%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV088^5 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 10:49:32 AM UTC 2026
% Result : Theorem 0.06s 0.31s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 24 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 246 ( 35 equ; 0 cnn)
% Maximal formula atoms : 2 ( 10 avg)
% Number of connectives : 1055 ( 143 ~; 78 |; 16 &; 814 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 226 ( 226 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 88 ( 0 ^; 80 !; 8 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_Xx,type,
sK1_Xx: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_sK2_SY10,type,
sK2_SY10: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(tp_sK3_Xx,type,
sK3_Xx: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_sK4_SY11,type,
sK4_SY11: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_sK5_SY16,type,
sK5_SY16: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_sK6_SY22,type,
sK6_SY22: ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(1,conjecture,
? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
( ( ! [Xw_2: $i] :
( ( Xr_27 @ Xx @ Xy @ Xw_2 )
| ( Xr_28 @ Xx @ Xy @ Xw_2 ) )
& ! [Xw_2: $i] :
( ( Xr_27 @ Xy @ Xz @ Xw_2 )
| ( Xr_28 @ Xy @ Xz @ Xw_2 ) ) )
=> ! [Xw_2: $i] :
( ( Xr_27 @ Xx @ Xz @ Xw_2 )
| ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) )
& ! [Xx: $i > $o,Xw_2: $i] :
( ( Xr_27 @ Xx @ Xx @ Xw_2 )
| ( Xr_28 @ Xx @ Xx @ Xw_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120G_pme) ).
thf(2,negated_conjecture,
( ( ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
( ( ! [Xw_2: $i] :
( ( Xr_27 @ Xx @ Xy @ Xw_2 )
| ( Xr_28 @ Xx @ Xy @ Xw_2 ) )
& ! [Xw_2: $i] :
( ( Xr_27 @ Xy @ Xz @ Xw_2 )
| ( Xr_28 @ Xy @ Xz @ Xw_2 ) ) )
=> ! [Xw_2: $i] :
( ( Xr_27 @ Xx @ Xz @ Xw_2 )
| ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) )
& ! [Xx: $i > $o,Xw_2: $i] :
( ( Xr_27 @ Xx @ Xx @ Xw_2 )
| ( Xr_28 @ Xx @ Xx @ Xw_2 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
( ( ! [Xw_2: $i] :
( ( Xr_27 @ Xx @ Xy @ Xw_2 )
| ( Xr_28 @ Xx @ Xy @ Xw_2 ) )
& ! [Xw_2: $i] :
( ( Xr_27 @ Xy @ Xz @ Xw_2 )
| ( Xr_28 @ Xy @ Xz @ Xw_2 ) ) )
=> ! [Xw_2: $i] :
( ( Xr_27 @ Xx @ Xz @ Xw_2 )
| ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) )
& ! [Xx: $i > $o,Xw_2: $i] :
( ( Xr_27 @ Xx @ Xx @ Xw_2 )
| ( Xr_28 @ Xx @ Xx @ Xw_2 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
( ( ! [Xw_2: $i] :
( ( Xr_27 @ Xx @ Xy @ Xw_2 )
| ( Xr_28 @ Xx @ Xy @ Xw_2 ) )
& ! [Xw_2: $i] :
( ( Xr_27 @ Xy @ Xz @ Xw_2 )
| ( Xr_28 @ Xy @ Xz @ Xw_2 ) ) )
=> ! [Xw_2: $i] :
( ( Xr_27 @ Xx @ Xz @ Xw_2 )
| ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) )
& ! [Xx: $i > $o,Xw_2: $i] :
( ( Xr_27 @ Xx @ Xx @ Xw_2 )
| ( Xr_28 @ Xx @ Xx @ Xw_2 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ! [SY17: $i] :
( ( Xr_27 @ ( sK3_Xx @ Xr_27 @ Xr_28 ) @ ( sK4_SY11 @ Xr_27 @ Xr_28 ) @ SY17 )
| ( Xr_28 @ ( sK3_Xx @ Xr_27 @ Xr_28 ) @ ( sK4_SY11 @ Xr_27 @ Xr_28 ) @ SY17 ) )
& ! [SY21: $i] :
( ( Xr_27 @ ( sK4_SY11 @ Xr_27 @ Xr_28 ) @ ( sK5_SY16 @ Xr_27 @ Xr_28 ) @ SY21 )
| ( Xr_28 @ ( sK4_SY11 @ Xr_27 @ Xr_28 ) @ ( sK5_SY16 @ Xr_27 @ Xr_28 ) @ SY21 ) )
& ~ ( Xr_27 @ ( sK3_Xx @ Xr_27 @ Xr_28 ) @ ( sK5_SY16 @ Xr_27 @ Xr_28 ) @ ( sK6_SY22 @ Xr_27 @ Xr_28 ) )
& ~ ( Xr_28 @ ( sK3_Xx @ Xr_27 @ Xr_28 ) @ ( sK5_SY16 @ Xr_27 @ Xr_28 ) @ ( sK6_SY22 @ Xr_27 @ Xr_28 ) ) )
| ( ~ ( Xr_27 @ ( sK1_Xx @ Xr_27 @ Xr_28 ) @ ( sK1_Xx @ Xr_27 @ Xr_28 ) @ ( sK2_SY10 @ Xr_27 @ Xr_28 ) )
& ~ ( Xr_28 @ ( sK1_Xx @ Xr_27 @ Xr_28 ) @ ( sK1_Xx @ Xr_27 @ Xr_28 ) @ ( sK2_SY10 @ Xr_27 @ Xr_28 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ! [SY17: $i] :
( ( Xr_27 @ ( sK3_Xx @ Xr_27 @ Xr_28 ) @ ( sK4_SY11 @ Xr_27 @ Xr_28 ) @ SY17 )
| ( Xr_28 @ ( sK3_Xx @ Xr_27 @ Xr_28 ) @ ( sK4_SY11 @ Xr_27 @ Xr_28 ) @ SY17 ) )
& ! [SY21: $i] :
( ( Xr_27 @ ( sK4_SY11 @ Xr_27 @ Xr_28 ) @ ( sK5_SY16 @ Xr_27 @ Xr_28 ) @ SY21 )
| ( Xr_28 @ ( sK4_SY11 @ Xr_27 @ Xr_28 ) @ ( sK5_SY16 @ Xr_27 @ Xr_28 ) @ SY21 ) )
& ~ ( Xr_27 @ ( sK3_Xx @ Xr_27 @ Xr_28 ) @ ( sK5_SY16 @ Xr_27 @ Xr_28 ) @ ( sK6_SY22 @ Xr_27 @ Xr_28 ) )
& ~ ( Xr_28 @ ( sK3_Xx @ Xr_27 @ Xr_28 ) @ ( sK5_SY16 @ Xr_27 @ Xr_28 ) @ ( sK6_SY22 @ Xr_27 @ Xr_28 ) ) )
| ( ~ ( Xr_27 @ ( sK1_Xx @ Xr_27 @ Xr_28 ) @ ( sK1_Xx @ Xr_27 @ Xr_28 ) @ ( sK2_SY10 @ Xr_27 @ Xr_28 ) )
& ~ ( Xr_28 @ ( sK1_Xx @ Xr_27 @ Xr_28 ) @ ( sK1_Xx @ Xr_27 @ Xr_28 ) @ ( sK2_SY10 @ Xr_27 @ Xr_28 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SX0: ( $i > $o ) > ( $i > $o ) > $i > $o,SX1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ( SX1 @ ( sK3_Xx @ SX1 @ SX0 ) @ ( sK4_SY11 @ SX1 @ SX0 ) @ SX2 )
| ( SX0 @ ( sK3_Xx @ SX1 @ SX0 ) @ ( sK4_SY11 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ! [SX2: $i] :
( ( SX1 @ ( sK4_SY11 @ SX1 @ SX0 ) @ ( sK5_SY16 @ SX1 @ SX0 ) @ SX2 )
| ( SX0 @ ( sK4_SY11 @ SX1 @ SX0 ) @ ( sK5_SY16 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ~ ( ~ ~ ( SX1 @ ( sK3_Xx @ SX1 @ SX0 ) @ ( sK5_SY16 @ SX1 @ SX0 ) @ ( sK6_SY22 @ SX1 @ SX0 ) )
| ~ ~ ( SX0 @ ( sK3_Xx @ SX1 @ SX0 ) @ ( sK5_SY16 @ SX1 @ SX0 ) @ ( sK6_SY22 @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ~ ( SX1 @ ( sK1_Xx @ SX1 @ SX0 ) @ ( sK1_Xx @ SX1 @ SX0 ) @ ( sK2_SY10 @ SX1 @ SX0 ) )
| ~ ~ ( SX0 @ ( sK1_Xx @ SX1 @ SX0 ) @ ( sK1_Xx @ SX1 @ SX0 ) @ ( sK2_SY10 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ! [SY23: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ~ ~ ( ~ ! [SY24: $i] :
( ( SY23 @ ( sK3_Xx @ SY23 @ SV1 ) @ ( sK4_SY11 @ SY23 @ SV1 ) @ SY24 )
| ( SV1 @ ( sK3_Xx @ SY23 @ SV1 ) @ ( sK4_SY11 @ SY23 @ SV1 ) @ SY24 ) )
| ~ ! [SY25: $i] :
( ( SY23 @ ( sK4_SY11 @ SY23 @ SV1 ) @ ( sK5_SY16 @ SY23 @ SV1 ) @ SY25 )
| ( SV1 @ ( sK4_SY11 @ SY23 @ SV1 ) @ ( sK5_SY16 @ SY23 @ SV1 ) @ SY25 ) ) )
| ~ ~ ( ~ ~ ( SY23 @ ( sK3_Xx @ SY23 @ SV1 ) @ ( sK5_SY16 @ SY23 @ SV1 ) @ ( sK6_SY22 @ SY23 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK3_Xx @ SY23 @ SV1 ) @ ( sK5_SY16 @ SY23 @ SV1 ) @ ( sK6_SY22 @ SY23 @ SV1 ) ) ) )
| ~ ( ~ ~ ( SY23 @ ( sK1_Xx @ SY23 @ SV1 ) @ ( sK1_Xx @ SY23 @ SV1 ) @ ( sK2_SY10 @ SY23 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK1_Xx @ SY23 @ SV1 ) @ ( sK1_Xx @ SY23 @ SV1 ) @ ( sK2_SY10 @ SY23 @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $i > $o,SV2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ~ ( ~ ~ ( ~ ! [SY26: $i] :
( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK4_SY11 @ SV2 @ SV1 ) @ SY26 )
| ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK4_SY11 @ SV2 @ SV1 ) @ SY26 ) )
| ~ ! [SY27: $i] :
( ( SV2 @ ( sK4_SY11 @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ SY27 )
| ( SV1 @ ( sK4_SY11 @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ SY27 ) ) )
| ~ ~ ( ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) ) ) )
| ~ ( ~ ~ ( SV2 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $i > $o,SV2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ~ ( ~ ~ ( ~ ! [SY26: $i] :
( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK4_SY11 @ SV2 @ SV1 ) @ SY26 )
| ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK4_SY11 @ SV2 @ SV1 ) @ SY26 ) )
| ~ ! [SY27: $i] :
( ( SV2 @ ( sK4_SY11 @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ SY27 )
| ( SV1 @ ( sK4_SY11 @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ SY27 ) ) )
| ~ ~ ( ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( SV2 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $i > $o,SV2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ~ ~ ( ~ ! [SY26: $i] :
( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK4_SY11 @ SV2 @ SV1 ) @ SY26 )
| ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK4_SY11 @ SV2 @ SV1 ) @ SY26 ) )
| ~ ! [SY27: $i] :
( ( SV2 @ ( sK4_SY11 @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ SY27 )
| ( SV1 @ ( sK4_SY11 @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ SY27 ) ) )
| ~ ~ ( ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( SV2 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $i > $o,SV2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ~ ~ ( ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( SV2 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(15,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $i > $o,SV2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ~ ( ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( SV2 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $i > $o,SV2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( SV2 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $i > $o,SV2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( SV2 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(24,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $i > $o,SV2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( SV2 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(28,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $i > $o,SV2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) )
= $false )
| ( ( ~ ( ~ ~ ( SV2 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $i > $o,SV2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ~ ~ ( SV2 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) )
| ~ ~ ( SV1 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) ) )
= $false )
| ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $i > $o,SV2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ~ ~ ( SV2 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) ) )
= $false )
| ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(44,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $i > $o,SV2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( ~ ( SV2 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) ) )
= $true )
| ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(52,plain,
! [SV1: ( $i > $o ) > ( $i > $o ) > $i > $o,SV2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( SV2 @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK1_Xx @ SV2 @ SV1 ) @ ( sK2_SY10 @ SV2 @ SV1 ) )
= $false )
| ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) @ ( sK5_SY16 @ SV2 @ SV1 ) @ ( sK6_SY22 @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(63,plain,
( ( $true = $false )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[52:[bind(SV2,$thf( ^ [SV22: $i > $o] : ^ [SV23: $i > $o] : ^ [SV24: $i] : $true ))]]) ).
thf(176,plain,
$false = $true,
inference(sim,[status(thm)],[63]) ).
thf(177,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV088^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.06/0.19 % Computer : n019.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Oct 6 15:41:16 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.31
% 0.06/0.31 No.of.Axioms: 0
% 0.06/0.31
% 0.06/0.31 Length.of.Defs: 0
% 0.06/0.31
% 0.06/0.31 Contains.Choice.Funs: false
% 0.06/0.31 ....
% 0.06/0.31
% 0.06/0.31 ********************************
% 0.06/0.31 * All subproblems solved! *
% 0.06/0.31 ********************************
% 0.06/0.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:176,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.06/0.31
% 0.06/0.31 %**** Beginning of derivation protocol ****
% 0.06/0.31 % SZS output start CNFRefutation
% See solution above
% 0.06/0.31
% 0.06/0.31 %**** End of derivation protocol ****
% 0.06/0.31 %**** no. of clauses in derivation: 24 ****
% 0.06/0.31 %**** clause counter: 176 ****
% 0.06/0.31
% 0.06/0.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:176,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------