ sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: lst,X1: lst] :
( ( ap @ xs @ ( ap @ X0 @ X1 ) )
!= ( ap @ ( ap @ xs @ X0 ) @ X1 ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: lst,X1: lst] :
( ( ap @ xs @ ( ap @ X0 @ X1 ) )
= ( ap @ ( ap @ xs @ X0 ) @ X1 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X1: lst,X2: lst] :
( ( ap @ xs @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ xs @ X1 ) @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X1: lst,X2: lst] :
( ( ap @ xs @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ xs @ X1 ) @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.ueLwQxY4i2/DTF2THF_27460.p',conj_0) ).
thf(f45,plain,
spl8_1,
inference(avatar_contradiction_clause,[status(thm)],[f44]) ).
thf(f44,plain,
( $false
| spl8_1 ),
inference(subsumption_resolution,[status(thm)],[f43,f26]) ).
thf(f26,plain,
! [X0: lst] :
( ( ap @ nl @ X0 )
= X0 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: lst] :
( ( ap @ nl @ X0 )
= X0 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X7: lst] :
( ( ap @ nl @ X7 )
= X7 ),
file('/export/starexec/sandbox2/tmp/tmp.ueLwQxY4i2/DTF2THF_27460.p',fact_2p_Osimps_I1_J) ).
thf(f43,plain,
( ( ( ap @ sK2 @ sK3 )
!= ( ap @ nl @ ( ap @ sK2 @ sK3 ) ) )
| spl8_1 ),
inference(superposition,[status(thm)],[f30,f26]) ).
thf(f30,plain,
( ( ( ap @ ( ap @ nl @ sK2 ) @ sK3 )
!= ( ap @ nl @ ( ap @ sK2 @ sK3 ) ) )
| spl8_1 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f28,definition,
( spl8_1
<=> ( ( ap @ ( ap @ nl @ sK2 ) @ sK3 )
= ( ap @ nl @ ( ap @ sK2 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition]) ).
thf(f42,plain,
( ~ spl8_1
| spl8_3
| spl8_4 ),
inference(avatar_split_clause,[status(thm)],[f24,f40,f36,f28]) ).
thf(f24,plain,
! [X10: lst,X0: lst,X8: lst,X9: lst,X7: lst] :
( ( ( ap @ ( ap @ nl @ sK2 ) @ sK3 )
!= ( ap @ nl @ ( ap @ sK2 @ sK3 ) ) )
| ( ( ap @ X0 @ ( ap @ X9 @ X10 ) )
= ( ap @ ( ap @ X0 @ X9 ) @ X10 ) )
| ( ( ap @ ( ap @ sK5 @ X8 ) @ X7 )
= ( ap @ sK5 @ ( ap @ X8 @ X7 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: lst] :
( ( ( ap @ ( ap @ nl @ sK2 ) @ sK3 )
!= ( ap @ nl @ ( ap @ sK2 @ sK3 ) ) )
| ( ( ( ap @ ( ap @ ( cns @ sK4 @ sK5 ) @ sK7 ) @ sK6 )
!= ( ap @ ( cns @ sK4 @ sK5 ) @ ( ap @ sK7 @ sK6 ) ) )
& ! [X7: lst,X8: lst] :
( ( ap @ ( ap @ sK5 @ X8 ) @ X7 )
= ( ap @ sK5 @ ( ap @ X8 @ X7 ) ) ) )
| ! [X9: lst,X10: lst] :
( ( ap @ X0 @ ( ap @ X9 @ X10 ) )
= ( ap @ ( ap @ X0 @ X9 ) @ X10 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7])],[f17,f20,f19,f18]) ).
thf(f18,plain,
( ? [X1: lst,X2: lst] :
( ( ap @ nl @ ( ap @ X1 @ X2 ) )
!= ( ap @ ( ap @ nl @ X1 ) @ X2 ) )
=> ( ( ap @ ( ap @ nl @ sK2 ) @ sK3 )
!= ( ap @ nl @ ( ap @ sK2 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X3: a,X4: lst] :
( ? [X5: lst,X6: lst] :
( ( ap @ ( ap @ ( cns @ X3 @ X4 ) @ X6 ) @ X5 )
!= ( ap @ ( cns @ X3 @ X4 ) @ ( ap @ X6 @ X5 ) ) )
& ! [X7: lst,X8: lst] :
( ( ap @ ( ap @ X4 @ X8 ) @ X7 )
= ( ap @ X4 @ ( ap @ X8 @ X7 ) ) ) )
=> ( ? [X6: lst,X5: lst] :
( ( ap @ ( ap @ ( cns @ sK4 @ sK5 ) @ X6 ) @ X5 )
!= ( ap @ ( cns @ sK4 @ sK5 ) @ ( ap @ X6 @ X5 ) ) )
& ! [X8: lst,X7: lst] :
( ( ap @ ( ap @ sK5 @ X8 ) @ X7 )
= ( ap @ sK5 @ ( ap @ X8 @ X7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ? [X6: lst,X5: lst] :
( ( ap @ ( ap @ ( cns @ sK4 @ sK5 ) @ X6 ) @ X5 )
!= ( ap @ ( cns @ sK4 @ sK5 ) @ ( ap @ X6 @ X5 ) ) )
=> ( ( ap @ ( ap @ ( cns @ sK4 @ sK5 ) @ sK7 ) @ sK6 )
!= ( ap @ ( cns @ sK4 @ sK5 ) @ ( ap @ sK7 @ sK6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
! [X0: lst] :
( ? [X1: lst,X2: lst] :
( ( ap @ nl @ ( ap @ X1 @ X2 ) )
!= ( ap @ ( ap @ nl @ X1 ) @ X2 ) )
| ? [X3: a,X4: lst] :
( ? [X5: lst,X6: lst] :
( ( ap @ ( ap @ ( cns @ X3 @ X4 ) @ X6 ) @ X5 )
!= ( ap @ ( cns @ X3 @ X4 ) @ ( ap @ X6 @ X5 ) ) )
& ! [X7: lst,X8: lst] :
( ( ap @ ( ap @ X4 @ X8 ) @ X7 )
= ( ap @ X4 @ ( ap @ X8 @ X7 ) ) ) )
| ! [X9: lst,X10: lst] :
( ( ap @ X0 @ ( ap @ X9 @ X10 ) )
= ( ap @ ( ap @ X0 @ X9 ) @ X10 ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: lst] :
( ? [X2: lst,X1: lst] :
( ( ap @ ( ap @ nl @ X2 ) @ X1 )
!= ( ap @ nl @ ( ap @ X2 @ X1 ) ) )
| ? [X3: a,X4: lst] :
( ? [X7: lst,X8: lst] :
( ( ap @ ( cns @ X3 @ X4 ) @ ( ap @ X8 @ X7 ) )
!= ( ap @ ( ap @ ( cns @ X3 @ X4 ) @ X8 ) @ X7 ) )
& ! [X5: lst,X6: lst] :
( ( ap @ ( ap @ X4 @ X6 ) @ X5 )
= ( ap @ X4 @ ( ap @ X6 @ X5 ) ) ) )
| ! [X10: lst,X9: lst] :
( ( ap @ X0 @ ( ap @ X10 @ X9 ) )
= ( ap @ ( ap @ X0 @ X10 ) @ X9 ) ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: lst] :
( ! [X10: lst,X9: lst] :
( ( ap @ X0 @ ( ap @ X10 @ X9 ) )
= ( ap @ ( ap @ X0 @ X10 ) @ X9 ) )
| ? [X3: a,X4: lst] :
( ? [X7: lst,X8: lst] :
( ( ap @ ( cns @ X3 @ X4 ) @ ( ap @ X8 @ X7 ) )
!= ( ap @ ( ap @ ( cns @ X3 @ X4 ) @ X8 ) @ X7 ) )
& ! [X5: lst,X6: lst] :
( ( ap @ ( ap @ X4 @ X6 ) @ X5 )
= ( ap @ X4 @ ( ap @ X6 @ X5 ) ) ) )
| ? [X2: lst,X1: lst] :
( ( ap @ ( ap @ nl @ X2 ) @ X1 )
!= ( ap @ nl @ ( ap @ X2 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: lst] :
( ! [X1: lst,X2: lst] :
( ( ap @ ( ap @ nl @ X2 ) @ X1 )
= ( ap @ nl @ ( ap @ X2 @ X1 ) ) )
=> ( ! [X3: a,X4: lst] :
( ! [X5: lst,X6: lst] :
( ( ap @ ( ap @ X4 @ X6 ) @ X5 )
= ( ap @ X4 @ ( ap @ X6 @ X5 ) ) )
=> ! [X8: lst,X7: lst] :
( ( ap @ ( cns @ X3 @ X4 ) @ ( ap @ X8 @ X7 ) )
= ( ap @ ( ap @ ( cns @ X3 @ X4 ) @ X8 ) @ X7 ) ) )
=> ! [X10: lst,X9: lst] :
( ( ap @ X0 @ ( ap @ X10 @ X9 ) )
= ( ap @ ( ap @ X0 @ X10 ) @ X9 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: lst] :
( ! [X2: lst,X1: lst] :
( ( ap @ nl @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ nl @ X1 ) @ X2 ) )
=> ( ! [X3: a,X4: lst] :
( ! [X6: lst,X5: lst] :
( ( ap @ X4 @ ( ap @ X5 @ X6 ) )
= ( ap @ ( ap @ X4 @ X5 ) @ X6 ) )
=> ! [X2: lst,X1: lst] :
( ( ap @ ( cns @ X3 @ X4 ) @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ ( cns @ X3 @ X4 ) @ X1 ) @ X2 ) ) )
=> ! [X6: lst,X5: lst] :
( ( ap @ X0 @ ( ap @ X5 @ X6 ) )
= ( ap @ ( ap @ X0 @ X5 ) @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ueLwQxY4i2/DTF2THF_27460.p',fact_0_lst_Oinduct_091where_AP_A_061_A_C_Fxs_O_AALL_Ays_Azs_O_Aap_Axs_A_Iap_Ays_Azs_J_A_061_Aap_A_Iap_Axs_Ays_J_Azs_C_093) ).
thf(f38,plain,
( ~ spl8_1
| ~ spl8_2
| spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f25,f36,f32,f28]) ).
thf(f25,plain,
! [X10: lst,X0: lst,X9: lst] :
( ( ( ap @ X0 @ ( ap @ X9 @ X10 ) )
= ( ap @ ( ap @ X0 @ X9 ) @ X10 ) )
| ( ( ap @ ( ap @ ( cns @ sK4 @ sK5 ) @ sK7 ) @ sK6 )
!= ( ap @ ( cns @ sK4 @ sK5 ) @ ( ap @ sK7 @ sK6 ) ) )
| ( ( ap @ ( ap @ nl @ sK2 ) @ sK3 )
!= ( ap @ nl @ ( ap @ sK2 @ sK3 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT056^1 : TPTP v9.2.1. Released v5.4.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 06:06:22 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : DAT056^1 : TPTP v9.2.1. Released v5.4.0.
% 0.30/0.46 % Domain : Data Structures
% 0.30/0.46 % Problem : List operation requiring induction
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bla12] Blanchette (2012), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bla12]
% 0.30/0.46 % Names : easy.tptp [Bla12]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.33 v5.4.0
% 0.30/0.46 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 0 def)
% 0.30/0.46 % Number of atoms : 7 ( 7 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 4 ( 1 avg)
% 0.30/0.46 % Number of connectives : 57 ( 0 ~; 0 |; 0 &; 54 @)
% 0.30/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 9 ( 5 avg)
% 0.30/0.46 % Number of types : 2 ( 2 usr)
% 0.30/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : Induction principle is preinstantiated with the conjecture.
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 %----Should-be-implicit typings (2)
% 0.30/0.46 thf(ty_n_tc__Foo__Olst_It__J,type,
% 0.30/0.46 lst: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_n_t_,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 %----Explicit typings (4)
% 0.30/0.46 thf(sy_c_Foo_Oap_001t_,type,
% 0.30/0.46 ap: lst > lst > lst ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Foo_Olst_OCns_001t_,type,
% 0.30/0.46 cns: a > lst > lst ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Foo_Olst_ONl_001t_,type,
% 0.30/0.46 nl: lst ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_xs,type,
% 0.30/0.46 xs: lst ).
% 0.30/0.46
% 0.30/0.46 %----Relevant facts (3)
% 0.30/0.46 thf(fact_0_lst_Oinduct_091where_AP_A_061_A_C_Fxs_O_AALL_Ays_Azs_O_Aap_Axs_A_Iap_Ays_Azs_J_A_061_Aap_A_Iap_Axs_Ays_J_Azs_C_093,axiom,
% 0.30/0.46 ! [Lst: lst] :
% 0.30/0.46 ( ! [Ys: lst,Zs: lst] :
% 0.30/0.46 ( ( ap @ nl @ ( ap @ Ys @ Zs ) )
% 0.30/0.46 = ( ap @ ( ap @ nl @ Ys ) @ Zs ) )
% 0.30/0.46 => ( ! [A: a,Lst2: lst] :
% 0.30/0.46 ( ! [Ys3: lst,Zs2: lst] :
% 0.30/0.46 ( ( ap @ Lst2 @ ( ap @ Ys3 @ Zs2 ) )
% 0.30/0.46 = ( ap @ ( ap @ Lst2 @ Ys3 ) @ Zs2 ) )
% 0.30/0.46 => ! [Ys: lst,Zs: lst] :
% 0.30/0.46 ( ( ap @ ( cns @ A @ Lst2 ) @ ( ap @ Ys @ Zs ) )
% 0.30/0.46 = ( ap @ ( ap @ ( cns @ A @ Lst2 ) @ Ys ) @ Zs ) ) )
% 0.30/0.46 => ! [Ys3: lst,Zs2: lst] :
% 0.30/0.46 ( ( ap @ Lst @ ( ap @ Ys3 @ Zs2 ) )
% 0.30/0.46 = ( ap @ ( ap @ Lst @ Ys3 ) @ Zs2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(fact_1p_Osimps_I2_J,axiom,
% 0.30/0.46 ! [Ys2: lst,Xs: lst,X: a] :
% 0.30/0.46 ( ( ap @ ( cns @ X @ Xs ) @ Ys2 )
% 0.30/0.46 = ( cns @ X @ ( ap @ Xs @ Ys2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(fact_2p_Osimps_I1_J,axiom,
% 0.30/0.46 ! [Ys2: lst] :
% 0.30/0.46 ( ( ap @ nl @ Ys2 )
% 0.30/0.46 = Ys2 ) ).
% 0.30/0.46
% 0.30/0.46 %----Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 ! [Ys: lst,Zs: lst] :
% 0.30/0.46 ( ( ap @ xs @ ( ap @ Ys @ Zs ) )
% 0.30/0.46 = ( ap @ ( ap @ xs @ Ys ) @ Zs ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.50/1.25 ---- Embedded in THF ---
% 1.50/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.25 %%% Generated on Tue Feb 24 06:06:23 EST 2026
% 1.50/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.25 %%% Logic specification used:
% 1.50/1.25 %%% thf(spec, logic, $$dhol).
% 1.50/1.25
% 1.50/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ueLwQxY4i2/DTF2DTF27460.p
% See solution above
% 1.50/1.25 ------------------------
% 1.50/1.26 ---- Cleaned THF ---
% 1.50/1.26 thf(ty_n_tc__Foo__Olst_It__J,type,
% 1.50/1.26 lst: $tType ).
% 1.50/1.26
% 1.50/1.26 thf(ty_n_t_,type,
% 1.50/1.26 a: $tType ).
% 1.50/1.26
% 1.50/1.26 thf(sy_c_Foo_Oap_001t_,type,
% 1.50/1.26 ap: lst > lst > lst ).
% 1.50/1.26
% 1.50/1.26 thf(sy_c_Foo_Olst_OCns_001t_,type,
% 1.50/1.26 cns: a > lst > lst ).
% 1.50/1.26
% 1.50/1.26 thf(sy_c_Foo_Olst_ONl_001t_,type,
% 1.50/1.26 nl: lst ).
% 1.50/1.26
% 1.50/1.26 thf(sy_v_xs,type,
% 1.50/1.26 xs: lst ).
% 1.50/1.26
% 1.50/1.26 thf(fact_0_lst_Oinduct_091where_AP_A_061_A_C_Fxs_O_AALL_Ays_Azs_O_Aap_Axs_A_Iap_Ays_Azs_J_A_061_Aap_A_Iap_Axs_Ays_J_Azs_C_093,axiom,
% 1.50/1.26 ! [Lst: lst] :
% 1.50/1.26 ( ! [Ys: lst,Zs: lst] :
% 1.50/1.26 ( ( ap @ nl @ ( ap @ Ys @ Zs ) )
% 1.50/1.26 = ( ap @ ( ap @ nl @ Ys ) @ Zs ) )
% 1.50/1.26 => ( ! [A: a,Lst2: lst] :
% 1.50/1.26 ( ! [Ys3: lst,Zs2: lst] :
% 1.50/1.26 ( ( ap @ Lst2 @ ( ap @ Ys3 @ Zs2 ) )
% 1.50/1.26 = ( ap @ ( ap @ Lst2 @ Ys3 ) @ Zs2 ) )
% 1.50/1.26 => ! [Ys: lst,Zs: lst] :
% 1.50/1.26 ( ( ap @ ( cns @ A @ Lst2 ) @ ( ap @ Ys @ Zs ) )
% 1.50/1.26 = ( ap @ ( ap @ ( cns @ A @ Lst2 ) @ Ys ) @ Zs ) ) )
% 1.50/1.26 => ! [Ys3: lst,Zs2: lst] :
% 1.50/1.26 ( ( ap @ Lst @ ( ap @ Ys3 @ Zs2 ) )
% 1.50/1.26 = ( ap @ ( ap @ Lst @ Ys3 ) @ Zs2 ) ) ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(fact_1p_Osimps_I2_J,axiom,
% 1.50/1.26 ! [Ys2: lst,Xs: lst,X: a] :
% 1.50/1.26 ( ( ap @ ( cns @ X @ Xs ) @ Ys2 )
% 1.50/1.26 = ( cns @ X @ ( ap @ Xs @ Ys2 ) ) ) ).
% 1.50/1.26
% 1.50/1.26 thf(fact_2p_Osimps_I1_J,axiom,
% 1.50/1.26 ! [Ys2: lst] :
% 1.50/1.26 ( ( ap @ nl @ Ys2 )
% 1.50/1.26 = Ys2 ) ).
% 1.50/1.26
% 1.50/1.26 thf(conj_0,conjecture,
% 1.50/1.26 ! [Ys: lst,Zs: lst] :
% 1.50/1.26 ( ( ap @ xs @ ( ap @ Ys @ Zs ) )
% 1.50/1.26 = ( ap @ ( ap @ xs @ Ys ) @ Zs ) ) ).
% 1.50/1.26 ------------------------
% 1.50/1.28 % (27735)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_27460 for (2999ds/275Mi)
% 1.50/1.28 % (27734)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_27460 for (2999ds/2Mi)
% 1.50/1.28 % (27735)Refutation not found, incomplete strategy
% 1.50/1.28 % (27735)------------------------------
% 1.50/1.28 % (27735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (27735)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.28
% 1.50/1.28
% 1.50/1.28 % (27735)Memory used [KB]: 5373
% 1.50/1.28 % (27735)Time elapsed: 0.002 s
% 1.50/1.28 % (27735)Instructions burned: 1 (million)
% 1.50/1.28 % (27735)------------------------------
% 1.50/1.28 % (27735)------------------------------
% 1.50/1.28 % (27734)Instruction limit reached!
% 1.50/1.28 % (27734)------------------------------
% 1.50/1.28 % (27734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (27734)Termination reason: Unknown
% 1.50/1.28 % (27734)Termination phase: Preprocessing 3
% 1.50/1.28
% 1.50/1.28 % (27734)Memory used [KB]: 1023
% 1.50/1.28 % (27734)Time elapsed: 0.002 s
% 1.50/1.28 % (27734)Instructions burned: 3 (million)
% 1.50/1.28 % (27734)------------------------------
% 1.50/1.28 % (27734)------------------------------
% 1.50/1.29 % (27729)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27460 for (2999ds/183Mi)
% 1.50/1.29 % (27730)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_27460 for (2999ds/4Mi)
% 1.50/1.29 % (27731)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 DTF2THF_27460 for (2999ds/27Mi)
% 1.50/1.29 % (27732)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27460 for (2999ds/2Mi)
% 1.50/1.29 % (27736)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27460 for (2999ds/18Mi)
% 1.50/1.29 % (27732)Instruction limit reached!
% 1.50/1.29 % (27732)------------------------------
% 1.50/1.29 % (27732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (27732)Termination reason: Unknown
% 1.50/1.29 % (27732)Termination phase: Preprocessing 3
% 1.50/1.29
% 1.50/1.29 % (27732)Memory used [KB]: 895
% 1.50/1.29 % (27732)Time elapsed: 0.003 s
% 1.50/1.29 % (27732)Instructions burned: 2 (million)
% 1.50/1.29 % (27732)------------------------------
% 1.50/1.29 % (27732)------------------------------
% 1.50/1.29 % (27730)Instruction limit reached!
% 1.50/1.29 % (27730)------------------------------
% 1.50/1.29 % (27730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (27730)Termination reason: Unknown
% 1.50/1.29 % (27730)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (27730)Memory used [KB]: 5500
% 1.50/1.29 % (27730)Time elapsed: 0.005 s
% 1.50/1.29 % (27730)Instructions burned: 5 (million)
% 1.50/1.29 % (27730)------------------------------
% 1.50/1.29 % (27730)------------------------------
% 1.50/1.29 % (27738)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_27460 for (2999ds/37Mi)
% 1.50/1.29 % (27729)First to succeed.
% 1.50/1.29 % (27731)Also succeeded, but the first one will report.
% 1.50/1.29 % (27729)Refutation found. Thanks to Tanya!
% 1.50/1.29 % SZS status Theorem for DTF2THF_27460
% 1.50/1.29 % SZS output start Proof for DTF2THF_27460
% 1.50/1.29 thf(type_def_5, type, lst: $tType).
% 1.50/1.29 thf(type_def_7, type, a: $tType).
% 1.50/1.29 thf(func_def_0, type, lst: $tType).
% 1.50/1.29 thf(func_def_1, type, a: $tType).
% 1.50/1.29 thf(func_def_2, type, ap: lst > lst > lst).
% 1.50/1.29 thf(func_def_3, type, cns: a > lst > lst).
% 1.50/1.29 thf(func_def_4, type, nl: lst).
% 1.50/1.29 thf(func_def_5, type, xs: lst).
% 1.50/1.29 thf(func_def_9, type, sK0: lst).
% 1.50/1.29 thf(func_def_10, type, sK1: lst).
% 1.50/1.29 thf(func_def_11, type, sK2: lst).
% 1.50/1.29 thf(func_def_12, type, sK3: lst).
% 1.50/1.29 thf(func_def_13, type, sK4: a).
% 1.50/1.29 thf(func_def_14, type, sK5: lst).
% 1.50/1.29 thf(func_def_15, type, sK6: lst).
% 1.50/1.29 thf(func_def_16, type, sK7: lst).
% 1.50/1.29 thf(f60,plain,(
% 1.50/1.29 $false),
% 1.50/1.29 inference(avatar_sat_refutation,[status(thm)],[f38,f42,f45,f53,f59])).
% 1.50/1.29 thf(f59,plain,(
% 1.50/1.29 spl8_2 | ~spl8_4),
% 1.50/1.29 inference(avatar_contradiction_clause,[status(thm)],[f58])).
% 1.50/1.29 thf(f58,plain,(
% 1.50/1.29 $false | (spl8_2 | ~spl8_4)),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f57])).
% 1.50/1.29 thf(f57,plain,(
% 1.50/1.29 ((cns @ sK4 @ (ap @ sK5 @ (ap @ sK7 @ sK6))) != (cns @ sK4 @ (ap @ sK5 @ (ap @ sK7 @ sK6)))) | (spl8_2 | ~spl8_4)),
% 1.50/1.29 inference(superposition,[status(thm)],[f56,f41])).
% 1.50/1.29 thf(f41,plain,(
% 1.50/1.29 ( ! [X8 : lst,X7 : lst] : (((ap @ (ap @ sK5 @ X8) @ X7) = (ap @ sK5 @ (ap @ X8 @ X7)))) ) | ~spl8_4),
% 1.50/1.29 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.50/1.29 thf(f40,definition,(
% 1.50/1.29 spl8_4 <=> ! [X7 : lst,X8 : lst] : ((ap @ (ap @ sK5 @ X8) @ X7) = (ap @ sK5 @ (ap @ X8 @ X7)))),
% 1.50/1.29 introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition])).
% 1.50/1.29 thf(f56,plain,(
% 1.50/1.29 ((cns @ sK4 @ (ap @ sK5 @ (ap @ sK7 @ sK6))) != (cns @ sK4 @ (ap @ (ap @ sK5 @ sK7) @ sK6))) | spl8_2),
% 1.50/1.29 inference(superposition,[status(thm)],[f55,f22])).
% 1.50/1.29 thf(f22,plain,(
% 1.50/1.29 ( ! [X2 : a,X0 : lst,X1 : lst] : (((ap @ (cns @ X2 @ X0) @ X1) = (cns @ X2 @ (ap @ X0 @ X1)))) )),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f14])).
% 1.50/1.29 thf(f14,plain,(
% 1.50/1.29 ! [X0 : lst,X1 : lst,X2 : a] : ((ap @ (cns @ X2 @ X0) @ X1) = (cns @ X2 @ (ap @ X0 @ X1)))),
% 1.50/1.29 inference(rectify,[status(thm)],[f7])).
% 1.50/1.30 thf(f7,plain,(
% 1.50/1.30 ! [X0 : lst,X2 : lst,X1 : a] : ((ap @ (cns @ X1 @ X0) @ X2) = (cns @ X1 @ (ap @ X0 @ X2)))),
% 1.50/1.30 inference(rectify,[status(thm)],[f2])).
% 1.50/1.30 thf(f2,axiom,(
% 1.50/1.30 ! [X8 : lst,X9 : a,X7 : lst] : ((ap @ (cns @ X9 @ X8) @ X7) = (cns @ X9 @ (ap @ X8 @ X7)))),
% 1.50/1.30 file('/export/starexec/sandbox2/tmp/tmp.ueLwQxY4i2/DTF2THF_27460.p',fact_1p_Osimps_I2_J)).
% 1.50/1.30 thf(f55,plain,(
% 1.50/1.30 ((ap @ (cns @ sK4 @ sK5) @ (ap @ sK7 @ sK6)) != (cns @ sK4 @ (ap @ (ap @ sK5 @ sK7) @ sK6))) | spl8_2),
% 1.50/1.30 inference(superposition,[status(thm)],[f54,f22])).
% 1.50/1.30 thf(f54,plain,(
% 1.50/1.30 ((ap @ (cns @ sK4 @ sK5) @ (ap @ sK7 @ sK6)) != (ap @ (cns @ sK4 @ (ap @ sK5 @ sK7)) @ sK6)) | spl8_2),
% 1.50/1.30 inference(superposition,[status(thm)],[f34,f22])).
% 1.50/1.30 thf(f34,plain,(
% 1.50/1.30 ((ap @ (ap @ (cns @ sK4 @ sK5) @ sK7) @ sK6) != (ap @ (cns @ sK4 @ sK5) @ (ap @ sK7 @ sK6))) | spl8_2),
% 1.50/1.30 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.50/1.30 thf(f32,definition,(
% 1.50/1.30 spl8_2 <=> ((ap @ (ap @ (cns @ sK4 @ sK5) @ sK7) @ sK6) = (ap @ (cns @ sK4 @ sK5) @ (ap @ sK7 @ sK6)))),
% 1.50/1.30 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 1.50/1.30 thf(f53,plain,(
% 1.50/1.30 ~spl8_3),
% 1.50/1.30 inference(avatar_contradiction_clause,[status(thm)],[f52])).
% 1.50/1.30 thf(f52,plain,(
% 1.50/1.30 $false | ~spl8_3),
% 1.50/1.30 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.50/1.30 thf(f51,plain,(
% 1.50/1.30 ((ap @ xs @ (ap @ sK0 @ sK1)) != (ap @ xs @ (ap @ sK0 @ sK1))) | ~spl8_3),
% 1.50/1.30 inference(superposition,[status(thm)],[f23,f37])).
% 1.50/1.30 thf(f37,plain,(
% 1.50/1.30 ( ! [X10 : lst,X0 : lst,X9 : lst] : (((ap @ X0 @ (ap @ X9 @ X10)) = (ap @ (ap @ X0 @ X9) @ X10))) ) | ~spl8_3),
% 1.50/1.30 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.50/1.30 thf(f36,definition,(
% 1.50/1.30 spl8_3 <=> ! [X9 : lst,X0 : lst,X10 : lst] : ((ap @ X0 @ (ap @ X9 @ X10)) = (ap @ (ap @ X0 @ X9) @ X10))),
% 1.50/1.30 introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition])).
% 1.50/1.30 thf(f23,plain,(
% 1.50/1.30 ((ap @ (ap @ xs @ sK0) @ sK1) != (ap @ xs @ (ap @ sK0 @ sK1)))),
% 1.50/1.30 inference(cnf_transformation,[status(thm)],[f16])).
% 1.50/1.30 thf(f16,plain,(
% 1.50/1.30 ((ap @ (ap @ xs @ sK0) @ sK1) != (ap @ xs @ (ap @ sK0 @ sK1)))),
% 1.50/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f15])).
% 1.50/1.30 thf(f15,plain,(
% 1.50/1.30 ? [X0 : lst,X1 : lst] : ((ap @ xs @ (ap @ X0 @ X1)) != (ap @ (ap @ xs @ X0) @ X1)) => ((ap @ (ap @ xs @ sK0) @ sK1) != (ap @ xs @ (ap @ sK0 @ sK1)))),
% 1.50/1.30 introduced(definition,[],[choice_axiom])).
% 1.50/1.30 thf(f13,plain,(
% 1.50/1.30 ? [X0 : lst,X1 : lst] : ((ap @ xs @ (ap @ X0 @ X1)) != (ap @ (ap @ xs @ X0) @ X1))),
% 1.50/1.30 inference(ennf_transformation,[status(thm)],[f9])).
% 1.50/1.30 thf(f9,plain,(
% 1.50/1.30 ~! [X0 : lst,X1 : lst] : ((ap @ xs @ (ap @ X0 @ X1)) = (ap @ (ap @ xs @ X0) @ X1))),
% 1.50/1.30 inference(rectify,[status(thm)],[f5])).
% 1.50/1.30 thf(f5,negated_conjecture,(
% 1.50/1.30 ~! [X1 : lst,X2 : lst] : ((ap @ xs @ (ap @ X1 @ X2)) = (ap @ (ap @ xs @ X1) @ X2))),
% 1.50/1.30 inference(negated_conjecture,[status(cth)],[f4])).
% 1.50/1.30 thf(f4,conjecture,(
% 1.50/1.30 ! [X1 : lst,X2 : lst] : ((ap @ xs @ (ap @ X1 @ X2)) = (ap @ (ap @ xs @ X1) @ X2))),
% 1.50/1.30 file('/export/starexec/sandbox2/tmp/tmp.ueLwQxY4i2/DTF2THF_27460.p',conj_0)).
% 1.50/1.30 thf(f45,plain,(
% 1.50/1.30 spl8_1),
% 1.50/1.30 inference(avatar_contradiction_clause,[status(thm)],[f44])).
% 1.50/1.30 thf(f44,plain,(
% 1.50/1.30 $false | spl8_1),
% 1.50/1.30 inference(subsumption_resolution,[status(thm)],[f43,f26])).
% 1.50/1.30 thf(f26,plain,(
% 1.50/1.30 ( ! [X0 : lst] : (((ap @ nl @ X0) = X0)) )),
% 1.50/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.50/1.30 thf(f10,plain,(
% 1.50/1.30 ! [X0 : lst] : ((ap @ nl @ X0) = X0)),
% 1.50/1.30 inference(rectify,[status(thm)],[f3])).
% 1.50/1.30 thf(f3,axiom,(
% 1.50/1.30 ! [X7 : lst] : ((ap @ nl @ X7) = X7)),
% 1.50/1.30 file('/export/starexec/sandbox2/tmp/tmp.ueLwQxY4i2/DTF2THF_27460.p',fact_2p_Osimps_I1_J)).
% 1.50/1.30 thf(f43,plain,(
% 1.50/1.30 ((ap @ sK2 @ sK3) != (ap @ nl @ (ap @ sK2 @ sK3))) | spl8_1),
% 1.50/1.30 inference(superposition,[status(thm)],[f30,f26])).
% 1.50/1.30 thf(f30,plain,(
% 1.50/1.30 ((ap @ (ap @ nl @ sK2) @ sK3) != (ap @ nl @ (ap @ sK2 @ sK3))) | spl8_1),
% 1.50/1.30 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.50/1.30 thf(f28,definition,(
% 1.50/1.30 spl8_1 <=> ((ap @ (ap @ nl @ sK2) @ sK3) = (ap @ nl @ (ap @ sK2 @ sK3)))),
% 1.50/1.30 introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 1.50/1.30 thf(f42,plain,(
% 1.50/1.30 ~spl8_1 | spl8_3 | spl8_4),
% 1.50/1.30 inference(avatar_split_clause,[status(thm)],[f24,f40,f36,f28])).
% 1.50/1.30 thf(f24,plain,(
% 1.50/1.30 ( ! [X10 : lst,X0 : lst,X8 : lst,X9 : lst,X7 : lst] : (((ap @ (ap @ nl @ sK2) @ sK3) != (ap @ nl @ (ap @ sK2 @ sK3))) | ((ap @ X0 @ (ap @ X9 @ X10)) = (ap @ (ap @ X0 @ X9) @ X10)) | ((ap @ (ap @ sK5 @ X8) @ X7) = (ap @ sK5 @ (ap @ X8 @ X7)))) )),
% 1.50/1.30 inference(cnf_transformation,[status(thm)],[f21])).
% 1.50/1.30 thf(f21,plain,(
% 1.50/1.30 ! [X0 : lst] : (((ap @ (ap @ nl @ sK2) @ sK3) != (ap @ nl @ (ap @ sK2 @ sK3))) | (((ap @ (ap @ (cns @ sK4 @ sK5) @ sK7) @ sK6) != (ap @ (cns @ sK4 @ sK5) @ (ap @ sK7 @ sK6))) & ! [X7 : lst,X8 : lst] : ((ap @ (ap @ sK5 @ X8) @ X7) = (ap @ sK5 @ (ap @ X8 @ X7)))) | ! [X9 : lst,X10 : lst] : ((ap @ X0 @ (ap @ X9 @ X10)) = (ap @ (ap @ X0 @ X9) @ X10)))),
% 1.50/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7])],[f17,f20,f19,f18])).
% 1.50/1.30 thf(f18,plain,(
% 1.50/1.30 ? [X1 : lst,X2 : lst] : ((ap @ nl @ (ap @ X1 @ X2)) != (ap @ (ap @ nl @ X1) @ X2)) => ((ap @ (ap @ nl @ sK2) @ sK3) != (ap @ nl @ (ap @ sK2 @ sK3)))),
% 1.50/1.30 introduced(definition,[],[choice_axiom])).
% 1.50/1.30 thf(f19,plain,(
% 1.50/1.30 ? [X3 : a,X4 : lst] : (? [X5 : lst,X6 : lst] : ((ap @ (ap @ (cns @ X3 @ X4) @ X6) @ X5) != (ap @ (cns @ X3 @ X4) @ (ap @ X6 @ X5))) & ! [X7 : lst,X8 : lst] : ((ap @ (ap @ X4 @ X8) @ X7) = (ap @ X4 @ (ap @ X8 @ X7)))) => (? [X6 : lst,X5 : lst] : ((ap @ (ap @ (cns @ sK4 @ sK5) @ X6) @ X5) != (ap @ (cns @ sK4 @ sK5) @ (ap @ X6 @ X5))) & ! [X8 : lst,X7 : lst] : ((ap @ (ap @ sK5 @ X8) @ X7) = (ap @ sK5 @ (ap @ X8 @ X7))))),
% 1.50/1.30 introduced(definition,[],[choice_axiom])).
% 1.50/1.30 thf(f20,plain,(
% 1.50/1.30 ? [X6 : lst,X5 : lst] : ((ap @ (ap @ (cns @ sK4 @ sK5) @ X6) @ X5) != (ap @ (cns @ sK4 @ sK5) @ (ap @ X6 @ X5))) => ((ap @ (ap @ (cns @ sK4 @ sK5) @ sK7) @ sK6) != (ap @ (cns @ sK4 @ sK5) @ (ap @ sK7 @ sK6)))),
% 1.50/1.30 introduced(definition,[],[choice_axiom])).
% 1.50/1.30 thf(f17,plain,(
% 1.50/1.30 ! [X0 : lst] : (? [X1 : lst,X2 : lst] : ((ap @ nl @ (ap @ X1 @ X2)) != (ap @ (ap @ nl @ X1) @ X2)) | ? [X3 : a,X4 : lst] : (? [X5 : lst,X6 : lst] : ((ap @ (ap @ (cns @ X3 @ X4) @ X6) @ X5) != (ap @ (cns @ X3 @ X4) @ (ap @ X6 @ X5))) & ! [X7 : lst,X8 : lst] : ((ap @ (ap @ X4 @ X8) @ X7) = (ap @ X4 @ (ap @ X8 @ X7)))) | ! [X9 : lst,X10 : lst] : ((ap @ X0 @ (ap @ X9 @ X10)) = (ap @ (ap @ X0 @ X9) @ X10)))),
% 1.50/1.30 inference(rectify,[status(thm)],[f12])).
% 1.50/1.30 thf(f12,plain,(
% 1.50/1.30 ! [X0 : lst] : (? [X2 : lst,X1 : lst] : ((ap @ (ap @ nl @ X2) @ X1) != (ap @ nl @ (ap @ X2 @ X1))) | ? [X3 : a,X4 : lst] : (? [X7 : lst,X8 : lst] : ((ap @ (cns @ X3 @ X4) @ (ap @ X8 @ X7)) != (ap @ (ap @ (cns @ X3 @ X4) @ X8) @ X7)) & ! [X5 : lst,X6 : lst] : ((ap @ (ap @ X4 @ X6) @ X5) = (ap @ X4 @ (ap @ X6 @ X5)))) | ! [X10 : lst,X9 : lst] : ((ap @ X0 @ (ap @ X10 @ X9)) = (ap @ (ap @ X0 @ X10) @ X9)))),
% 1.50/1.30 inference(flattening,[status(thm)],[f11])).
% 1.50/1.30 thf(f11,plain,(
% 1.50/1.30 ! [X0 : lst] : ((! [X10 : lst,X9 : lst] : ((ap @ X0 @ (ap @ X10 @ X9)) = (ap @ (ap @ X0 @ X10) @ X9)) | ? [X3 : a,X4 : lst] : (? [X7 : lst,X8 : lst] : ((ap @ (cns @ X3 @ X4) @ (ap @ X8 @ X7)) != (ap @ (ap @ (cns @ X3 @ X4) @ X8) @ X7)) & ! [X5 : lst,X6 : lst] : ((ap @ (ap @ X4 @ X6) @ X5) = (ap @ X4 @ (ap @ X6 @ X5))))) | ? [X2 : lst,X1 : lst] : ((ap @ (ap @ nl @ X2) @ X1) != (ap @ nl @ (ap @ X2 @ X1))))),
% 1.50/1.30 inference(ennf_transformation,[status(thm)],[f8])).
% 1.50/1.30 thf(f8,plain,(
% 1.50/1.30 ! [X0 : lst] : (! [X1 : lst,X2 : lst] : ((ap @ (ap @ nl @ X2) @ X1) = (ap @ nl @ (ap @ X2 @ X1))) => (! [X3 : a,X4 : lst] : (! [X5 : lst,X6 : lst] : ((ap @ (ap @ X4 @ X6) @ X5) = (ap @ X4 @ (ap @ X6 @ X5))) => ! [X8 : lst,X7 : lst] : ((ap @ (cns @ X3 @ X4) @ (ap @ X8 @ X7)) = (ap @ (ap @ (cns @ X3 @ X4) @ X8) @ X7))) => ! [X10 : lst,X9 : lst] : ((ap @ X0 @ (ap @ X10 @ X9)) = (ap @ (ap @ X0 @ X10) @ X9))))),
% 1.50/1.30 inference(rectify,[status(thm)],[f1])).
% 1.50/1.30 thf(f1,axiom,(
% 1.50/1.30 ! [X0 : lst] : (! [X2 : lst,X1 : lst] : ((ap @ nl @ (ap @ X1 @ X2)) = (ap @ (ap @ nl @ X1) @ X2)) => (! [X3 : a,X4 : lst] : (! [X6 : lst,X5 : lst] : ((ap @ X4 @ (ap @ X5 @ X6)) = (ap @ (ap @ X4 @ X5) @ X6)) => ! [X2 : lst,X1 : lst] : ((ap @ (cns @ X3 @ X4) @ (ap @ X1 @ X2)) = (ap @ (ap @ (cns @ X3 @ X4) @ X1) @ X2))) => ! [X6 : lst,X5 : lst] : ((ap @ X0 @ (ap @ X5 @ X6)) = (ap @ (ap @ X0 @ X5) @ X6))))),
% 1.50/1.30 file('/export/starexec/sandbox2/tmp/tmp.ueLwQxY4i2/DTF2THF_27460.p',fact_0_lst_Oinduct_091where_AP_A_061_A_C_Fxs_O_AALL_Ays_Azs_O_Aap_Axs_A_Iap_Ays_Azs_J_A_061_Aap_A_Iap_Axs_Ays_J_Azs_C_093)).
% 1.50/1.30 thf(f38,plain,(
% 1.50/1.30 ~spl8_1 | ~spl8_2 | spl8_3),
% 1.50/1.30 inference(avatar_split_clause,[status(thm)],[f25,f36,f32,f28])).
% 1.50/1.30 thf(f25,plain,(
% 1.50/1.30 ( ! [X10 : lst,X0 : lst,X9 : lst] : (((ap @ X0 @ (ap @ X9 @ X10)) = (ap @ (ap @ X0 @ X9) @ X10)) | ((ap @ (ap @ (cns @ sK4 @ sK5) @ sK7) @ sK6) != (ap @ (cns @ sK4 @ sK5) @ (ap @ sK7 @ sK6))) | ((ap @ (ap @ nl @ sK2) @ sK3) != (ap @ nl @ (ap @ sK2 @ sK3)))) )),
% 1.50/1.30 inference(cnf_transformation,[status(thm)],[f21])).
% 1.50/1.30 % SZS output end Proof for DTF2THF_27460
% 1.50/1.30 % (27729)------------------------------
% 1.50/1.30 % (27729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.30 % (27729)Termination reason: Refutation
% 1.50/1.30
% 1.50/1.30 % (27729)Memory used [KB]: 5628
% 1.50/1.30 % (27729)Time elapsed: 0.009 s
% 1.50/1.30 % (27729)Instructions burned: 7 (million)
% 1.50/1.30 % (27729)------------------------------
% 1.50/1.30 % (27729)------------------------------
% 1.50/1.30 % (27728)Success in time 0.023 s
%------------------------------------------------------------------------------