%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU785^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n004.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 10:48:23 AM UTC 2026
% Result : Theorem 0.09s 0.23s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 69 ( 41 unt; 0 typ; 2 def)
% Number of atoms : 644 ( 140 equ; 0 cnn)
% Maximal formula atoms : 9 ( 9 avg)
% Number of connectives : 1548 ( 145 ~; 219 |; 0 &;1108 @)
% ( 0 <=>; 76 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 256 ( 0 ^; 256 !; 0 ?; 256 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binunion,type,
binunion: $i > $i > $i ).
thf(tp_breln1,type,
breln1: $i > $i > $o ).
thf(tp_breln1unionIL,type,
breln1unionIL: $o ).
thf(tp_breln1unionIR,type,
breln1unionIR: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY34,type,
sK2_SY34: $i ).
thf(tp_sK3_SY38,type,
sK3_SY38: $i ).
thf(tp_sK4_SY45,type,
sK4_SY45: $i ).
thf(tp_sK5_SY47,type,
sK5_SY47: $i ).
thf(breln1unionIL,definition,
( breln1unionIL
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionIL) ).
thf(breln1unionIR,definition,
( breln1unionIR
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionIR) ).
thf(1,conjecture,
( breln1unionIL
=> ( breln1unionIR
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionI) ).
thf(2,negated_conjecture,
( ( breln1unionIL
=> ( breln1unionIR
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) )
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,breln1unionIL,breln1unionIR]) ).
thf(4,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(10,plain,
( ( ~ ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ ( binunion @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,breln1unionIL,breln1unionIR]) ).
thf(12,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ ( binunion @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,breln1unionIL,breln1unionIR]) ).
thf(13,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) )
| ( in @ ( kpair @ SX3 @ SX4 ) @ ( binunion @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,breln1unionIL,breln1unionIR]) ).
thf(14,plain,
! [SV1: $i] :
( ( ! [SY20: $i] :
( ~ ( breln1 @ SV1 @ SY20 )
| ! [SY21: $i] :
( ~ ( breln1 @ SV1 @ SY21 )
| ! [SY22: $i] :
( ~ ( in @ SY22 @ SV1 )
| ! [SY23: $i] :
( ~ ( in @ SY23 @ SV1 )
| ~ ( in @ ( kpair @ SY22 @ SY23 ) @ SY21 )
| ( in @ ( kpair @ SY22 @ SY23 ) @ ( binunion @ SY20 @ SY21 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV2: $i] :
( ( ! [SY24: $i] :
( ~ ( breln1 @ SV2 @ SY24 )
| ! [SY25: $i] :
( ~ ( breln1 @ SV2 @ SY25 )
| ! [SY26: $i] :
( ~ ( in @ SY26 @ SV2 )
| ! [SY27: $i] :
( ~ ( in @ SY27 @ SV2 )
| ~ ( in @ ( kpair @ SY26 @ SY27 ) @ SY24 )
| ( in @ ( kpair @ SY26 @ SY27 ) @ ( binunion @ SY24 @ SY25 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) )
| ( in @ ( kpair @ SX3 @ SX4 ) @ ( binunion @ SX1 @ SX2 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( breln1 @ SV1 @ SV3 )
| ! [SY28: $i] :
( ~ ( breln1 @ SV1 @ SY28 )
| ! [SY29: $i] :
( ~ ( in @ SY29 @ SV1 )
| ! [SY30: $i] :
( ~ ( in @ SY30 @ SV1 )
| ~ ( in @ ( kpair @ SY29 @ SY30 ) @ SY28 )
| ( in @ ( kpair @ SY29 @ SY30 ) @ ( binunion @ SV3 @ SY28 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV4: $i,SV2: $i] :
( ( ~ ( breln1 @ SV2 @ SV4 )
| ! [SY31: $i] :
( ~ ( breln1 @ SV2 @ SY31 )
| ! [SY32: $i] :
( ~ ( in @ SY32 @ SV2 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SV2 )
| ~ ( in @ ( kpair @ SY32 @ SY33 ) @ SV4 )
| ( in @ ( kpair @ SY32 @ SY33 ) @ ( binunion @ SV4 @ SY31 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SY34: $i] :
( ~ ( breln1 @ sK1_SX0 @ SY34 )
| ! [SY35: $i] :
( ~ ( breln1 @ sK1_SX0 @ SY35 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ sK1_SX0 )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ sK1_SX0 )
| ~ ( ( in @ ( kpair @ SY36 @ SY37 ) @ SY34 )
| ( in @ ( kpair @ SY36 @ SY37 ) @ SY35 ) )
| ( in @ ( kpair @ SY36 @ SY37 ) @ ( binunion @ SY34 @ SY35 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(20,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( breln1 @ SV1 @ SV3 ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( breln1 @ SV1 @ SY28 )
| ! [SY29: $i] :
( ~ ( in @ SY29 @ SV1 )
| ! [SY30: $i] :
( ~ ( in @ SY30 @ SV1 )
| ~ ( in @ ( kpair @ SY29 @ SY30 ) @ SY28 )
| ( in @ ( kpair @ SY29 @ SY30 ) @ ( binunion @ SV3 @ SY28 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( breln1 @ SV2 @ SV4 ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( breln1 @ SV2 @ SY31 )
| ! [SY32: $i] :
( ~ ( in @ SY32 @ SV2 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SV2 )
| ~ ( in @ ( kpair @ SY32 @ SY33 ) @ SV4 )
| ( in @ ( kpair @ SY32 @ SY33 ) @ ( binunion @ SV4 @ SY31 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ( breln1 @ sK1_SX0 @ sK2_SY34 )
| ! [SY38: $i] :
( ~ ( breln1 @ sK1_SX0 @ SY38 )
| ! [SY39: $i] :
( ~ ( in @ SY39 @ sK1_SX0 )
| ! [SY40: $i] :
( ~ ( in @ SY40 @ sK1_SX0 )
| ~ ( ( in @ ( kpair @ SY39 @ SY40 ) @ sK2_SY34 )
| ( in @ ( kpair @ SY39 @ SY40 ) @ SY38 ) )
| ( in @ ( kpair @ SY39 @ SY40 ) @ ( binunion @ sK2_SY34 @ SY38 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(23,plain,
! [SV3: $i,SV1: $i] :
( ( ( breln1 @ SV1 @ SV3 )
= $false )
| ( ( ! [SY28: $i] :
( ~ ( breln1 @ SV1 @ SY28 )
| ! [SY29: $i] :
( ~ ( in @ SY29 @ SV1 )
| ! [SY30: $i] :
( ~ ( in @ SY30 @ SV1 )
| ~ ( in @ ( kpair @ SY29 @ SY30 ) @ SY28 )
| ( in @ ( kpair @ SY29 @ SY30 ) @ ( binunion @ SV3 @ SY28 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV4: $i,SV2: $i] :
( ( ( breln1 @ SV2 @ SV4 )
= $false )
| ( ( ! [SY31: $i] :
( ~ ( breln1 @ SV2 @ SY31 )
| ! [SY32: $i] :
( ~ ( in @ SY32 @ SV2 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SV2 )
| ~ ( in @ ( kpair @ SY32 @ SY33 ) @ SV4 )
| ( in @ ( kpair @ SY32 @ SY33 ) @ ( binunion @ SV4 @ SY31 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ( breln1 @ sK1_SX0 @ sK2_SY34 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( ! [SY38: $i] :
( ~ ( breln1 @ sK1_SX0 @ SY38 )
| ! [SY39: $i] :
( ~ ( in @ SY39 @ sK1_SX0 )
| ! [SY40: $i] :
( ~ ( in @ SY40 @ sK1_SX0 )
| ~ ( ( in @ ( kpair @ SY39 @ SY40 ) @ sK2_SY34 )
| ( in @ ( kpair @ SY39 @ SY40 ) @ SY38 ) )
| ( in @ ( kpair @ SY39 @ SY40 ) @ ( binunion @ sK2_SY34 @ SY38 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
! [SV3: $i,SV5: $i,SV1: $i] :
( ( ( ~ ( breln1 @ SV1 @ SV5 )
| ! [SY41: $i] :
( ~ ( in @ SY41 @ SV1 )
| ! [SY42: $i] :
( ~ ( in @ SY42 @ SV1 )
| ~ ( in @ ( kpair @ SY41 @ SY42 ) @ SV5 )
| ( in @ ( kpair @ SY41 @ SY42 ) @ ( binunion @ SV3 @ SV5 ) ) ) ) )
= $true )
| ( ( breln1 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV4: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( breln1 @ SV2 @ SV6 )
| ! [SY43: $i] :
( ~ ( in @ SY43 @ SV2 )
| ! [SY44: $i] :
( ~ ( in @ SY44 @ SV2 )
| ~ ( in @ ( kpair @ SY43 @ SY44 ) @ SV4 )
| ( in @ ( kpair @ SY43 @ SY44 ) @ ( binunion @ SV4 @ SV6 ) ) ) ) )
= $true )
| ( ( breln1 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( breln1 @ sK1_SX0 @ sK2_SY34 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( ~ ( breln1 @ sK1_SX0 @ sK3_SY38 )
| ! [SY45: $i] :
( ~ ( in @ SY45 @ sK1_SX0 )
| ! [SY46: $i] :
( ~ ( in @ SY46 @ sK1_SX0 )
| ~ ( ( in @ ( kpair @ SY45 @ SY46 ) @ sK2_SY34 )
| ( in @ ( kpair @ SY45 @ SY46 ) @ sK3_SY38 ) )
| ( in @ ( kpair @ SY45 @ SY46 ) @ ( binunion @ sK2_SY34 @ sK3_SY38 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(31,plain,
! [SV3: $i,SV5: $i,SV1: $i] :
( ( ( ~ ( breln1 @ SV1 @ SV5 ) )
= $true )
| ( ( ! [SY41: $i] :
( ~ ( in @ SY41 @ SV1 )
| ! [SY42: $i] :
( ~ ( in @ SY42 @ SV1 )
| ~ ( in @ ( kpair @ SY41 @ SY42 ) @ SV5 )
| ( in @ ( kpair @ SY41 @ SY42 ) @ ( binunion @ SV3 @ SV5 ) ) ) ) )
= $true )
| ( ( breln1 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV4: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( breln1 @ SV2 @ SV6 ) )
= $true )
| ( ( ! [SY43: $i] :
( ~ ( in @ SY43 @ SV2 )
| ! [SY44: $i] :
( ~ ( in @ SY44 @ SV2 )
| ~ ( in @ ( kpair @ SY43 @ SY44 ) @ SV4 )
| ( in @ ( kpair @ SY43 @ SY44 ) @ ( binunion @ SV4 @ SV6 ) ) ) ) )
= $true )
| ( ( breln1 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( ~ ( breln1 @ sK1_SX0 @ sK3_SY38 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(34,plain,
( ( ! [SY45: $i] :
( ~ ( in @ SY45 @ sK1_SX0 )
| ! [SY46: $i] :
( ~ ( in @ SY46 @ sK1_SX0 )
| ~ ( ( in @ ( kpair @ SY45 @ SY46 ) @ sK2_SY34 )
| ( in @ ( kpair @ SY45 @ SY46 ) @ sK3_SY38 ) )
| ( in @ ( kpair @ SY45 @ SY46 ) @ ( binunion @ sK2_SY34 @ sK3_SY38 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV3: $i,SV5: $i,SV1: $i] :
( ( ( breln1 @ SV1 @ SV5 )
= $false )
| ( ( ! [SY41: $i] :
( ~ ( in @ SY41 @ SV1 )
| ! [SY42: $i] :
( ~ ( in @ SY42 @ SV1 )
| ~ ( in @ ( kpair @ SY41 @ SY42 ) @ SV5 )
| ( in @ ( kpair @ SY41 @ SY42 ) @ ( binunion @ SV3 @ SV5 ) ) ) ) )
= $true )
| ( ( breln1 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV4: $i,SV6: $i,SV2: $i] :
( ( ( breln1 @ SV2 @ SV6 )
= $false )
| ( ( ! [SY43: $i] :
( ~ ( in @ SY43 @ SV2 )
| ! [SY44: $i] :
( ~ ( in @ SY44 @ SV2 )
| ~ ( in @ ( kpair @ SY43 @ SY44 ) @ SV4 )
| ( in @ ( kpair @ SY43 @ SY44 ) @ ( binunion @ SV4 @ SV6 ) ) ) ) )
= $true )
| ( ( breln1 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
( ( breln1 @ sK1_SX0 @ sK3_SY38 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(38,plain,
( ( ~ ( in @ sK4_SY45 @ sK1_SX0 )
| ! [SY47: $i] :
( ~ ( in @ SY47 @ sK1_SX0 )
| ~ ( ( in @ ( kpair @ sK4_SY45 @ SY47 ) @ sK2_SY34 )
| ( in @ ( kpair @ sK4_SY45 @ SY47 ) @ sK3_SY38 ) )
| ( in @ ( kpair @ sK4_SY45 @ SY47 ) @ ( binunion @ sK2_SY34 @ sK3_SY38 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(39,plain,
! [SV3: $i,SV5: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV1 )
| ! [SY48: $i] :
( ~ ( in @ SY48 @ SV1 )
| ~ ( in @ ( kpair @ SV7 @ SY48 ) @ SV5 )
| ( in @ ( kpair @ SV7 @ SY48 ) @ ( binunion @ SV3 @ SV5 ) ) ) )
= $true )
| ( ( breln1 @ SV1 @ SV5 )
= $false )
| ( ( breln1 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV6: $i,SV4: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV2 )
| ! [SY49: $i] :
( ~ ( in @ SY49 @ SV2 )
| ~ ( in @ ( kpair @ SV8 @ SY49 ) @ SV4 )
| ( in @ ( kpair @ SV8 @ SY49 ) @ ( binunion @ SV4 @ SV6 ) ) ) )
= $true )
| ( ( breln1 @ SV2 @ SV6 )
= $false )
| ( ( breln1 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(41,plain,
( ( ~ ( in @ sK4_SY45 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
( ( ! [SY47: $i] :
( ~ ( in @ SY47 @ sK1_SX0 )
| ~ ( ( in @ ( kpair @ sK4_SY45 @ SY47 ) @ sK2_SY34 )
| ( in @ ( kpair @ sK4_SY45 @ SY47 ) @ sK3_SY38 ) )
| ( in @ ( kpair @ sK4_SY45 @ SY47 ) @ ( binunion @ sK2_SY34 @ sK3_SY38 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV3: $i,SV5: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV1 ) )
= $true )
| ( ( ! [SY48: $i] :
( ~ ( in @ SY48 @ SV1 )
| ~ ( in @ ( kpair @ SV7 @ SY48 ) @ SV5 )
| ( in @ ( kpair @ SV7 @ SY48 ) @ ( binunion @ SV3 @ SV5 ) ) ) )
= $true )
| ( ( breln1 @ SV1 @ SV5 )
= $false )
| ( ( breln1 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV6: $i,SV4: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV2 ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ SV2 )
| ~ ( in @ ( kpair @ SV8 @ SY49 ) @ SV4 )
| ( in @ ( kpair @ SV8 @ SY49 ) @ ( binunion @ SV4 @ SV6 ) ) ) )
= $true )
| ( ( breln1 @ SV2 @ SV6 )
= $false )
| ( ( breln1 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(45,plain,
( ( in @ sK4_SY45 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(46,plain,
( ( ~ ( in @ sK5_SY47 @ sK1_SX0 )
| ~ ( ( in @ ( kpair @ sK4_SY45 @ sK5_SY47 ) @ sK2_SY34 )
| ( in @ ( kpair @ sK4_SY45 @ sK5_SY47 ) @ sK3_SY38 ) )
| ( in @ ( kpair @ sK4_SY45 @ sK5_SY47 ) @ ( binunion @ sK2_SY34 @ sK3_SY38 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(47,plain,
! [SV3: $i,SV5: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ SV1 )
= $false )
| ( ( ! [SY48: $i] :
( ~ ( in @ SY48 @ SV1 )
| ~ ( in @ ( kpair @ SV7 @ SY48 ) @ SV5 )
| ( in @ ( kpair @ SV7 @ SY48 ) @ ( binunion @ SV3 @ SV5 ) ) ) )
= $true )
| ( ( breln1 @ SV1 @ SV5 )
= $false )
| ( ( breln1 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV6: $i,SV4: $i,SV2: $i,SV8: $i] :
( ( ( in @ SV8 @ SV2 )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ SV2 )
| ~ ( in @ ( kpair @ SV8 @ SY49 ) @ SV4 )
| ( in @ ( kpair @ SV8 @ SY49 ) @ ( binunion @ SV4 @ SV6 ) ) ) )
= $true )
| ( ( breln1 @ SV2 @ SV6 )
= $false )
| ( ( breln1 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
( ( ~ ( in @ sK5_SY47 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(50,plain,
( ( ~ ( ( in @ ( kpair @ sK4_SY45 @ sK5_SY47 ) @ sK2_SY34 )
| ( in @ ( kpair @ sK4_SY45 @ sK5_SY47 ) @ sK3_SY38 ) )
| ( in @ ( kpair @ sK4_SY45 @ sK5_SY47 ) @ ( binunion @ sK2_SY34 @ sK3_SY38 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV3: $i,SV5: $i,SV7: $i,SV1: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV1 )
| ~ ( in @ ( kpair @ SV7 @ SV9 ) @ SV5 )
| ( in @ ( kpair @ SV7 @ SV9 ) @ ( binunion @ SV3 @ SV5 ) ) )
= $true )
| ( ( in @ SV7 @ SV1 )
= $false )
| ( ( breln1 @ SV1 @ SV5 )
= $false )
| ( ( breln1 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV6: $i,SV4: $i,SV8: $i,SV2: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV2 )
| ~ ( in @ ( kpair @ SV8 @ SV10 ) @ SV4 )
| ( in @ ( kpair @ SV8 @ SV10 ) @ ( binunion @ SV4 @ SV6 ) ) )
= $true )
| ( ( in @ SV8 @ SV2 )
= $false )
| ( ( breln1 @ SV2 @ SV6 )
= $false )
| ( ( breln1 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(53,plain,
( ( in @ sK5_SY47 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(54,plain,
( ( ~ ( ( in @ ( kpair @ sK4_SY45 @ sK5_SY47 ) @ sK2_SY34 )
| ( in @ ( kpair @ sK4_SY45 @ sK5_SY47 ) @ sK3_SY38 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(55,plain,
( ( in @ ( kpair @ sK4_SY45 @ sK5_SY47 ) @ ( binunion @ sK2_SY34 @ sK3_SY38 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(56,plain,
! [SV3: $i,SV5: $i,SV7: $i,SV1: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV1 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV7 @ SV9 ) @ SV5 )
| ( in @ ( kpair @ SV7 @ SV9 ) @ ( binunion @ SV3 @ SV5 ) ) )
= $true )
| ( ( in @ SV7 @ SV1 )
= $false )
| ( ( breln1 @ SV1 @ SV5 )
= $false )
| ( ( breln1 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV6: $i,SV4: $i,SV8: $i,SV2: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV2 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV8 @ SV10 ) @ SV4 )
| ( in @ ( kpair @ SV8 @ SV10 ) @ ( binunion @ SV4 @ SV6 ) ) )
= $true )
| ( ( in @ SV8 @ SV2 )
= $false )
| ( ( breln1 @ SV2 @ SV6 )
= $false )
| ( ( breln1 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(58,plain,
( ( ( in @ ( kpair @ sK4_SY45 @ sK5_SY47 ) @ sK2_SY34 )
| ( in @ ( kpair @ sK4_SY45 @ sK5_SY47 ) @ sK3_SY38 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV3: $i,SV5: $i,SV7: $i,SV1: $i,SV9: $i] :
( ( ( in @ SV9 @ SV1 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV7 @ SV9 ) @ SV5 )
| ( in @ ( kpair @ SV7 @ SV9 ) @ ( binunion @ SV3 @ SV5 ) ) )
= $true )
| ( ( in @ SV7 @ SV1 )
= $false )
| ( ( breln1 @ SV1 @ SV5 )
= $false )
| ( ( breln1 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV6: $i,SV4: $i,SV8: $i,SV2: $i,SV10: $i] :
( ( ( in @ SV10 @ SV2 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV8 @ SV10 ) @ SV4 )
| ( in @ ( kpair @ SV8 @ SV10 ) @ ( binunion @ SV4 @ SV6 ) ) )
= $true )
| ( ( in @ SV8 @ SV2 )
= $false )
| ( ( breln1 @ SV2 @ SV6 )
= $false )
| ( ( breln1 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(61,plain,
( ( ( in @ ( kpair @ sK4_SY45 @ sK5_SY47 ) @ sK2_SY34 )
= $true )
| ( ( in @ ( kpair @ sK4_SY45 @ sK5_SY47 ) @ sK3_SY38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV1: $i,SV3: $i,SV5: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( kpair @ SV7 @ SV9 ) @ SV5 ) )
= $true )
| ( ( in @ ( kpair @ SV7 @ SV9 ) @ ( binunion @ SV3 @ SV5 ) )
= $true )
| ( ( in @ SV9 @ SV1 )
= $false )
| ( ( in @ SV7 @ SV1 )
= $false )
| ( ( breln1 @ SV1 @ SV5 )
= $false )
| ( ( breln1 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV2: $i,SV6: $i,SV4: $i,SV10: $i,SV8: $i] :
( ( ( ~ ( in @ ( kpair @ SV8 @ SV10 ) @ SV4 ) )
= $true )
| ( ( in @ ( kpair @ SV8 @ SV10 ) @ ( binunion @ SV4 @ SV6 ) )
= $true )
| ( ( in @ SV10 @ SV2 )
= $false )
| ( ( in @ SV8 @ SV2 )
= $false )
| ( ( breln1 @ SV2 @ SV6 )
= $false )
| ( ( breln1 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV1: $i,SV3: $i,SV5: $i,SV9: $i,SV7: $i] :
( ( ( in @ ( kpair @ SV7 @ SV9 ) @ SV5 )
= $false )
| ( ( in @ ( kpair @ SV7 @ SV9 ) @ ( binunion @ SV3 @ SV5 ) )
= $true )
| ( ( in @ SV9 @ SV1 )
= $false )
| ( ( in @ SV7 @ SV1 )
= $false )
| ( ( breln1 @ SV1 @ SV5 )
= $false )
| ( ( breln1 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV2: $i,SV6: $i,SV4: $i,SV10: $i,SV8: $i] :
( ( ( in @ ( kpair @ SV8 @ SV10 ) @ SV4 )
= $false )
| ( ( in @ ( kpair @ SV8 @ SV10 ) @ ( binunion @ SV4 @ SV6 ) )
= $true )
| ( ( in @ SV10 @ SV2 )
= $false )
| ( ( in @ SV8 @ SV2 )
= $false )
| ( ( breln1 @ SV2 @ SV6 )
= $false )
| ( ( breln1 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(66,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[29,65,64,61,55,53,45,37]) ).
thf(67,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU785^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.09/0.18 % Computer : n004.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 15:34:24 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.23
% 0.09/0.23 No.of.Axioms: 0
% 0.09/0.23
% 0.09/0.23 Length.of.Defs: 636
% 0.09/0.23
% 0.09/0.23 Contains.Choice.Funs: false
% 0.09/0.23 ...
% 0.09/0.23
% 0.09/0.23 ********************************
% 0.09/0.23 * All subproblems solved! *
% 0.09/0.23 ********************************
% 0.09/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:66,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.23
% 0.09/0.23 %**** Beginning of derivation protocol ****
% 0.09/0.23 % SZS output start CNFRefutation
% See solution above
% 0.09/0.23
% 0.09/0.23 %**** End of derivation protocol ****
% 0.09/0.23 %**** no. of clauses in derivation: 67 ****
% 0.09/0.23 %**** clause counter: 66 ****
% 0.09/0.23
% 0.09/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:66,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------