%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : DAT056^1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 : Wed Oct 7 10:16:32 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 251 ( 176 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1076 ( 23 ~; 52 |; 0 &; 992 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 206 ( 0 ^; 206 !; 0 ?; 206 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_lst,type,
lst: $tType ).
thf(tp_ap,type,
ap: lst > lst > lst ).
thf(tp_cns,type,
cns: a > lst > lst ).
thf(tp_nl,type,
nl: lst ).
thf(tp_sK1_Ys,type,
sK1_Ys: lst ).
thf(tp_sK2_SY17,type,
sK2_SY17: lst ).
thf(tp_sK3_SX1,type,
sK3_SX1: lst > lst ).
thf(tp_sK4_SY31,type,
sK4_SY31: lst > lst ).
thf(tp_sK5_SX1,type,
sK5_SX1: lst > a ).
thf(tp_sK6_SY32,type,
sK6_SY32: lst > lst ).
thf(tp_sK7_SY39,type,
sK7_SY39: lst > lst ).
thf(tp_sK8_SY41,type,
sK8_SY41: lst > lst ).
thf(tp_xs,type,
xs: lst ).
thf(1,axiom,
! [Ys2: lst] :
( ( ap @ nl @ Ys2 )
= Ys2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2p_Osimps_I1_J) ).
thf(2,axiom,
! [Ys2: lst,Xs: lst,X: a] :
( ( ap @ ( cns @ X @ Xs ) @ Ys2 )
= ( cns @ X @ ( ap @ Xs @ Ys2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1p_Osimps_I2_J) ).
thf(3,axiom,
! [Lst: lst] :
( ! [Ys: lst,Zs: lst] :
( ( ap @ nl @ ( ap @ Ys @ Zs ) )
= ( ap @ ( ap @ nl @ Ys ) @ Zs ) )
=> ( ! [A: a,Lst2: lst] :
( ! [Ys3: lst,Zs2: lst] :
( ( ap @ Lst2 @ ( ap @ Ys3 @ Zs2 ) )
= ( ap @ ( ap @ Lst2 @ Ys3 ) @ Zs2 ) )
=> ! [Ys: lst,Zs: lst] :
( ( ap @ ( cns @ A @ Lst2 ) @ ( ap @ Ys @ Zs ) )
= ( ap @ ( ap @ ( cns @ A @ Lst2 ) @ Ys ) @ Zs ) ) )
=> ! [Ys3: lst,Zs2: lst] :
( ( ap @ Lst @ ( ap @ Ys3 @ Zs2 ) )
= ( ap @ ( ap @ Lst @ Ys3 ) @ Zs2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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(4,conjecture,
! [Ys: lst,Zs: lst] :
( ( ap @ xs @ ( ap @ Ys @ Zs ) )
= ( ap @ ( ap @ xs @ Ys ) @ Zs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(5,negated_conjecture,
( ( ! [Ys: lst,Zs: lst] :
( ( ap @ xs @ ( ap @ Ys @ Zs ) )
= ( ap @ ( ap @ xs @ Ys ) @ Zs ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ! [Ys: lst,Zs: lst] :
( ( ap @ xs @ ( ap @ Ys @ Zs ) )
= ( ap @ ( ap @ xs @ Ys ) @ Zs ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [Ys2: lst] :
( ( ap @ nl @ Ys2 )
= Ys2 ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [Ys2: lst,Xs: lst,X: a] :
( ( ap @ ( cns @ X @ Xs ) @ Ys2 )
= ( cns @ X @ ( ap @ Xs @ Ys2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ! [Lst: lst] :
( ! [Ys: lst,Zs: lst] :
( ( ap @ nl @ ( ap @ Ys @ Zs ) )
= ( ap @ ( ap @ nl @ Ys ) @ Zs ) )
=> ( ! [A: a,Lst2: lst] :
( ! [Ys3: lst,Zs2: lst] :
( ( ap @ Lst2 @ ( ap @ Ys3 @ Zs2 ) )
= ( ap @ ( ap @ Lst2 @ Ys3 ) @ Zs2 ) )
=> ! [Ys: lst,Zs: lst] :
( ( ap @ ( cns @ A @ Lst2 ) @ ( ap @ Ys @ Zs ) )
= ( ap @ ( ap @ ( cns @ A @ Lst2 ) @ Ys ) @ Zs ) ) )
=> ! [Ys3: lst,Zs2: lst] :
( ( ap @ Lst @ ( ap @ Ys3 @ Zs2 ) )
= ( ap @ ( ap @ Lst @ Ys3 ) @ Zs2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [SY17: lst] :
( ( ap @ xs @ ( ap @ sK1_Ys @ SY17 ) )
= ( ap @ ( ap @ xs @ sK1_Ys ) @ SY17 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(11,plain,
( ( ( ap @ xs @ ( ap @ sK1_Ys @ sK2_SY17 ) )
= ( ap @ ( ap @ xs @ sK1_Ys ) @ sK2_SY17 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(12,plain,
( ( ( ap @ xs @ ( ap @ sK1_Ys @ sK2_SY17 ) )
!= ( ap @ ( ap @ xs @ sK1_Ys ) @ sK2_SY17 ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [Lst: lst] :
( ! [Ys: lst,Zs: lst] :
( ( ap @ nl @ ( ap @ Ys @ Zs ) )
= ( ap @ ( ap @ nl @ Ys ) @ Zs ) )
=> ( ! [A: a,Lst2: lst] :
( ! [Ys3: lst,Zs2: lst] :
( ( ap @ Lst2 @ ( ap @ Ys3 @ Zs2 ) )
= ( ap @ ( ap @ Lst2 @ Ys3 ) @ Zs2 ) )
=> ! [Ys: lst,Zs: lst] :
( ( ap @ ( cns @ A @ Lst2 ) @ ( ap @ Ys @ Zs ) )
= ( ap @ ( ap @ ( cns @ A @ Lst2 ) @ Ys ) @ Zs ) ) )
=> ! [Ys3: lst,Zs2: lst] :
( ( ap @ Lst @ ( ap @ Ys3 @ Zs2 ) )
= ( ap @ ( ap @ Lst @ Ys3 ) @ Zs2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(14,plain,
( ( ! [Ys2: lst,Xs: lst,X: a] :
( ( ap @ ( cns @ X @ Xs ) @ Ys2 )
= ( cns @ X @ ( ap @ Xs @ Ys2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(15,plain,
( ( ! [Ys2: lst] :
( ( ap @ nl @ Ys2 )
= Ys2 ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(16,plain,
( ( ( ap @ xs @ ( ap @ sK1_Ys @ sK2_SY17 ) )
!= ( ap @ ( ap @ xs @ sK1_Ys ) @ sK2_SY17 ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [SX0: lst] :
( ~ ! [SX1: lst,SX2: lst] :
( ( ap @ nl @ ( ap @ SX1 @ SX2 ) )
= ( ap @ ( ap @ nl @ SX1 ) @ SX2 ) )
| ~ ! [SX1: a,SX2: lst] :
( ~ ! [SX3: lst,SX4: lst] :
( ( ap @ SX2 @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ SX2 @ SX3 ) @ SX4 ) )
| ! [SX3: lst,SX4: lst] :
( ( ap @ ( cns @ SX1 @ SX2 ) @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ ( cns @ SX1 @ SX2 ) @ SX3 ) @ SX4 ) ) )
| ! [SX1: lst,SX2: lst] :
( ( ap @ SX0 @ ( ap @ SX1 @ SX2 ) )
= ( ap @ ( ap @ SX0 @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(18,plain,
! [SV1: lst] :
( ( ! [SY18: lst,SY19: a] :
( ( ap @ ( cns @ SY19 @ SY18 ) @ SV1 )
= ( cns @ SY19 @ ( ap @ SY18 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV2: lst] :
( ( ( ap @ nl @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
( ( ( ap @ xs @ ( ap @ sK1_Ys @ sK2_SY17 ) )
= ( ap @ ( ap @ xs @ sK1_Ys ) @ sK2_SY17 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV3: lst] :
( ( ~ ! [SX1: lst,SX2: lst] :
( ( ap @ nl @ ( ap @ SX1 @ SX2 ) )
= ( ap @ ( ap @ nl @ SX1 ) @ SX2 ) )
| ~ ! [SX1: a,SX2: lst] :
( ~ ! [SX3: lst,SX4: lst] :
( ( ap @ SX2 @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ SX2 @ SX3 ) @ SX4 ) )
| ! [SX3: lst,SX4: lst] :
( ( ap @ ( cns @ SX1 @ SX2 ) @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ ( cns @ SX1 @ SX2 ) @ SX3 ) @ SX4 ) ) )
| ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV1: lst,SV4: lst] :
( ( ! [SY30: a] :
( ( ap @ ( cns @ SY30 @ SV4 ) @ SV1 )
= ( cns @ SY30 @ ( ap @ SV4 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV3: lst] :
( ( ( ~ ! [SX1: lst,SX2: lst] :
( ( ap @ nl @ ( ap @ SX1 @ SX2 ) )
= ( ap @ ( ap @ nl @ SX1 ) @ SX2 ) ) )
= $true )
| ( ( ~ ! [SX1: a,SX2: lst] :
( ~ ! [SX3: lst,SX4: lst] :
( ( ap @ SX2 @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ SX2 @ SX3 ) @ SX4 ) )
| ! [SX3: lst,SX4: lst] :
( ( ap @ ( cns @ SX1 @ SX2 ) @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ ( cns @ SX1 @ SX2 ) @ SX3 ) @ SX4 ) ) )
| ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV1: lst,SV4: lst,SV5: a] :
( ( ( ap @ ( cns @ SV5 @ SV4 ) @ SV1 )
= ( cns @ SV5 @ ( ap @ SV4 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV3: lst] :
( ( ( ! [SX1: lst,SX2: lst] :
( ( ap @ nl @ ( ap @ SX1 @ SX2 ) )
= ( ap @ ( ap @ nl @ SX1 ) @ SX2 ) ) )
= $false )
| ( ( ~ ! [SX1: a,SX2: lst] :
( ~ ! [SX3: lst,SX4: lst] :
( ( ap @ SX2 @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ SX2 @ SX3 ) @ SX4 ) )
| ! [SX3: lst,SX4: lst] :
( ( ap @ ( cns @ SX1 @ SX2 ) @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ ( cns @ SX1 @ SX2 ) @ SX3 ) @ SX4 ) ) )
| ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV3: lst] :
( ( ( ! [SY31: lst] :
( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ SY31 ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ SY31 ) ) )
= $false )
| ( ( ~ ! [SX1: a,SX2: lst] :
( ~ ! [SX3: lst,SX4: lst] :
( ( ap @ SX2 @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ SX2 @ SX3 ) @ SX4 ) )
| ! [SX3: lst,SX4: lst] :
( ( ap @ ( cns @ SX1 @ SX2 ) @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ ( cns @ SX1 @ SX2 ) @ SX3 ) @ SX4 ) ) )
| ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(27,plain,
! [SV3: lst] :
( ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false )
| ( ( ~ ! [SX1: a,SX2: lst] :
( ~ ! [SX3: lst,SX4: lst] :
( ( ap @ SX2 @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ SX2 @ SX3 ) @ SX4 ) )
| ! [SX3: lst,SX4: lst] :
( ( ap @ ( cns @ SX1 @ SX2 ) @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ ( cns @ SX1 @ SX2 ) @ SX3 ) @ SX4 ) ) )
| ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(28,plain,
! [SV3: lst] :
( ( ( ~ ! [SX1: a,SX2: lst] :
( ~ ! [SX3: lst,SX4: lst] :
( ( ap @ SX2 @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ SX2 @ SX3 ) @ SX4 ) )
| ! [SX3: lst,SX4: lst] :
( ( ap @ ( cns @ SX1 @ SX2 ) @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ ( cns @ SX1 @ SX2 ) @ SX3 ) @ SX4 ) ) ) )
= $true )
| ( ( ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true )
| ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(29,plain,
! [SV3: lst] :
( ( ( ! [SX1: a,SX2: lst] :
( ~ ! [SX3: lst,SX4: lst] :
( ( ap @ SX2 @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ SX2 @ SX3 ) @ SX4 ) )
| ! [SX3: lst,SX4: lst] :
( ( ap @ ( cns @ SX1 @ SX2 ) @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ ( cns @ SX1 @ SX2 ) @ SX3 ) @ SX4 ) ) ) )
= $false )
| ( ( ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true )
| ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(30,plain,
! [SV3: lst] :
( ( ( ! [SY32: lst] :
( ~ ! [SX3: lst,SX4: lst] :
( ( ap @ SY32 @ ( ap @ SX3 @ SX4 ) )
= ( ap @ ( ap @ SY32 @ SX3 ) @ SX4 ) )
| ! [SY35: lst,SY36: lst] :
( ( ap @ ( cns @ ( sK5_SX1 @ SV3 ) @ SY32 ) @ ( ap @ SY35 @ SY36 ) )
= ( ap @ ( ap @ ( cns @ ( sK5_SX1 @ SV3 ) @ SY32 ) @ SY35 ) @ SY36 ) ) ) )
= $false )
| ( ( ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true )
| ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(31,plain,
! [SV3: lst] :
( ( ( ~ ! [SY37: lst,SY38: lst] :
( ( ap @ ( sK6_SY32 @ SV3 ) @ ( ap @ SY37 @ SY38 ) )
= ( ap @ ( ap @ ( sK6_SY32 @ SV3 ) @ SY37 ) @ SY38 ) )
| ! [SY39: lst,SY40: lst] :
( ( ap @ ( cns @ ( sK5_SX1 @ SV3 ) @ ( sK6_SY32 @ SV3 ) ) @ ( ap @ SY39 @ SY40 ) )
= ( ap @ ( ap @ ( cns @ ( sK5_SX1 @ SV3 ) @ ( sK6_SY32 @ SV3 ) ) @ SY39 ) @ SY40 ) ) )
= $false )
| ( ( ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true )
| ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(32,plain,
! [SV3: lst] :
( ( ( ~ ! [SY37: lst,SY38: lst] :
( ( ap @ ( sK6_SY32 @ SV3 ) @ ( ap @ SY37 @ SY38 ) )
= ( ap @ ( ap @ ( sK6_SY32 @ SV3 ) @ SY37 ) @ SY38 ) ) )
= $false )
| ( ( ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true )
| ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(33,plain,
! [SV3: lst] :
( ( ( ! [SY39: lst,SY40: lst] :
( ( ap @ ( cns @ ( sK5_SX1 @ SV3 ) @ ( sK6_SY32 @ SV3 ) ) @ ( ap @ SY39 @ SY40 ) )
= ( ap @ ( ap @ ( cns @ ( sK5_SX1 @ SV3 ) @ ( sK6_SY32 @ SV3 ) ) @ SY39 ) @ SY40 ) ) )
= $false )
| ( ( ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true )
| ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(34,plain,
! [SV3: lst] :
( ( ( ! [SY37: lst,SY38: lst] :
( ( ap @ ( sK6_SY32 @ SV3 ) @ ( ap @ SY37 @ SY38 ) )
= ( ap @ ( ap @ ( sK6_SY32 @ SV3 ) @ SY37 ) @ SY38 ) ) )
= $true )
| ( ( ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true )
| ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(35,plain,
! [SV3: lst] :
( ( ( ! [SY41: lst] :
( ( ap @ ( cns @ ( sK5_SX1 @ SV3 ) @ ( sK6_SY32 @ SV3 ) ) @ ( ap @ ( sK7_SY39 @ SV3 ) @ SY41 ) )
= ( ap @ ( ap @ ( cns @ ( sK5_SX1 @ SV3 ) @ ( sK6_SY32 @ SV3 ) ) @ ( sK7_SY39 @ SV3 ) ) @ SY41 ) ) )
= $false )
| ( ( ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true )
| ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[33]) ).
thf(36,plain,
! [SV6: lst,SV3: lst] :
( ( ( ! [SY42: lst] :
( ( ap @ ( sK6_SY32 @ SV3 ) @ ( ap @ SV6 @ SY42 ) )
= ( ap @ ( ap @ ( sK6_SY32 @ SV3 ) @ SV6 ) @ SY42 ) ) )
= $true )
| ( ( ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true )
| ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV3: lst] :
( ( ( ( ap @ ( cns @ ( sK5_SX1 @ SV3 ) @ ( sK6_SY32 @ SV3 ) ) @ ( ap @ ( sK7_SY39 @ SV3 ) @ ( sK8_SY41 @ SV3 ) ) )
= ( ap @ ( ap @ ( cns @ ( sK5_SX1 @ SV3 ) @ ( sK6_SY32 @ SV3 ) ) @ ( sK7_SY39 @ SV3 ) ) @ ( sK8_SY41 @ SV3 ) ) )
= $false )
| ( ( ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true )
| ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(38,plain,
! [SV7: lst,SV6: lst,SV3: lst] :
( ( ( ( ap @ ( sK6_SY32 @ SV3 ) @ ( ap @ SV6 @ SV7 ) )
= ( ap @ ( ap @ ( sK6_SY32 @ SV3 ) @ SV6 ) @ SV7 ) )
= $true )
| ( ( ! [SY28: lst,SY29: lst] :
( ( ap @ SV3 @ ( ap @ SY28 @ SY29 ) )
= ( ap @ ( ap @ SV3 @ SY28 ) @ SY29 ) ) )
= $true )
| ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV8: lst,SV3: lst] :
( ( ( ! [SY43: lst] :
( ( ap @ SV3 @ ( ap @ SV8 @ SY43 ) )
= ( ap @ ( ap @ SV3 @ SV8 ) @ SY43 ) ) )
= $true )
| ( ( ( ap @ ( cns @ ( sK5_SX1 @ SV3 ) @ ( sK6_SY32 @ SV3 ) ) @ ( ap @ ( sK7_SY39 @ SV3 ) @ ( sK8_SY41 @ SV3 ) ) )
= ( ap @ ( ap @ ( cns @ ( sK5_SX1 @ SV3 ) @ ( sK6_SY32 @ SV3 ) ) @ ( sK7_SY39 @ SV3 ) ) @ ( sK8_SY41 @ SV3 ) ) )
= $false )
| ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV7: lst,SV6: lst,SV9: lst,SV3: lst] :
( ( ( ! [SY44: lst] :
( ( ap @ SV3 @ ( ap @ SV9 @ SY44 ) )
= ( ap @ ( ap @ SV3 @ SV9 ) @ SY44 ) ) )
= $true )
| ( ( ( ap @ ( sK6_SY32 @ SV3 ) @ ( ap @ SV6 @ SV7 ) )
= ( ap @ ( ap @ ( sK6_SY32 @ SV3 ) @ SV6 ) @ SV7 ) )
= $true )
| ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV10: lst,SV8: lst,SV3: lst] :
( ( ( ( ap @ SV3 @ ( ap @ SV8 @ SV10 ) )
= ( ap @ ( ap @ SV3 @ SV8 ) @ SV10 ) )
= $true )
| ( ( ( ap @ ( cns @ ( sK5_SX1 @ SV3 ) @ ( sK6_SY32 @ SV3 ) ) @ ( ap @ ( sK7_SY39 @ SV3 ) @ ( sK8_SY41 @ SV3 ) ) )
= ( ap @ ( ap @ ( cns @ ( sK5_SX1 @ SV3 ) @ ( sK6_SY32 @ SV3 ) ) @ ( sK7_SY39 @ SV3 ) ) @ ( sK8_SY41 @ SV3 ) ) )
= $false )
| ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV7: lst,SV6: lst,SV11: lst,SV9: lst,SV3: lst] :
( ( ( ( ap @ SV3 @ ( ap @ SV9 @ SV11 ) )
= ( ap @ ( ap @ SV3 @ SV9 ) @ SV11 ) )
= $true )
| ( ( ( ap @ ( sK6_SY32 @ SV3 ) @ ( ap @ SV6 @ SV7 ) )
= ( ap @ ( ap @ ( sK6_SY32 @ SV3 ) @ SV6 ) @ SV7 ) )
= $true )
| ( ( ( ap @ nl @ ( ap @ ( sK3_SX1 @ SV3 ) @ ( sK4_SY31 @ SV3 ) ) )
= ( ap @ ( ap @ nl @ ( sK3_SX1 @ SV3 ) ) @ ( sK4_SY31 @ SV3 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(43,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,42,41,24,20]) ).
thf(44,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT056^1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 19:01:54 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 3
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 0
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23 ..
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:43,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23
% 0.08/0.23 %**** End of derivation protocol ****
% 0.08/0.23 %**** no. of clauses in derivation: 44 ****
% 0.08/0.23 %**** clause counter: 43 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:43,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------