%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU632^2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 10:45:45 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 61 ( 42 unt; 0 typ; 4 def)
% Number of atoms : 337 ( 128 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1755 ( 136 ~; 74 |; 28 &;1503 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 8 con; 0-3 aty)
% Number of variables : 161 ( 3 ^; 140 !; 18 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_cartprodmempair1,type,
cartprodmempair1: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_iskpair,type,
iskpair: $i > $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_kpairp,type,
kpairp: $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY35,type,
sK2_SY35: $i ).
thf(tp_sK3_SY39,type,
sK3_SY39: $i ).
thf(tp_sK4_SY8,type,
sK4_SY8: $i > $i > $i ).
thf(tp_sK5_SY44,type,
sK5_SY44: $i > $i > $i ).
thf(tp_sK6_SY13,type,
sK6_SY13: $i > $i > $i > $i ).
thf(tp_sK7_SY45,type,
sK7_SY45: $i > $i > $i > $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(cartprodmempair1,definition,
( cartprodmempair1
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(iskpair,definition,
( iskpair
= ( ^ [A: $i] :
? [Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
& ? [Xy: $i] :
( ( in @ Xy @ ( setunion @ A ) )
& ( A
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iskpair) ).
thf(kpair,definition,
( kpair
= ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair) ).
thf(kpairp,definition,
( kpairp
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(1,conjecture,
( kpairp
=> ( cartprodmempair1
=> ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(2,negated_conjecture,
( ( kpairp
=> ( cartprodmempair1
=> ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY5: $i,SY6: $i] :
? [SY8: $i] :
( ( in @ SY8 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY9: $i] :
( ( in @ SY9 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY8 @ ( setadjoin @ SY9 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [SY10: $i,SY11: $i,SY12: $i] :
( ( in @ SY12 @ ( cartprod @ SY10 @ SY11 ) )
=> ? [SY13: $i] :
( ( in @ SY13 @ SY10 )
& ? [SY14: $i] :
( ( in @ SY14 @ SY11 )
& ( SY12
= ( setadjoin @ ( setadjoin @ SY13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY13 @ ( setadjoin @ SY14 @ emptyset ) ) @ emptyset ) ) ) ) ) )
=> ! [SY0: $i,SY1: $i,SY2: $i] :
( ( in @ SY2 @ ( cartprod @ SY0 @ SY1 ) )
=> ? [SY3: $i] :
( ( in @ SY3 @ ( setunion @ SY2 ) )
& ? [SY4: $i] :
( ( in @ SY4 @ ( setunion @ SY2 ) )
& ( SY2
= ( setadjoin @ ( setadjoin @ SY3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3 @ ( setadjoin @ SY4 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cartprodmempair1,iskpair,kpair,kpairp]) ).
thf(4,plain,
( ( ! [SY5: $i,SY6: $i] :
? [SY8: $i] :
( ( in @ SY8 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY9: $i] :
( ( in @ SY9 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY8 @ ( setadjoin @ SY9 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY10: $i,SY11: $i,SY12: $i] :
( ( in @ SY12 @ ( cartprod @ SY10 @ SY11 ) )
=> ? [SY13: $i] :
( ( in @ SY13 @ SY10 )
& ? [SY14: $i] :
( ( in @ SY14 @ SY11 )
& ( SY12
= ( setadjoin @ ( setadjoin @ SY13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY13 @ ( setadjoin @ SY14 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [SY0: $i,SY1: $i,SY2: $i] :
( ( in @ SY2 @ ( cartprod @ SY0 @ SY1 ) )
=> ? [SY3: $i] :
( ( in @ SY3 @ ( setunion @ SY2 ) )
& ? [SY4: $i] :
( ( in @ SY4 @ ( setunion @ SY2 ) )
& ( SY2
= ( setadjoin @ ( setadjoin @ SY3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3 @ ( setadjoin @ SY4 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [SY0: $i,SY1: $i,SY2: $i] :
( ( in @ SY2 @ ( cartprod @ SY0 @ SY1 ) )
=> ? [SY3: $i] :
( ( in @ SY3 @ ( setunion @ SY2 ) )
& ? [SY4: $i] :
( ( in @ SY4 @ ( setunion @ SY2 ) )
& ( SY2
= ( setadjoin @ ( setadjoin @ SY3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3 @ ( setadjoin @ SY4 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( in @ sK3_SY39 @ ( cartprod @ sK1_SY0 @ sK2_SY35 ) )
& ! [SY42: $i] :
( ! [SY43: $i] :
( ( sK3_SY39
!= ( setadjoin @ ( setadjoin @ SY42 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY42 @ ( setadjoin @ SY43 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SY43 @ ( setunion @ sK3_SY39 ) ) )
| ~ ( in @ SY42 @ ( setunion @ sK3_SY39 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [SY5: $i,SY6: $i] :
( ( ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SY6 @ SY5 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SY6 @ SY5 ) @ ( setadjoin @ ( sK5_SY44 @ SY6 @ SY5 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( sK5_SY44 @ SY6 @ SY5 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( sK4_SY8 @ SY6 @ SY5 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [SY10: $i,SY11: $i,SY12: $i] :
( ~ ( in @ SY12 @ ( cartprod @ SY10 @ SY11 ) )
| ( ( SY12
= ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SY12 @ SY11 @ SY10 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SY12 @ SY11 @ SY10 ) @ ( setadjoin @ ( sK7_SY45 @ SY12 @ SY11 @ SY10 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( sK7_SY45 @ SY12 @ SY11 @ SY10 ) @ SY11 )
& ( in @ ( sK6_SY13 @ SY12 @ SY11 @ SY10 ) @ SY10 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(11,plain,
( ( ! [SY10: $i,SY11: $i,SY12: $i] :
( ~ ( in @ SY12 @ ( cartprod @ SY10 @ SY11 ) )
| ( ( SY12
= ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SY12 @ SY11 @ SY10 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SY12 @ SY11 @ SY10 ) @ ( setadjoin @ ( sK7_SY45 @ SY12 @ SY11 @ SY10 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( sK7_SY45 @ SY12 @ SY11 @ SY10 ) @ SY11 )
& ( in @ ( sK6_SY13 @ SY12 @ SY11 @ SY10 ) @ SY10 ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [SY5: $i,SY6: $i] :
( ( ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SY6 @ SY5 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SY6 @ SY5 ) @ ( setadjoin @ ( sK5_SY44 @ SY6 @ SY5 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( sK5_SY44 @ SY6 @ SY5 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( sK4_SY8 @ SY6 @ SY5 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY5 @ ( setadjoin @ SY6 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ( in @ sK3_SY39 @ ( cartprod @ sK1_SY0 @ sK2_SY35 ) )
& ! [SY42: $i] :
( ! [SY43: $i] :
( ( sK3_SY39
!= ( setadjoin @ ( setadjoin @ SY42 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY42 @ ( setadjoin @ SY43 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SY43 @ ( setunion @ sK3_SY39 ) ) )
| ~ ( in @ SY42 @ ( setunion @ sK3_SY39 ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ( ~ ( in @ sK3_SY39 @ ( cartprod @ sK1_SY0 @ sK2_SY35 ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( sK3_SY39
!= ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SX1 @ ( setunion @ sK3_SY39 ) ) )
| ~ ( in @ SX0 @ ( setunion @ sK3_SY39 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,cartprodmempair1,iskpair,kpair,kpairp]) ).
thf(15,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SX1 @ SX0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SX1 @ SX0 ) @ ( setadjoin @ ( sK5_SY44 @ SX1 @ SX0 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK5_SY44 @ SX1 @ SX0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK4_SY8 @ SX1 @ SX0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,cartprodmempair1,iskpair,kpair,kpairp]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( ( SX2
!= ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SX2 @ SX1 @ SX0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SX2 @ SX1 @ SX0 ) @ ( setadjoin @ ( sK7_SY45 @ SX2 @ SX1 @ SX0 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK7_SY45 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( sK6_SY13 @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,cartprodmempair1,iskpair,kpair,kpairp]) ).
thf(17,plain,
( ( ~ ( in @ sK3_SY39 @ ( cartprod @ sK1_SY0 @ sK2_SY35 ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( sK3_SY39
!= ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SX1 @ ( setunion @ sK3_SY39 ) ) )
| ~ ( in @ SX0 @ ( setunion @ sK3_SY39 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: $i] :
( ( ! [SY46: $i] :
~ ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SY46 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SY46 @ SV1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SY46 @ SV1 ) @ ( setadjoin @ ( sK5_SY44 @ SY46 @ SV1 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK5_SY44 @ SY46 @ SV1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SY46 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK4_SY8 @ SY46 @ SV1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SY46 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ~ ( in @ SY48 @ ( cartprod @ SV2 @ SY47 ) )
| ~ ( ~ ~ ( ( SY48
!= ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SY48 @ SY47 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SY48 @ SY47 @ SV2 ) @ ( setadjoin @ ( sK7_SY45 @ SY48 @ SY47 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK7_SY45 @ SY48 @ SY47 @ SV2 ) @ SY47 ) )
| ~ ( in @ ( sK6_SY13 @ SY48 @ SY47 @ SV2 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( in @ sK3_SY39 @ ( cartprod @ sK1_SY0 @ sK2_SY35 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ( sK3_SY39
!= ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SX1 @ ( setunion @ sK3_SY39 ) ) )
| ~ ( in @ SX0 @ ( setunion @ sK3_SY39 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SV3 @ SV1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SV3 @ SV1 ) @ ( setadjoin @ ( sK5_SY44 @ SV3 @ SV1 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK5_SY44 @ SV3 @ SV1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK4_SY8 @ SV3 @ SV1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY49: $i] :
( ~ ( in @ SY49 @ ( cartprod @ SV2 @ SV4 ) )
| ~ ( ~ ~ ( ( SY49
!= ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SY49 @ SV4 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SY49 @ SV4 @ SV2 ) @ ( setadjoin @ ( sK7_SY45 @ SY49 @ SV4 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK7_SY45 @ SY49 @ SV4 @ SV2 ) @ SV4 ) )
| ~ ( in @ ( sK6_SY13 @ SY49 @ SV4 @ SV2 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( in @ sK3_SY39 @ ( cartprod @ sK1_SY0 @ sK2_SY35 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ( sK3_SY39
!= ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SX1 @ ( setunion @ sK3_SY39 ) ) )
| ~ ( in @ SX0 @ ( setunion @ sK3_SY39 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SV3 @ SV1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SV3 @ SV1 ) @ ( setadjoin @ ( sK5_SY44 @ SV3 @ SV1 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK5_SY44 @ SV3 @ SV1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK4_SY8 @ SV3 @ SV1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
| ~ ( ~ ~ ( ( SV5
!= ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ ( setadjoin @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ SV4 ) )
| ~ ( in @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV6: $i] :
( ( ! [SY50: $i] :
( ( sK3_SY39
!= ( setadjoin @ ( setadjoin @ SV6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV6 @ ( setadjoin @ SY50 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SY50 @ ( setunion @ sK3_SY39 ) ) )
| ~ ( in @ SV6 @ ( setunion @ sK3_SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SV3 @ SV1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SV3 @ SV1 ) @ ( setadjoin @ ( sK5_SY44 @ SV3 @ SV1 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK5_SY44 @ SV3 @ SV1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( in @ ( sK4_SY8 @ SV3 @ SV1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(31,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ ( cartprod @ SV2 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV5
!= ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ ( setadjoin @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ SV4 ) )
| ~ ( in @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV6: $i] :
( ( ( ! [SY50: $i] :
( ( sK3_SY39
!= ( setadjoin @ ( setadjoin @ SV6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV6 @ ( setadjoin @ SY50 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SY50 @ ( setunion @ sK3_SY39 ) ) ) )
= $true )
| ( ( ~ ( in @ SV6 @ ( setunion @ sK3_SY39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SV3 @ SV1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SV3 @ SV1 ) @ ( setadjoin @ ( sK5_SY44 @ SV3 @ SV1 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK5_SY44 @ SV3 @ SV1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV1: $i,SV3: $i] :
( ( in @ ( sK4_SY8 @ SV3 @ SV1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ( in @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV5
!= ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ ( setadjoin @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ SV4 ) )
| ~ ( in @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV7: $i,SV6: $i] :
( ( ( ( sK3_SY39
!= ( setadjoin @ ( setadjoin @ SV6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV6 @ ( setadjoin @ SV7 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SV7 @ ( setunion @ sK3_SY39 ) ) )
= $true )
| ( ( ~ ( in @ SV6 @ ( setunion @ sK3_SY39 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV3: $i,SV1: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SV3 @ SV1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SV3 @ SV1 ) @ ( setadjoin @ ( sK5_SY44 @ SV3 @ SV1 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK5_SY44 @ SV3 @ SV1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV2: $i,SV4: $i,SV5: $i] :
( ( ( ~ ~ ( ( SV5
!= ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ ( setadjoin @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ SV4 ) )
| ~ ( in @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ SV2 ) )
= $false )
| ( ( in @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV7: $i,SV6: $i] :
( ( ( sK3_SY39
!= ( setadjoin @ ( setadjoin @ SV6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV6 @ ( setadjoin @ SV7 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( ~ ( in @ SV7 @ ( setunion @ sK3_SY39 ) ) )
= $true )
| ( ( ~ ( in @ SV6 @ ( setunion @ sK3_SY39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV3: $i,SV1: $i] :
( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SV3 @ SV1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SV3 @ SV1 ) @ ( setadjoin @ ( sK5_SY44 @ SV3 @ SV1 ) @ emptyset ) ) @ emptyset ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(41,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( in @ ( sK5_SY44 @ SV3 @ SV1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(42,plain,
! [SV2: $i,SV4: $i,SV5: $i] :
( ( ( ~ ~ ( ( SV5
!= ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ ( setadjoin @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ SV4 ) ) )
= $false )
| ( ( in @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV2: $i,SV4: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ SV2 ) )
= $false )
| ( ( in @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(44,plain,
! [SV7: $i,SV6: $i] :
( ( ( sK3_SY39
= ( setadjoin @ ( setadjoin @ SV6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV6 @ ( setadjoin @ SV7 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ~ ( in @ SV7 @ ( setunion @ sK3_SY39 ) ) )
= $true )
| ( ( ~ ( in @ SV6 @ ( setunion @ sK3_SY39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV3: $i,SV1: $i] :
( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SV3 @ SV1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY8 @ SV3 @ SV1 ) @ ( setadjoin @ ( sK5_SY44 @ SV3 @ SV1 ) @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV1: $i,SV3: $i] :
( ( in @ ( sK5_SY44 @ SV3 @ SV1 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV2: $i,SV4: $i,SV5: $i] :
( ( ( ~ ( ( SV5
!= ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ ( setadjoin @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ SV4 ) ) )
= $true )
| ( ( in @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(48,plain,
! [SV2: $i,SV4: $i,SV5: $i] :
( ( ( in @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ SV2 )
= $true )
| ( ( in @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(49,plain,
! [SV6: $i,SV7: $i] :
( ( ( in @ SV7 @ ( setunion @ sK3_SY39 ) )
= $false )
| ( ( sK3_SY39
= ( setadjoin @ ( setadjoin @ SV6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV6 @ ( setadjoin @ SV7 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ~ ( in @ SV6 @ ( setunion @ sK3_SY39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV2: $i,SV4: $i,SV5: $i] :
( ( ( ( SV5
!= ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ ( setadjoin @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ SV4 ) )
= $false )
| ( ( in @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV7: $i,SV6: $i] :
( ( ( in @ SV6 @ ( setunion @ sK3_SY39 ) )
= $false )
| ( ( sK3_SY39
= ( setadjoin @ ( setadjoin @ SV6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV6 @ ( setadjoin @ SV7 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV7 @ ( setunion @ sK3_SY39 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV2: $i,SV4: $i,SV5: $i] :
( ( ( SV5
!= ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ ( setadjoin @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(53,plain,
! [SV2: $i,SV4: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ SV4 ) )
= $false )
| ( ( in @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(54,plain,
! [SV2: $i,SV4: $i,SV5: $i] :
( ( ( SV5
= ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY13 @ SV5 @ SV4 @ SV2 ) @ ( setadjoin @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( in @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(55,plain,
! [SV2: $i,SV4: $i,SV5: $i] :
( ( ( in @ ( sK7_SY45 @ SV5 @ SV4 @ SV2 ) @ SV4 )
= $true )
| ( ( in @ SV5 @ ( cartprod @ SV2 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(56,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,55,54,51,48,46,45,34]) ).
thf(57,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU632^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n014.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 15:29:26 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.25
% 0.08/0.25 No.of.Axioms: 0
% 0.08/0.25
% 0.08/0.25 Length.of.Defs: 936
% 0.08/0.25
% 0.08/0.25 Contains.Choice.Funs: false
% 0.08/0.25 ....
% 0.08/0.25
% 0.08/0.25 ********************************
% 0.08/0.25 * All subproblems solved! *
% 0.08/0.25 ********************************
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:56,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.08/0.25
% 0.08/0.25 %**** Beginning of derivation protocol ****
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25
% 0.08/0.25 %**** End of derivation protocol ****
% 0.08/0.25 %**** no. of clauses in derivation: 57 ****
% 0.08/0.25 %**** clause counter: 56 ****
% 0.08/0.25
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:56,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------