%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL739^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 10:30:07 AM UTC 2026
% Result : Theorem 0.08s 0.13s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 54 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 219 ( 80 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 809 ( 93 ~; 81 |; 0 &; 621 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 370 ( 370 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 2 con; 0-4 aty)
% Number of variables : 246 ( 0 ^; 224 !; 22 ?; 246 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_b,type,
b: $tType ).
thf(tp_sK1_SY24,type,
sK1_SY24: ( ( b > $o ) > b ) > b > $o ).
thf(tp_sK2_SY18,type,
sK2_SY18: ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > b > $o ).
thf(tp_sK3_SY26,type,
sK3_SY26: ( ( b > $o ) > b ) > b ).
thf(tp_sK4_SY29,type,
sK4_SY29: b > ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > b ).
thf(tp_sK5_SY21,type,
sK5_SY21: b > ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > ( b > $o ) > b ).
thf(tp_sK6_SY21,type,
sK6_SY21: b > ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > ( b > $o ) > b ).
thf(tp_sK7_Eigen,type,
sK7_Eigen: ( b > $o ) > b ).
thf(1,conjecture,
( ! [Xr_24: ( b > $o ) > b > b > $o,Xr_23: ( b > $o ) > b > b > $o] :
( ! [Xx: b > $o] :
? [Xy: b] :
! [Xw_6: b] :
( ( Xr_23 @ Xx @ Xy @ Xw_6 )
| ( Xr_24 @ Xx @ Xy @ Xw_6 ) )
=> ? [Xf: ( b > $o ) > b] :
! [Xx: b > $o,Xw_6: b] :
( ( Xr_23 @ Xx @ ( Xf @ Xx ) @ Xw_6 )
| ( Xr_24 @ Xx @ ( Xf @ Xx ) @ Xw_6 ) ) )
=> ? [Xj: ( b > $o ) > b] :
! [Xp: b > $o] :
( ? [Xz: b] : ( Xp @ Xz )
=> ( Xp @ ( Xj @ Xp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5310_SUB2) ).
thf(2,negated_conjecture,
( ( ! [Xr_24: ( b > $o ) > b > b > $o,Xr_23: ( b > $o ) > b > b > $o] :
( ! [Xx: b > $o] :
? [Xy: b] :
! [Xw_6: b] :
( ( Xr_23 @ Xx @ Xy @ Xw_6 )
| ( Xr_24 @ Xx @ Xy @ Xw_6 ) )
=> ? [Xf: ( b > $o ) > b] :
! [Xx: b > $o,Xw_6: b] :
( ( Xr_23 @ Xx @ ( Xf @ Xx ) @ Xw_6 )
| ( Xr_24 @ Xx @ ( Xf @ Xx ) @ Xw_6 ) ) )
=> ? [Xj: ( b > $o ) > b] :
! [Xp: b > $o] :
( ? [Xz: b] : ( Xp @ Xz )
=> ( Xp @ ( Xj @ Xp ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xr_24: ( b > $o ) > b > b > $o,Xr_23: ( b > $o ) > b > b > $o] :
( ! [Xx: b > $o] :
? [Xy: b] :
! [Xw_6: b] :
( ( Xr_23 @ Xx @ Xy @ Xw_6 )
| ( Xr_24 @ Xx @ Xy @ Xw_6 ) )
=> ? [Xf: ( b > $o ) > b] :
! [Xx: b > $o,Xw_6: b] :
( ( Xr_23 @ Xx @ ( Xf @ Xx ) @ Xw_6 )
| ( Xr_24 @ Xx @ ( Xf @ Xx ) @ Xw_6 ) ) )
=> ? [Xj: ( b > $o ) > b] :
! [Xp: b > $o] :
( ? [Xz: b] : ( Xp @ Xz )
=> ( Xp @ ( Xj @ Xp ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xr_24: ( b > $o ) > b > b > $o,Xr_23: ( b > $o ) > b > b > $o] :
( ! [Xx: b > $o] :
? [Xy: b] :
! [Xw_6: b] :
( ( Xr_23 @ Xx @ Xy @ Xw_6 )
| ( Xr_24 @ Xx @ Xy @ Xw_6 ) )
=> ? [Xf: ( b > $o ) > b] :
! [Xx: b > $o,Xw_6: b] :
( ( Xr_23 @ Xx @ ( Xf @ Xx ) @ Xw_6 )
| ( Xr_24 @ Xx @ ( Xf @ Xx ) @ Xw_6 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ? [Xj: ( b > $o ) > b] :
! [Xp: b > $o] :
( ? [Xz: b] : ( Xp @ Xz )
=> ( Xp @ ( Xj @ Xp ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ? [Xj: ( b > $o ) > b] :
! [Xp: b > $o] :
( ? [Xz: b] : ( Xp @ Xz )
=> ( Xp @ ( Xj @ Xp ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [Xr_24: ( b > $o ) > b > b > $o,Xr_23: ( b > $o ) > b > b > $o] :
( ! [Xx: b > $o] :
? [Xy: b] :
! [Xw_6: b] :
( ( Xr_23 @ Xx @ Xy @ Xw_6 )
| ( Xr_24 @ Xx @ Xy @ Xw_6 ) )
=> ? [Xf: ( b > $o ) > b] :
! [Xx: b > $o,Xw_6: b] :
( ( Xr_23 @ Xx @ ( Xf @ Xx ) @ Xw_6 )
| ( Xr_24 @ Xx @ ( Xf @ Xx ) @ Xw_6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ? [Xj: ( b > $o ) > b] :
! [Xp: b > $o] :
( ? [Xz: b] : ( Xp @ Xz )
=> ( Xp @ ( Xj @ Xp ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ~ ! [SX0: ( b > $o ) > b] :
~ ! [SX1: b > $o] :
( ~ ~ ! [SX2: b] :
~ ( SX1 @ SX2 )
| ( SX1 @ ( SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SX0: ( b > $o ) > b > b > $o,SX1: ( b > $o ) > b > b > $o] :
( ~ ! [SX2: b > $o] :
~ ! [SX3: b] :
~ ! [SX4: b] :
( ( SX1 @ SX2 @ SX3 @ SX4 )
| ( SX0 @ SX2 @ SX3 @ SX4 ) )
| ~ ! [SX2: ( b > $o ) > b] :
~ ! [SX3: b > $o,SX4: b] :
( ( SX1 @ SX3 @ ( SX2 @ SX3 ) @ SX4 )
| ( SX0 @ SX3 @ ( SX2 @ SX3 ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ! [SX0: ( b > $o ) > b] :
~ ! [SX1: b > $o] :
( ~ ~ ! [SX2: b] :
~ ( SX1 @ SX2 )
| ( SX1 @ ( SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: ( b > $o ) > b > b > $o] :
( ( ! [SY11: ( b > $o ) > b > b > $o] :
( ~ ! [SY12: b > $o] :
~ ! [SY13: b] :
~ ! [SY14: b] :
( ( SY11 @ SY12 @ SY13 @ SY14 )
| ( SV1 @ SY12 @ SY13 @ SY14 ) )
| ~ ! [SY15: ( b > $o ) > b] :
~ ! [SY16: b > $o,SY17: b] :
( ( SY11 @ SY16 @ ( SY15 @ SY16 ) @ SY17 )
| ( SV1 @ SY16 @ ( SY15 @ SY16 ) @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SX0: ( b > $o ) > b] :
~ ! [SX1: b > $o] :
( ~ ~ ! [SX2: b] :
~ ( SX1 @ SX2 )
| ( SX1 @ ( SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: ( b > $o ) > b > b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ~ ! [SY18: b > $o] :
~ ! [SY19: b] :
~ ! [SY20: b] :
( ( SV2 @ SY18 @ SY19 @ SY20 )
| ( SV1 @ SY18 @ SY19 @ SY20 ) )
| ~ ! [SY21: ( b > $o ) > b] :
~ ! [SY22: b > $o,SY23: b] :
( ( SV2 @ SY22 @ ( SY21 @ SY22 ) @ SY23 )
| ( SV1 @ SY22 @ ( SY21 @ SY22 ) @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV3: ( b > $o ) > b] :
( ( ~ ! [SY24: b > $o] :
( ~ ~ ! [SX2: b] :
~ ( SY24 @ SX2 )
| ( SY24 @ ( SV3 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: ( b > $o ) > b > b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( ~ ! [SY18: b > $o] :
~ ! [SY19: b] :
~ ! [SY20: b] :
( ( SV2 @ SY18 @ SY19 @ SY20 )
| ( SV1 @ SY18 @ SY19 @ SY20 ) ) )
= $true )
| ( ( ~ ! [SY21: ( b > $o ) > b] :
~ ! [SY22: b > $o,SY23: b] :
( ( SV2 @ SY22 @ ( SY21 @ SY22 ) @ SY23 )
| ( SV1 @ SY22 @ ( SY21 @ SY22 ) @ SY23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV3: ( b > $o ) > b] :
( ( ! [SY24: b > $o] :
( ~ ~ ! [SX2: b] :
~ ( SY24 @ SX2 )
| ( SY24 @ ( SV3 @ SY24 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: ( b > $o ) > b > b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( ! [SY18: b > $o] :
~ ! [SY19: b] :
~ ! [SY20: b] :
( ( SV2 @ SY18 @ SY19 @ SY20 )
| ( SV1 @ SY18 @ SY19 @ SY20 ) ) )
= $false )
| ( ( ~ ! [SY21: ( b > $o ) > b] :
~ ! [SY22: b > $o,SY23: b] :
( ( SV2 @ SY22 @ ( SY21 @ SY22 ) @ SY23 )
| ( SV1 @ SY22 @ ( SY21 @ SY22 ) @ SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
! [SV3: ( b > $o ) > b] :
( ( ~ ~ ! [SY26: b] :
~ ( sK1_SY24 @ SV3 @ SY26 )
| ( sK1_SY24 @ SV3 @ ( SV3 @ ( sK1_SY24 @ SV3 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(20,plain,
! [SV1: ( b > $o ) > b > b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( ~ ! [SY27: b] :
~ ! [SY28: b] :
( ( SV2 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SY27 @ SY28 )
| ( SV1 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SY27 @ SY28 ) ) )
= $false )
| ( ( ~ ! [SY21: ( b > $o ) > b] :
~ ! [SY22: b > $o,SY23: b] :
( ( SV2 @ SY22 @ ( SY21 @ SY22 ) @ SY23 )
| ( SV1 @ SY22 @ ( SY21 @ SY22 ) @ SY23 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(21,plain,
! [SV3: ( b > $o ) > b] :
( ( ~ ~ ! [SY26: b] :
~ ( sK1_SY24 @ SV3 @ SY26 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(22,plain,
! [SV3: ( b > $o ) > b] :
( ( sK1_SY24 @ SV3 @ ( SV3 @ ( sK1_SY24 @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: ( b > $o ) > b > b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( ! [SY27: b] :
~ ! [SY28: b] :
( ( SV2 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SY27 @ SY28 )
| ( SV1 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SY27 @ SY28 ) ) )
= $true )
| ( ( ~ ! [SY21: ( b > $o ) > b] :
~ ! [SY22: b > $o,SY23: b] :
( ( SV2 @ SY22 @ ( SY21 @ SY22 ) @ SY23 )
| ( SV1 @ SY22 @ ( SY21 @ SY22 ) @ SY23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV3: ( b > $o ) > b] :
( ( ~ ! [SY26: b] :
~ ( sK1_SY24 @ SV3 @ SY26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV4: b,SV1: ( b > $o ) > b > b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( ~ ! [SY29: b] :
( ( SV2 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ SY29 )
| ( SV1 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ SY29 ) ) )
= $true )
| ( ( ~ ! [SY21: ( b > $o ) > b] :
~ ! [SY22: b > $o,SY23: b] :
( ( SV2 @ SY22 @ ( SY21 @ SY22 ) @ SY23 )
| ( SV1 @ SY22 @ ( SY21 @ SY22 ) @ SY23 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV3: ( b > $o ) > b] :
( ( ! [SY26: b] :
~ ( sK1_SY24 @ SV3 @ SY26 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV4: b,SV1: ( b > $o ) > b > b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( ! [SY29: b] :
( ( SV2 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ SY29 )
| ( SV1 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ SY29 ) ) )
= $false )
| ( ( ~ ! [SY21: ( b > $o ) > b] :
~ ! [SY22: b > $o,SY23: b] :
( ( SV2 @ SY22 @ ( SY21 @ SY22 ) @ SY23 )
| ( SV1 @ SY22 @ ( SY21 @ SY22 ) @ SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV3: ( b > $o ) > b] :
( ( ~ ( sK1_SY24 @ SV3 @ ( sK3_SY26 @ SV3 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(29,plain,
! [SV4: b,SV1: ( b > $o ) > b > b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( ( SV2 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) )
| ( SV1 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) ) )
= $false )
| ( ( ~ ! [SY21: ( b > $o ) > b] :
~ ! [SY22: b > $o,SY23: b] :
( ( SV2 @ SY22 @ ( SY21 @ SY22 ) @ SY23 )
| ( SV1 @ SY22 @ ( SY21 @ SY22 ) @ SY23 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(30,plain,
! [SV3: ( b > $o ) > b] :
( ( sK1_SY24 @ SV3 @ ( sK3_SY26 @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(31,plain,
! [SV4: b,SV1: ( b > $o ) > b > b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( SV2 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) )
= $false )
| ( ( ~ ! [SY21: ( b > $o ) > b] :
~ ! [SY22: b > $o,SY23: b] :
( ( SV2 @ SY22 @ ( SY21 @ SY22 ) @ SY23 )
| ( SV1 @ SY22 @ ( SY21 @ SY22 ) @ SY23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(32,plain,
! [SV4: b,SV2: ( b > $o ) > b > b > $o,SV1: ( b > $o ) > b > b > $o] :
( ( ( SV1 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) )
= $false )
| ( ( ~ ! [SY21: ( b > $o ) > b] :
~ ! [SY22: b > $o,SY23: b] :
( ( SV2 @ SY22 @ ( SY21 @ SY22 ) @ SY23 )
| ( SV1 @ SY22 @ ( SY21 @ SY22 ) @ SY23 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV4: b,SV1: ( b > $o ) > b > b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( ! [SY21: ( b > $o ) > b] :
~ ! [SY22: b > $o,SY23: b] :
( ( SV2 @ SY22 @ ( SY21 @ SY22 ) @ SY23 )
| ( SV1 @ SY22 @ ( SY21 @ SY22 ) @ SY23 ) ) )
= $false )
| ( ( SV2 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV4: b,SV1: ( b > $o ) > b > b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( ! [SY21: ( b > $o ) > b] :
~ ! [SY22: b > $o,SY23: b] :
( ( SV2 @ SY22 @ ( SY21 @ SY22 ) @ SY23 )
| ( SV1 @ SY22 @ ( SY21 @ SY22 ) @ SY23 ) ) )
= $false )
| ( ( SV1 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV1: ( b > $o ) > b > b > $o,SV4: b,SV2: ( b > $o ) > b > b > $o] :
( ( ( ~ ! [SY30: b > $o,SY31: b] :
( ( SV2 @ SY30 @ ( sK5_SY21 @ SV4 @ SV1 @ SV2 @ SY30 ) @ SY31 )
| ( SV1 @ SY30 @ ( sK5_SY21 @ SV4 @ SV1 @ SV2 @ SY30 ) @ SY31 ) ) )
= $false )
| ( ( SV2 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[33]) ).
thf(36,plain,
! [SV1: ( b > $o ) > b > b > $o,SV4: b,SV2: ( b > $o ) > b > b > $o] :
( ( ( ~ ! [SY32: b > $o,SY33: b] :
( ( SV2 @ SY32 @ ( sK6_SY21 @ SV4 @ SV1 @ SV2 @ SY32 ) @ SY33 )
| ( SV1 @ SY32 @ ( sK6_SY21 @ SV4 @ SV1 @ SV2 @ SY32 ) @ SY33 ) ) )
= $false )
| ( ( SV1 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(37,plain,
! [SV1: ( b > $o ) > b > b > $o,SV4: b,SV2: ( b > $o ) > b > b > $o] :
( ( ( ! [SY30: b > $o,SY31: b] :
( ( SV2 @ SY30 @ ( sK5_SY21 @ SV4 @ SV1 @ SV2 @ SY30 ) @ SY31 )
| ( SV1 @ SY30 @ ( sK5_SY21 @ SV4 @ SV1 @ SV2 @ SY30 ) @ SY31 ) ) )
= $true )
| ( ( SV2 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(38,plain,
! [SV1: ( b > $o ) > b > b > $o,SV4: b,SV2: ( b > $o ) > b > b > $o] :
( ( ( ! [SY32: b > $o,SY33: b] :
( ( SV2 @ SY32 @ ( sK6_SY21 @ SV4 @ SV1 @ SV2 @ SY32 ) @ SY33 )
| ( SV1 @ SY32 @ ( sK6_SY21 @ SV4 @ SV1 @ SV2 @ SY32 ) @ SY33 ) ) )
= $true )
| ( ( SV1 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(39,plain,
! [SV1: ( b > $o ) > b > b > $o,SV4: b,SV5: b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( ! [SY34: b] :
( ( SV2 @ SV5 @ ( sK5_SY21 @ SV4 @ SV1 @ SV2 @ SV5 ) @ SY34 )
| ( SV1 @ SV5 @ ( sK5_SY21 @ SV4 @ SV1 @ SV2 @ SV5 ) @ SY34 ) ) )
= $true )
| ( ( SV2 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV1: ( b > $o ) > b > b > $o,SV4: b,SV6: b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( ! [SY35: b] :
( ( SV2 @ SV6 @ ( sK6_SY21 @ SV4 @ SV1 @ SV2 @ SV6 ) @ SY35 )
| ( SV1 @ SV6 @ ( sK6_SY21 @ SV4 @ SV1 @ SV2 @ SV6 ) @ SY35 ) ) )
= $true )
| ( ( SV1 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV7: b,SV1: ( b > $o ) > b > b > $o,SV4: b,SV5: b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( ( SV2 @ SV5 @ ( sK5_SY21 @ SV4 @ SV1 @ SV2 @ SV5 ) @ SV7 )
| ( SV1 @ SV5 @ ( sK5_SY21 @ SV4 @ SV1 @ SV2 @ SV5 ) @ SV7 ) )
= $true )
| ( ( SV2 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV8: b,SV1: ( b > $o ) > b > b > $o,SV4: b,SV6: b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( ( SV2 @ SV6 @ ( sK6_SY21 @ SV4 @ SV1 @ SV2 @ SV6 ) @ SV8 )
| ( SV1 @ SV6 @ ( sK6_SY21 @ SV4 @ SV1 @ SV2 @ SV6 ) @ SV8 ) )
= $true )
| ( ( SV1 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV7: b,SV1: ( b > $o ) > b > b > $o,SV4: b,SV5: b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( SV2 @ SV5 @ ( sK5_SY21 @ SV4 @ SV1 @ SV2 @ SV5 ) @ SV7 )
= $true )
| ( ( SV1 @ SV5 @ ( sK5_SY21 @ SV4 @ SV1 @ SV2 @ SV5 ) @ SV7 )
= $true )
| ( ( SV2 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV8: b,SV1: ( b > $o ) > b > b > $o,SV4: b,SV6: b > $o,SV2: ( b > $o ) > b > b > $o] :
( ( ( SV2 @ SV6 @ ( sK6_SY21 @ SV4 @ SV1 @ SV2 @ SV6 ) @ SV8 )
= $true )
| ( ( SV1 @ SV6 @ ( sK6_SY21 @ SV4 @ SV1 @ SV2 @ SV6 ) @ SV8 )
= $true )
| ( ( SV1 @ ( sK2_SY18 @ SV1 @ SV2 ) @ SV4 @ ( sK4_SY29 @ SV4 @ SV1 @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(45,plain,
( ( sK1_SY24 @ sK7_Eigen @ ( sK7_Eigen @ ( sK1_SY24 @ sK7_Eigen ) ) )
= $false ),
inference(instantiate,[status(thm)],[22:[bind(SV3,$thf( sK7_Eigen ))]]) ).
thf(46,plain,
! [SV3: ( b > $o ) > b] :
( ( ~ ~ ! [SV9: b] :
~ ( sK1_SY24 @ SV3 @ SV9 )
| ( sK1_SY24 @ SV3 @ ( sK7_Eigen @ ( sK1_SY24 @ SV3 ) ) ) )
= $true ),
inference(choice,[status(thm)],[22]) ).
thf(47,plain,
! [SV10: ( b > $o ) > b] :
( ( ~ ~ ! [SX0: b] :
~ ( sK1_SY24 @ SV10 @ SX0 )
| ( sK1_SY24 @ SV10 @ ( sK7_Eigen @ ( sK1_SY24 @ SV10 ) ) ) )
= $true ),
inference(rename,[status(thm)],[46]) ).
thf(48,plain,
! [SV10: ( b > $o ) > b] :
( ( ( ~ ~ ! [SX0: b] :
~ ( sK1_SY24 @ SV10 @ SX0 ) )
= $true )
| ( ( sK1_SY24 @ SV10 @ ( sK7_Eigen @ ( sK1_SY24 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(49,plain,
! [SV10: ( b > $o ) > b] :
( ( ( ~ ! [SX0: b] :
~ ( sK1_SY24 @ SV10 @ SX0 ) )
= $false )
| ( ( sK1_SY24 @ SV10 @ ( sK7_Eigen @ ( sK1_SY24 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(50,plain,
! [SV10: ( b > $o ) > b] :
( ( ( ! [SX0: b] :
~ ( sK1_SY24 @ SV10 @ SX0 ) )
= $true )
| ( ( sK1_SY24 @ SV10 @ ( sK7_Eigen @ ( sK1_SY24 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(51,plain,
! [SV11: b,SV10: ( b > $o ) > b] :
( ( ( ~ ( sK1_SY24 @ SV10 @ SV11 ) )
= $true )
| ( ( sK1_SY24 @ SV10 @ ( sK7_Eigen @ ( sK1_SY24 @ SV10 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(52,plain,
! [SV11: b,SV10: ( b > $o ) > b] :
( ( ( sK1_SY24 @ SV10 @ SV11 )
= $false )
| ( ( sK1_SY24 @ SV10 @ ( sK7_Eigen @ ( sK1_SY24 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(53,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,52,45,44,43,30]) ).
thf(54,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL739^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 12:32:46 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.13
% 0.08/0.13 No.of.Axioms: 0
% 0.08/0.13
% 0.08/0.13 Length.of.Defs: 0
% 0.08/0.13
% 0.08/0.13 Contains.Choice.Funs: false
% 0.08/0.13 .
% 0.08/0.13
% 0.08/0.13 *** Modified list of choice operators: sK7_Eigen ***
% 0.08/0.13 .
% 0.08/0.13
% 0.08/0.13 ********************************
% 0.08/0.13 * All subproblems solved! *
% 0.08/0.13 ********************************
% 0.08/0.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,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:53,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.08/0.13
% 0.08/0.13 %**** Beginning of derivation protocol ****
% 0.08/0.13 % SZS output start CNFRefutation
% See solution above
% 0.08/0.13
% 0.08/0.13 %**** End of derivation protocol ****
% 0.08/0.13 %**** no. of clauses in derivation: 54 ****
% 0.08/0.13 %**** clause counter: 53 ****
% 0.08/0.13
% 0.08/0.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,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:53,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------